fix: color_xrange 范围限定 d_max + color_driver + color 范围改为 [0,1] + bug 修复

将 DLL 标记为 binary，禁止行尾转换

.gitattributes

@@ -1,7 +1,9 @@
-# 全部使用 LF 换行，仓库内外一致，不随系统自动转换
-* text eol=lf
+# 引擎 DLL 是二进制文件，禁止行尾转换
+engines/release/*.dll binary
 
-# 二进制文件不转换
-*.png binary
-*.jpg binary
-*.ico binary
+# Python 源码使用 LF
+*.py text eol=lf
+
+# Makefile 使用 LF
+Makefile text eol=lf
+*.mk text eol=lf

.gitignore

@@ -18,10 +18,9 @@ pip-wheel-metadata/
 venv/
 ENV/
 
-# ── C / C++ 编译产物 ─────────────────────────────────────────
-# Makefile 构建输出（engines/c/build/）
-engines/c/build/
-engines/cpp/build/
+# ── C / C++ / Fortran 编译产物 ────────────────────────
+# 源码目录 engines/src/*/ 中可能产生的构建输出
+engines/src/*/build/
 
 # CMake 构建目录（根目录或自定义 build 目录）
 CMakeCache.txt
@@ -42,12 +41,11 @@ build_*/
 *.so
 *.so.*
 *.dylib
-*.dll
 
 # 可执行文件（保留源码，排除编译出的二进制）
 # 注意：Windows 下 .exe 后缀的可执行文件
 *.exe
-# 但 engines/c/Makefile 里指定了 build/ 目录，已由上面覆盖
+# 可在 engines/src/*/ 中用 make dll 编译引擎 DLL
 
 # 运行时生成的引擎参数文件（每次运行都会覆盖）
 engines/*/param.json
@@ -99,3 +97,7 @@ desktop.ini
 *.zip
 *.tar.gz
 *.tar.bz2
+output_test/
+
+optimization
+optimization/*

draw.py

@@ -1,9 +1,8 @@
 """VisPy 演示：加载预计算轨迹数据，驱动小球运动动画。
 
 计算与显示完全分离：
-  1. 先运行 compute.py  → 生成 output/trajectory.txt（全量 NT 步轨迹）
-  2. 再运行 sample.py  → 从 output/trajectory.txt 抽帧生成 output/display.txt
-  3. 本文件加载 output/display.txt，按帧播放动画
+  1. 运行 run_dynamics.py  → 生成 output/display.txt（新格式，直接抽帧）
+  2. 本文件加载 output/display.txt，按帧播放动画
 
 用法：
     python draw.py                                          # 使用 dynamics 根目录下的 output/
@@ -11,6 +10,7 @@
 """
 
 import numpy as np
+import json
 import os
 import sys
 from vispy import app, scene
@@ -30,89 +30,348 @@ else:
     output_dir = compute.get_output_dir(script_dir)
 os.environ["DYNAMICS_OUTPUT_DIR"] = output_dir
 disp_path = os.path.join(output_dir, "display.txt")
+npz_path  = os.path.join(output_dir, "display.npz")
 
-if not os.path.exists(disp_path):
+if not os.path.exists(npz_path) and not os.path.exists(disp_path):
     raise FileNotFoundError(
-        f"找不到 display.txt！\n"
-        f"期望路径: {disp_path}\n"
+        f"找不到 display.npz 或 display.txt！\n"
+        f"期望路径: {output_dir}\n"
         f"请先运行 compute.py 计算轨迹，再运行 sample.py 生成显示数组。\n"
         f"用法: python draw.py [案例输出目录]"
     )
 
-disp_data = compute.load_text_data(disp_path)
+# 优先读二进制 npz（加载速度约快 5-10x）
+if os.path.exists(npz_path):
+    disp_data = compute.load_display_npz(npz_path)
+else:
+    disp_data = compute.load_display_txt(disp_path)
 
-# 单原子数据（plot_atom：用于信息显示）
-DISP_X    = disp_data["disp_x"]
-DISP_Y    = disp_data["disp_y"]
-DISP_Z    = disp_data["disp_z"]
-DISP_VX   = disp_data["disp_vx"]
-DISP_VY   = disp_data["disp_vy"]
-DISP_VZ   = disp_data["disp_vz"]
+# ── 从 input.txt 读取参数（替代 display.npz 中的 meta）──
+try:
+    import yaml
+    _have_yaml = True
+except ImportError:
+    _have_yaml = False
 
-# 全原子数据（用于多球绘制）
-DISP_ALL_X  = disp_data["disp_all_x"]     # (n_frames, n_atoms)
-DISP_ALL_Y  = disp_data["disp_all_y"]
-DISP_ALL_Z  = disp_data["disp_all_z"]
-DISP_ALL_VX = disp_data["disp_all_vx"]
-DISP_ALL_VY = disp_data["disp_all_vy"]
-DISP_ALL_VZ = disp_data["disp_all_vz"]
+input_dir = os.path.join(os.path.dirname(output_dir), "input")
+input_path = os.path.join(input_dir, "input.txt")
 
-DISP_T    = disp_data["disp_t"]
-DISP_STEP = disp_data["disp_step"]
-N_FRAMES  = int(disp_data["n_frames"])
-NT        = int(disp_data["NT"])
-DT        = float(disp_data["DT"])
-NSTEP     = int(disp_data["NSTEP"])
+if _have_yaml and os.path.exists(input_path):
+    try:
+        with open(input_path, "r", encoding="utf-8") as f:
+            config = yaml.safe_load(f)
+    except Exception:
+        config = {}
+else:
+    config = {}
+# 兼容旧版：若 input.txt 不存在或解析失败，降级到 display.npz 的 meta
+if not config:
+    config = disp_data.get("header_fields", {})
+
+# ── 从 coord.txt 读取平衡位置 ─────────────────
+# 注意: config 中的 *_file 可能带 "input/" 前缀，但 input_dir 已指向 input/ 目录
+_coord_file_raw = config.get("coord_file", "coord.txt")
+coord_path = os.path.join(input_dir, os.path.basename(_coord_file_raw))
+if os.path.exists(coord_path):
+    try:
+        _ids, _masses, _radii, _pos, _vel, _fixed = compute.load_coord_file(coord_path)
+        EQ_POS = _pos                             # (n_atoms, 3)
+        ATOM_FIXED = _fixed                        # (n_atoms, 3)
+    except Exception:
+        EQ_POS = None
+        ATOM_FIXED = None
+else:
+    EQ_POS = None
+    ATOM_FIXED = None
+
+# ── 从 connection.txt 读取成键信息（若 meta 中没有）──
+BOND_PAIRS = disp_data.get("bond_pairs", [])
+if not BOND_PAIRS and 'bond_pairs' not in disp_data:
+    conn_path = os.path.join(input_dir, os.path.basename(config.get("connection_file", "connection.txt")))
+    if os.path.exists(conn_path):
+        try:
+            _pairs = []
+            with open(conn_path, "r", encoding="utf-8") as _f:
+                _f.readline()  # skip header
+                for _line in _f:
+                    _line = _line.strip()
+                    if not _line or _line.startswith("#"):
+                        continue
+                    _parts = _line.split()
+                    if len(_parts) >= 2:
+                        _pairs.append([int(_parts[0]) - 1, int(_parts[1]) - 1])
+            BOND_PAIRS = np.array(_pairs, dtype=np.int32) if _pairs else []
+        except Exception:
+            BOND_PAIRS = []
+    BOND_PAIRS = BOND_PAIRS.tolist() if hasattr(BOND_PAIRS, 'tolist') else BOND_PAIRS
+
+# 全原子帧数据
+DISP_ALL_X  = disp_data["frames_x"]       # (n_frames, n_atoms)
+DISP_ALL_Y  = disp_data["frames_y"]
+DISP_ALL_Z  = disp_data["frames_z"]
+DISP_ALL_VX = disp_data["frames_vx"]
+DISP_ALL_VY = disp_data["frames_vy"]
+DISP_ALL_VZ = disp_data["frames_vz"]
+
+# 第一个原子的轨迹（用于信息显示）
+DISP_X    = DISP_ALL_X[:, 0]
+DISP_Y    = DISP_ALL_Y[:, 0]
+DISP_Z    = DISP_ALL_Z[:, 0]
+DISP_VX   = DISP_ALL_VX[:, 0]
+DISP_VY   = DISP_ALL_VY[:, 0]
+DISP_VZ   = DISP_ALL_VZ[:, 0]
+
+N_FRAMES  = DISP_ALL_X.shape[0]
+NT        = int(disp_data["n_total_frames"])
+N_ATOMS   = int(disp_data["n_total_particles"])
+DT        = float(config.get("DT", 0.001))
+
+# 视觉位移放大：display_amp: [ax, ay, az]，对偏离平衡位置的位移乘以倍数
+_damp_raw = config.get("display_amp", "")
+if isinstance(_damp_raw, (list, tuple)):
+    _damp = np.array(_damp_raw, dtype=np.float64)
+elif isinstance(_damp_raw, str) and _damp_raw.strip():
+    import ast as _ast
+    _damp = np.array(_ast.literal_eval(_damp_raw.strip()), dtype=np.float64)
+else:
+    _damp = None
+if _damp is not None and _damp.shape == (3,) and not np.allclose(_damp, 1.0):
+        if EQ_POS is not None:
+            _eq_x = EQ_POS[None, :, 0]   # coord.txt 平衡位置
+            _eq_y = EQ_POS[None, :, 1]
+            _eq_z = EQ_POS[None, :, 2]
+        else:
+            _eq_x = DISP_ALL_X[0:1, :]   # 第0帧作为平衡位置参考
+            _eq_y = DISP_ALL_Y[0:1, :]
+            _eq_z = DISP_ALL_Z[0:1, :]
+        DISP_ALL_X = _eq_x + (DISP_ALL_X - _eq_x) * _damp[0]
+        DISP_ALL_Y = _eq_y + (DISP_ALL_Y - _eq_y) * _damp[1]
+        DISP_ALL_Z = _eq_z + (DISP_ALL_Z - _eq_z) * _damp[2]
+
+# ── 位移颜色映射 ──────────────────────────────
+# display_color: { mode: [enabled, [R,G,B]], ... }
+#   mode: x, y, z, xy, yz, zx, xyz
+#   enabled: 0=off, 1=on
+#   [R,G,B]: 最大位移时的颜色（渐变起点为白色）
+#   例：xyz: [1, [1.0,1.0,1.0]] → 三方向合成位移 → 白色渐变
+FRAME_COLORS = None
+_DC_MODE = None
+_DC_COLOR = None
+
+_raw_dc = config.get("display_color", "")
+if _raw_dc:
+    try:
+        dc = json.loads(_raw_dc) if isinstance(_raw_dc, str) else _raw_dc
+        if isinstance(dc, dict):
+            for mode, (enabled, color) in dc.items():
+                if int(enabled) and mode in ("x","y","z","xy","yz","zx","xyz"):
+                    _DC_MODE = mode
+                    _DC_COLOR = np.array(color, dtype=np.float32)
+                    break
+    except Exception:
+        pass
+
+if _DC_MODE is not None and _DC_COLOR is not None:
+    if EQ_POS is not None:
+        eq_x = EQ_POS[None, :, 0]  # coord.txt 平衡位置
+        eq_y = EQ_POS[None, :, 1]
+        eq_z = EQ_POS[None, :, 2]
+    else:
+        eq_x = DISP_ALL_X[0:1, :]  # 第0帧
+        eq_y = DISP_ALL_Y[0:1, :]
+        eq_z = DISP_ALL_Z[0:1, :]
+    dx = DISP_ALL_X - eq_x
+    dy = DISP_ALL_Y - eq_y
+    dz = DISP_ALL_Z - eq_z
+
+    if _DC_MODE == "x":
+        disp_mag = np.abs(dx)
+    elif _DC_MODE == "y":
+        disp_mag = np.abs(dy)
+    elif _DC_MODE == "z":
+        disp_mag = np.abs(dz)
+    elif _DC_MODE == "xy":
+        disp_mag = np.sqrt(dx**2 + dy**2)
+    elif _DC_MODE == "yz":
+        disp_mag = np.sqrt(dy**2 + dz**2)
+    elif _DC_MODE == "zx":
+        disp_mag = np.sqrt(dz**2 + dx**2)
+    else:  # xyz
+        disp_mag = np.sqrt(dx**2 + dy**2 + dz**2)
+
+    # ── color_xrange: 限定归一化基准的原子范围 ───────────
+    # 格式: [['min'|'mid'|'max'|数值, 'min'|'mid'|'max'|数值], ...] 对应 x,y,z
+    # 在此范围内的原子计算最大位移 d_max，所有原子以此基准归一化着色
+    _cxr = config.get("color_xrange", None)
+    _d_max_source = disp_mag  # 默认：所有原子
+    _range_label = "全部原子"
+    if _cxr and isinstance(_cxr, (list, tuple)) and len(_cxr) == 3:
+        try:
+            # 获取坐标极值
+            if EQ_POS is not None:
+                _eq_all = EQ_POS
+            else:
+                _eq_all = np.column_stack([
+                    DISP_ALL_X[0], DISP_ALL_Y[0], DISP_ALL_Z[0]])
+            _cmin = _eq_all.min(axis=0)
+            _cmax = _eq_all.max(axis=0)
+            _cmid = (_cmin + _cmax) / 2
+
+            _key_map = {"min": _cmin, "mid": _cmid, "max": _cmax}
+            _range_lo = np.zeros(3, dtype=np.float64)
+            _range_hi = np.zeros(3, dtype=np.float64)
+
+            for _i in range(3):
+                _lo = _cxr[_i][0]
+                _hi = _cxr[_i][1]
+                _range_lo[_i] = _key_map[_lo][_i] if _lo in _key_map else float(_lo)
+                _range_hi[_i] = _key_map[_hi][_i] if _hi in _key_map else float(_hi)
+
+            _in_x = (_eq_all[:, 0] >= _range_lo[0]) & (_eq_all[:, 0] <= _range_hi[0])
+            _in_y = (_eq_all[:, 1] >= _range_lo[1]) & (_eq_all[:, 1] <= _range_hi[1])
+            _in_z = (_eq_all[:, 2] >= _range_lo[2]) & (_eq_all[:, 2] <= _range_hi[2])
+            _color_mask = _in_x & _in_y & _in_z
+
+            _n_in_range = _color_mask.sum()
+            if _n_in_range > 0:
+                _d_max_source = disp_mag[:, _color_mask]  # 仅在范围内找最大位移
+                _range_label = (f"x[{_range_lo[0]:.1f},{_range_hi[0]:.1f}] "
+                                f"y[{_range_lo[1]:.1f},{_range_hi[1]:.1f}] "
+                                f"z[{_range_lo[2]:.1f},{_range_hi[2]:.1f}]")
+        except Exception as _e:
+            print(f"[draw] color_xrange 解析失败: {_e}")
+
+    # 用（范围限定的）最大位移归一化，所有原子统一着色
+    d_max = _d_max_source.max()
+    if d_max > 1e-12:
+        disp_norm = disp_mag / d_max
+    else:
+        disp_norm = disp_mag
+
+    FRAME_COLORS = np.ones((N_FRAMES, N_ATOMS, 4), dtype=np.float32)
+    t = disp_norm[..., None]
+    FRAME_COLORS[..., :3] = 1.0 + (_DC_COLOR - 1.0) * t
+    print(f"[draw] 位移颜色映射: mode={_DC_MODE}, color={_DC_COLOR.tolist()}, "
+          f"d_max={d_max:.4f}, 范围: {_range_label}")
+
+    # ── color_driver: 驱动原子 → 统一颜色 ──
+    _cd_raw = config.get("color_driver", None)
+    if _cd_raw is not None:
+        try:
+            _cd = np.array(_cd_raw, dtype=np.float32)
+            # 读取 driver.txt 获取驱动原子 ID
+            _driver_file = config.get("driver_file", "driver.txt")
+            _driver_path = os.path.join(input_dir, os.path.basename(_driver_file))
+            if os.path.exists(_driver_path):
+                _driver_ids = []
+                with open(_driver_path, "r", encoding="utf-8") as _df:
+                    _df.readline()  # skip header
+                    for _line in _df:
+                        _line = _line.strip()
+                        if not _line or _line.startswith("#"):
+                            continue
+                        _parts = _line.split()
+                        if _parts:
+                            _driver_ids.append(int(_parts[0]) - 1)  # 1-based → 0-based
+                if _driver_ids:
+                    FRAME_COLORS[:, _driver_ids, :3] = _cd
+                    print(f"[draw] color_driver: {len(_driver_ids)} 驱动原子 → RGB{_cd_raw}")
+        except Exception as _e:
+            print(f"[draw] color_driver 解析失败: {_e}")
+
+    # ── color_fix: 全固定原子 (fix_x=fix_y=fix_z=1) → 统一颜色 ──
+    _cf_raw = config.get("color_fix", None)
+    if _cf_raw is not None and ATOM_FIXED is not None:
+        try:
+            _cf = np.array(_cf_raw, dtype=np.float32)
+            _full_fixed = (ATOM_FIXED[:, 0] == 1) & (ATOM_FIXED[:, 1] == 1) & (ATOM_FIXED[:, 2] == 1)
+            _n_fix = _full_fixed.sum()
+            if _n_fix > 0:
+                FRAME_COLORS[:, _full_fixed, :3] = _cf
+                print(f"[draw] color_fix: {_n_fix} 全固定原子 → RGB{_cf_raw}")
+        except Exception as _e:
+            print(f"[draw] color_fix 解析失败: {_e}")
+NSTEP     = int(config.get("NSTEP", 1))
+DISP_STEP = np.arange(N_FRAMES) * NSTEP
+DISP_T    = DISP_STEP * DT
 
 # 原子信息
-ATOM_IDS  = disp_data.get("atom_ids", np.array([1]))
-ATOM_RADII = disp_data.get("atom_radii", np.array([float(disp_data["ball_radius"])]))
-N_ATOMS   = len(ATOM_IDS)
-PLOT_ATOM_ROW = int(disp_data.get("plot_atom_row", 0))
-PLOT_ATOM_ID  = int(disp_data.get("plot_atom_id", ATOM_IDS[0]))
-BOND_PAIRS = disp_data.get("bond_pairs", [])
+ATOM_IDS  = disp_data["atom_ids"]
+# 优先使用 per-atom 半径，否则用统一的 ball_radius
+_raw_radii = config.get("atom_radii", "")
+if _raw_radii.strip():
+    ATOM_RADII = np.array([float(x) for x in _raw_radii.split(",")])
+else:
+    ATOM_RADII = np.full(N_ATOMS, float(config.get("ball_radius", 0.5)))
+PLOT_ATOM_ROW = 0
+PLOT_ATOM_ID  = int(ATOM_IDS[0])
+# 成键信息已在上面从 connection.txt 加载
 
 # 渲染方式：0=Sphere(网格球体), 1=Marker(GPU点精灵)
-USE_MARKER = int(disp_data.get("use_marker", 0))
+USE_MARKER = int(config.get("use_marker", 0))
 
 if N_FRAMES <= 0:
     raise ValueError(
         "output/display.txt 中没有可播放的帧，请检查 sample_start/sample_end/NSTEP 配置。")
 
-# 保留模拟边界常量（用于场景缩放、相机等），从 output/display.txt 中读取
-X_MIN = float(disp_data["X_MIN"]); X_MAX = float(disp_data["X_MAX"])
-Y_MIN = float(disp_data["Y_MIN"]); Y_MAX = float(disp_data["Y_MAX"])
-Z_MIN = float(disp_data["Z_MIN"]); Z_MAX = float(disp_data["Z_MAX"])
-X0 = float(disp_data["X0"]); Y0 = float(disp_data["Y0"]); Z0 = float(disp_data["Z0"])
-raw_alpha = disp_data["alpha"]
-if isinstance(raw_alpha, (list, tuple, np.ndarray)):
-    alpha_list = [float(a) for a in raw_alpha]
-    if len(alpha_list) != 6:
-        raise ValueError(f"alpha 数组长度须为 6，实际为 {len(alpha_list)}")
+# 模拟边界（从 input.txt 的 box_a 计算）
+_box_a = float(config.get("box_a", 10.0))
+X_MIN = -_box_a; X_MAX = _box_a
+Y_MIN = -_box_a; Y_MAX = _box_a
+Z_MIN = -_box_a; Z_MAX = _box_a
+raw_alpha = config.get("alpha", "0.2")
+if isinstance(raw_alpha, (list, tuple)):
+    alpha_list = [float(x) for x in raw_alpha]
 else:
-    alpha_list = [float(raw_alpha)] * 6
+    try:
+        alpha_list = [float(x) for x in raw_alpha.split(",")]
+    except (ValueError, AttributeError):
+        alpha_list = [float(raw_alpha)] * 6
+if len(alpha_list) != 6:
+    alpha_list = (alpha_list * 6)[:6]
+
 # 绘图参数
-ball_radius = float(disp_data["ball_radius"])
-ball_color_r = float(disp_data["ball_color_r"])
-ball_color_g = float(disp_data["ball_color_g"])
-ball_color_b = float(disp_data["ball_color_b"])
-box_color_r = float(disp_data["box_color_r"])
-box_color_g = float(disp_data["box_color_g"])
-box_color_b = float(disp_data["box_color_b"])
+ball_radius = float(config.get("ball_radius", 0.5))
+ball_color_r = float(config.get("ball_color_r", 0.9))
+ball_color_g = float(config.get("ball_color_g", 0.2))
+ball_color_b = float(config.get("ball_color_b", 0.2))
+box_color_r = float(config.get("box_color_r", 0.8))
+box_color_g = float(config.get("box_color_g", 0.8))
+box_color_b = float(config.get("box_color_b", 0.85))
 
 
 # ===========================================================================
 # 图形界面无关的几何参数（不参与物理计算，仅用于场景外观）
 # ===========================================================================
 
-info_margin  = 36
+info_margin  = 8
 axis_length  = 10.0
 
+import math as _math_cam
+
+_cx = float(config.get("camera_center_x", 0.0))
+_cy = float(config.get("camera_center_y", 0.0))
+_cz = float(config.get("camera_center_z", 0.0))
+
+# 若 input.txt 指定了摄像机自身坐标，则由坐标反推 distance/elevation/azimuth
+if config.get("camera_pos_x") is not None:
+    _px = float(config.get("camera_pos_x"))
+    _py = float(config.get("camera_pos_y"))
+    _pz = float(config.get("camera_pos_z"))
+    _dx, _dy, _dz = _px - _cx, _py - _cy, _pz - _cz
+    _dist = _math_cam.sqrt(_dx*_dx + _dy*_dy + _dz*_dz) or 1.0
+    _elev = _math_cam.degrees(_math_cam.asin(max(-1.0, min(1.0, _dy / _dist))))
+    _azim = _math_cam.degrees(_math_cam.atan2(_dx, _dz))
+else:
+    _dist = float(config.get("camera_distance", 40.0))
+    _elev = float(config.get("camera_elevation", 0))
+    _azim = float(config.get("camera_azimuth", 0))
+
 initial_camera = {
-    "distance": 40.0,
-    "elevation": 0,
-    "azimuth": 0,
-    "center": (0, 0, 0),
+    "distance":  _dist,
+    "elevation": _elev,
+    "azimuth":   _azim,
+    "center":    (_cx, _cy, _cz),
 }
 
 
@@ -167,11 +426,11 @@ axes_group.append(scene.visuals.Arrow(
     parent=view.scene,
 ))
 
-axes_group.append(scene.visuals.Text(text="x", color=(1.0, 0.2, 0.2, 1.0), font_size=18,
+axes_group.append(scene.visuals.Text(text="x", color=(1.0, 0.2, 0.2, 1.0), font_size=14,
     pos=(axis_length + 0.2, 0, 0), anchor_x="left", anchor_y="center", parent=view.scene))
-axes_group.append(scene.visuals.Text(text="y", color=(0.2, 1.0, 0.2, 1.0), font_size=18,
+axes_group.append(scene.visuals.Text(text="y", color=(0.2, 1.0, 0.2, 1.0), font_size=14,
     pos=(0, axis_length + 0.2, 0), anchor_x="left", anchor_y="bottom", parent=view.scene))
-axes_group.append(scene.visuals.Text(text="z", color=(0.3, 0.6, 1.0, 1.0), font_size=18,
+axes_group.append(scene.visuals.Text(text="z", color=(0.3, 0.6, 1.0, 1.0), font_size=14,
     pos=(0, 0, axis_length + 0.2), anchor_x="left", anchor_y="bottom", parent=view.scene))
 
 # ── 原子渲染 ──────────────────────────────────
@@ -190,11 +449,14 @@ TAB10_RGB = np.array([
     [0.7373, 0.7412, 0.1333],   # 黄绿
     [0.0902, 0.7451, 0.8118],   # 青
 ])
-# 每个原子的颜色（循环使用 tab10 色板）
+# 每个原子的颜色（循环使用 tab10 色板，或按位移着色）
 atom_colors = np.zeros((N_ATOMS, 4), dtype=np.float32)
-for i in range(N_ATOMS):
-    r, g, b = TAB10_RGB[i % len(TAB10_RGB)]
-    atom_colors[i] = [r, g, b, 1.0]
+if FRAME_COLORS is not None:
+    atom_colors[:] = FRAME_COLORS[0]   # 初始帧颜色
+else:
+    for i in range(N_ATOMS):
+        r, g, b = TAB10_RGB[i % len(TAB10_RGB)]
+        atom_colors[i] = [r, g, b, 1.0]
 
 if USE_MARKER:
     # ── Marker 模式：GPU 实例化，一次 draw call ──
@@ -250,12 +512,12 @@ for f_idx, (pos, direction) in enumerate(faces):
 
 # 右上角：相机信息
 camera_info = scene.visuals.Text(
-    text="", color="white", font_size=14,
+    text="", color="white", font_size=12,
     pos=(0, 0), anchor_x="right", anchor_y="top", parent=canvas.scene)
 
 # 左上角：小球信息
 ball_info = scene.visuals.Text(
-    text="", color=(0.2, 1.0, 0.2, 1.0), font_size=28,
+    text="", color=(0.2, 1.0, 0.2, 1.0), font_size=14,
     pos=(0, 0), anchor_x="left", anchor_y="top",
     face="黑体", bold=True, parent=canvas.scene)
 
@@ -267,7 +529,7 @@ reset_button = scene.visuals.Rectangle(
     radius=6, color=(0.18, 0.35, 0.65, 0.85),
     border_color="white", parent=canvas.scene)
 reset_button_label = scene.visuals.Text(
-    text="reset", color="white", font_size=16,
+    text="reset", color="white", font_size=13,
     pos=(reset_btn_size[0] / 2 + 8, reset_btn_size[1] / 2 + 8),
     anchor_x="center", anchor_y="center",
     bold=True, parent=canvas.scene)
@@ -281,7 +543,7 @@ info_button = scene.visuals.Rectangle(
     radius=6, color=(0.9, 0.3, 0.3, 0.9),
     border_color="white", parent=canvas.scene)
 info_button_label = scene.visuals.Text(
-    text="info", color="white", font_size=16,
+    text="info", color="white", font_size=13,
     pos=(info_btn_size[0] / 2 + 8, info_btn_size[1] / 2 + 8),
     anchor_x="center", anchor_y="center",
     bold=True, parent=canvas.scene)
@@ -301,7 +563,7 @@ axes_button = scene.visuals.Rectangle(
     radius=6, color=(0.3, 0.7, 0.3, 0.9),
     border_color="white", parent=canvas.scene)
 axes_button_label = scene.visuals.Text(
-    text="axes", color="white", font_size=16,
+    text="axes", color="white", font_size=13,
     pos=(axes_btn_size[0] / 2 + 8, axes_btn_size[1] / 2 + 8),
     anchor_x="center", anchor_y="center",
     bold=True, parent=canvas.scene)
@@ -506,11 +768,15 @@ def handle_mouse_press(event):
 # ===========================================================================
 
 def _update_atom_positions(f_idx):
-    """更新所有原子到第 f_idx 帧的位置。"""
+    """更新所有原子到第 f_idx 帧的位置，必要时更新颜色。"""
     if USE_MARKER:
-        for i in range(N_ATOMS):
-            marker_pos[i] = [DISP_ALL_X[f_idx, i], DISP_ALL_Y[f_idx, i], DISP_ALL_Z[f_idx, i]]
-        balls.set_data(pos=marker_pos)
+        marker_pos[:, 0] = DISP_ALL_X[f_idx]
+        marker_pos[:, 1] = DISP_ALL_Y[f_idx]
+        marker_pos[:, 2] = DISP_ALL_Z[f_idx]
+        if FRAME_COLORS is not None:
+            balls.set_data(pos=marker_pos, face_color=FRAME_COLORS[f_idx])
+        else:
+            balls.set_data(pos=marker_pos)
     else:
         for i in range(N_ATOMS):
             balls[i].transform = STTransform(translate=(
@@ -549,9 +815,80 @@ print(f"[draw] 渲染方式: {mode_str}")
 print(f"[draw] 绘图参数: ball_radius={ball_radius}, box_color=({box_color_r:.2f},{box_color_g:.2f},{box_color_b:.2f}), alpha={alpha_list}")
 
 
-# ===========================================================================
-# 每帧回调：仅推进帧索引，从预存数组读取位置，零物理计算
-# ===========================================================================
+# 运动相机（速度段驱动）：优先读取 move_camera.txt，其次用 display.txt header 缓存
+import re as _re
+
+def _load_move_camera_txt():
+    """直接读取 input/move_camera.txt（与 output 同级的 input 目录）。"""
+    input_dir = os.path.join(os.path.dirname(output_dir), "input")
+    cam_path = os.path.join(input_dir, "move_camera.txt")
+    if not os.path.exists(cam_path):
+        return None
+    segs = []
+    with open(cam_path, "r", encoding="utf-8") as f:
+        for line in f:
+            line = line.strip()
+            if not line or line.startswith("#"):
+                continue
+            # 解析帧范围：支持 "all"（全程）或 "N-M"（区间）
+            if line.lower().startswith("all") or _re.match(r'^\s*all\s', line, _re.IGNORECASE):
+                start, end = 0, 10**9  # 用极大值表示全程
+            else:
+                m = _re.match(r'(\d+)\s*-\s*(\d+)', line)
+                if not m:
+                    continue
+                start, end = int(m.group(1)), int(m.group(2))
+            v, r = [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]
+            for i, axis in enumerate(['x', 'y', 'z']):
+                m2 = _re.search(r'v' + axis + r'\s*=\s*([-\d.]+)', line)
+                if m2: v[i] = float(m2.group(1))
+                m2 = _re.search(r'r' + axis + r'\s*=\s*([-\d.]+)', line)
+                if m2: r[i] = float(m2.group(1))
+            if any(v) or any(r):
+                segs.append({"start": start, "end": end, "v": v, "r": r})
+    return segs if segs else None
+
+# 先试 move_camera.txt 直读，没有则用 display.txt 缓存
+# header 中 camera_keyframes 为空字符串表示 move_camera=0（开关关闭），跳过文件加载
+_camera_motion_enabled = bool(config.get("camera_keyframes", ""))
+_CAM_MOTION = _load_move_camera_txt() if _camera_motion_enabled else None
+if not _CAM_MOTION:
+    _CAM_MOTION = json.loads(config.get("camera_keyframes", "null")) if config.get("camera_keyframes") else None
+if _CAM_MOTION:
+    _cam_center = [0.0, 0.0, 0.0]
+    _cam_elev = initial_camera["elevation"]
+    _cam_azim = initial_camera["azimuth"]
+    _cam_dist = initial_camera["distance"]
+    src = "move_camera.txt" if _load_move_camera_txt() else "display.txt header"
+    print(f"[draw] 运动相机已启用（数据来源: {src}，{len(_CAM_MOTION)} 段）")
+
+
+def _update_motion_camera(f_idx):
+    """速度段驱动：每帧累加平移/旋转。
+
+    时间交叠时所有段同时生效，按文件中出现的顺序依次作用。
+    只有当前帧存在活动段时才覆写相机，否则保留用户键盘/鼠标操作的结果。
+    """
+    if not _CAM_MOTION:
+        return
+    global _cam_center, _cam_elev, _cam_azim, _cam_dist
+    active = False
+    for seg in _CAM_MOTION:
+        if seg["start"] <= f_idx < seg["end"]:
+            _cam_center[0] += seg["v"][0]
+            _cam_center[1] += seg["v"][1]
+            _cam_center[2] += seg["v"][2]
+            _cam_elev += seg["r"][0]
+            _cam_azim += seg["r"][1]
+            active = True
+
+    if active:
+        view.camera.center    = tuple(_cam_center)
+        view.camera.distance  = _cam_dist
+        view.camera.elevation = _cam_elev
+        view.camera.azimuth   = _cam_azim
+
+
 def update(event):
     global frame_idx
     frame_idx = (frame_idx + 1) % N_FRAMES     # 循环播放
@@ -563,6 +900,9 @@ def update(event):
     if bond_lines is not None and len(BOND_PAIRS) > 0:
         _update_bond_positions(frame_idx)
 
+    # 运动相机：速度段驱动
+    _update_motion_camera(frame_idx)
+
     # 信息面板显示 plot_atom 的数据
     x = float(DISP_X[frame_idx])
     y = float(DISP_Y[frame_idx])

dynamics.py

@@ -14,6 +14,7 @@ import sys
 import subprocess
 import time
 import argparse
+import json
 from contextlib import contextmanager
 from pathlib import Path
 
@@ -25,6 +26,57 @@ sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
 import compute
 
 
+def _fmt_alpha(v):
+    """将 alpha 值格式化为逗号分隔字符串，兼容 numpy 数组/list/标量。"""
+    if isinstance(v, (list, tuple, np.ndarray)):
+        return ",".join(str(float(x)) for x in v)
+    return str(float(v))
+
+
+def _json_field(value):
+    """Serialize arrays/lists for display header metadata."""
+    if isinstance(value, np.ndarray):
+        value = value.tolist()
+    return json.dumps(value, ensure_ascii=False)
+
+
+def _load_camera_kf(config, runtime_base):
+    """加载 move_camera.txt（速度段格式）→ JSON 字符串。"""
+    import re, json
+    if not int(config.get("move_camera", 0)):
+        return ""
+    cam_file = str(config.get("move_camera_file",
+                    os.path.join("input", "move_camera.txt")))
+    cam_path = cam_file
+    if not os.path.isabs(cam_file):
+        cam_path = os.path.join(runtime_base, cam_file)
+    if not os.path.exists(cam_path):
+        return ""
+    segments = []
+    with open(cam_path, "r", encoding="utf-8") as f:
+        for line in f:
+            line = line.strip()
+            if not line or line.startswith("#"):
+                continue
+            # 解析帧范围：支持 "all"（全程）或 "N-M"（区间）
+            if line.lower().startswith("all") or re.match(r'^\s*all\s', line, re.IGNORECASE):
+                start, end = 0, 10**9
+            else:
+                m = re.match(r'(\d+)\s*-\s*(\d+)', line)
+                if not m:
+                    continue
+                start, end = int(m.group(1)), int(m.group(2))
+            v, r = [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]
+            for i, axis in enumerate(['x', 'y', 'z']):
+                m2 = re.search(r'v' + axis + r'\s*=\s*([-\d.]+)', line)
+                if m2: v[i] = float(m2.group(1))
+                m2 = re.search(r'r' + axis + r'\s*=\s*([-\d.]+)', line)
+                if m2: r[i] = float(m2.group(1))
+            if any(v) or any(r):
+                segments.append({"start": start, "end": end, "v": v, "r": r})
+    return json.dumps(segments) if segments else ""
+
+
 def read_optional_index(data, key, default_value):
     """Read an optional integer index from structured txt metadata."""
     if key not in data:
@@ -94,16 +146,6 @@ def build_sample_indices(total_steps, sample_step, sample_start, sample_end):
     return indices
 
 
-def save_display_txt(data, out_dir=None):
-    """将抽帧数据保存到 output/display.txt（含所有参数元数据）。"""
-    if out_dir is None:
-        out_dir = os.path.dirname(os.path.abspath(__file__))
-    disp_path = os.path.join(compute.get_output_dir(out_dir), "display.txt")
-    compute.save_text_data(disp_path, data)
-    print(f"[sample] 显示数组已保存至: {disp_path}")
-    return disp_path
-
-
 def run_case(config_path, runtime_base, input_dir="input", output_dir="output", no_plot=False):
     """Run one case with explicit program path, input path, and output path."""
     runtime_base = Path(runtime_base).resolve()
@@ -145,12 +187,11 @@ def run_case(config_path, runtime_base, input_dir="input", output_dir="output",
         disp_path = os.path.join(output_dir_abs, "display.txt")
 
         # ── 自动缓存检测 ───────────────────────────────────────
-        # force_calc=1: 强制重新计算，忽略缓存
-        # force_calc=0: 尊重 step_simulate 设置，不自动覆盖
+        # force_calc=1: 强制重新计算，忽略缓存（仅在 step_simulate=1 时生效）
+        # force_calc=0: 尊重 step_simulate 设置
         force_calc = int(config.get("force_calc", 0))
-        if force_calc:
+        if force_calc and config.get("step_simulate", 1):
             print(f"[run] force_calc=1，跳过缓存，强制重新计算")
-            config["step_simulate"] = 1
             config["step_sample"] = 1
         elif config.get("step_simulate", 1):
             # step_simulate=1 且 force_calc=0 → 按用户要求执行计算
@@ -183,8 +224,12 @@ def run_case(config_path, runtime_base, input_dir="input", output_dir="output",
                 print(f"[run] 没有可用的缓存输出，但 step_simulate=0，将跳过模拟")
 
         # 2. 运行物理模拟 → output/trajectory.txt
+        _engine_aliases = {"c++": "cpp", "f90": "fortran", "f": "fortran"}
+        engine = _engine_aliases.get(
+            str(config.get("engine", "python")).lower(),
+            str(config.get("engine", "python")).lower()
+        )
         if config.get("step_simulate", 1):
-            engine = config.get("engine", "python")
             total_steps = config["NT"]
             record_steps = total_steps - (config.get("warmup_steps") or 0)
             print(f"[run] 开始计算  总步数={total_steps}  记录步数={record_steps}  DT={config['DT']}")
@@ -193,273 +238,110 @@ def run_case(config_path, runtime_base, input_dir="input", output_dir="output",
             _t0 = _time.time()
 
             if engine == "python":
-                traj_x, traj_y, traj_z, traj_vx, traj_vy, traj_vz = compute.run_from_config(config, str(runtime_base))
-                compute.save_trajectory_txt(traj_x, traj_y, traj_z, traj_vx, traj_vy, traj_vz, str(runtime_base))
+                compute.run_from_config(config, str(runtime_base))
             else:
-                # 外部引擎：先加载配置到全局变量，再运行引擎，再用 save_trajectory_txt 补全 metadata
+                # 外部引擎：先加载配置到全局变量，再运行引擎
                 config["_skip_run"] = True
                 compute.run_from_config(config, str(runtime_base))
                 config.pop("_skip_run", None)
                 input_dir_abs = str(input_dir_path.resolve())
                 output_dir_abs = str(output_dir_path.resolve())
-                traj_x, traj_y, traj_z, traj_vx, traj_vy, traj_vz = compute.run_engine(
-                    engine, input_dir_abs, output_dir_abs, config)
-                compute.save_trajectory_txt(traj_x, traj_y, traj_z, traj_vx, traj_vy, traj_vz, str(runtime_base))
+
+                # ── DLL 路径（无文件 I/O，直接输出 display.npz）──
+                from engines.engine_dll import is_dll_available
+                if not is_dll_available(engine):
+                    raise FileNotFoundError(
+                        f"DLL 未找到（引擎 {engine}）。"
+                        f"请先编译：cd engines/{engine} && make dll")
+                compute.run_engine_dll(engine, output_dir_abs, config)
 
             _elapsed = _time.time() - _t0
             print(f"[run] 引擎: {engine}  计算完成: {record_steps} 步  {_elapsed:.3f} s")
         else:
-            print("[run] 步骤 [模拟] 已跳过，直接加载已有轨迹")
+            print("[run] 步骤 [模拟] 已跳过")
+
+        # 3. 检查/生成 display.txt
+        disp_path_new = os.path.join(output_dir_abs, "display.txt")
+        save_traj = int(config.get("save_trajectory", 0))
+        
+        if os.path.exists(disp_path_new):
+            # Python 引擎或新版外部引擎（save_trajectory=0）已直接写入
+            print(f"[run] 发现已有 display.txt（引擎直接抽帧）")
+        elif engine != "python" and os.path.exists(os.path.join(output_dir_abs, "trajectory.txt")):
+            # 旧版外部引擎：从 trajectory.txt 抽帧
+            traj_path = os.path.join(output_dir_abs, "trajectory.txt")
             if not os.path.exists(traj_path):
-                print(f"[run] 错误: trajectory.txt 不存在，无法跳过模拟")
+                print(f"[run] 错误: 找不到 trajectory.txt 或 display.txt")
                 sys.exit(1)
+            data = compute.load_text_data(traj_path)
+            NT = int(data["NT"]); DT = float(data["DT"]); NSTEP = int(data.get("NSTEP", 1))
+            record_steps = NT - int(data.get("warmup_steps", 0))
+            n_atoms = len(data["atom_ids"])
+            sample_start = 0
+            sample_end = NT
+            indices = np.arange(0, record_steps, NSTEP, dtype=np.int64)
+            if len(indices) == 0:
+                indices = np.array([0])
+                
+            traj_x = data["traj_x"]; traj_y = data["traj_y"]; traj_z = data["traj_z"]
+            traj_vx = data["traj_vx"]; traj_vy = data["traj_vy"]; traj_vz = data["traj_vz"]
+            
+            # 构建 header_fields
+            hf = {"DT": str(DT), "NSTEP": str(NSTEP), "method": str(data.get("method", "")),
+                  "warmup_steps": str(data.get("warmup_steps", 0)),
+                  "dynamic_steps": str(record_steps),
+                  "T_total": str(NT * DT),
+                  "X_MAX": str(data.get("X_MAX", 10)), "X_MIN": str(data.get("X_MIN", -10)),
+                  "Y_MAX": str(data.get("Y_MAX", 10)), "Y_MIN": str(data.get("Y_MIN", -10)),
+                  "Z_MAX": str(data.get("Z_MAX", 10)), "Z_MIN": str(data.get("Z_MIN", -10)),
+                  "ball_radius": str(data.get("ball_radius", 0.5)),
+                  "ball_color_r": str(data.get("ball_color_r", 0.9)),
+                  "ball_color_g": str(data.get("ball_color_g", 0.2)),
+                  "ball_color_b": str(data.get("ball_color_b", 0.2)),
+                  "box_color_r": str(data.get("box_color_r", 0.8)),
+                  "box_color_g": str(data.get("box_color_g", 0.8)),
+                  "box_color_b": str(data.get("box_color_b", 0.85)),
+                  "gravity_field": str(data.get("gravity_field", 1)),
+                  "gravity_interaction": str(data.get("gravity_interaction", 0)),
+                  "elastic_force": str(data.get("elastic_force", 1)),
+                  "damping_force": str(data.get("damping_force", 0)),
+                  "gravity_strength": str(data.get("gravity_strength", 1.0)),
+                  "driving_force": str(data.get("driving_force", 0)),
+                  "use_marker": str(config.get("use_marker", 0)),
+                  "alpha": _fmt_alpha(data.get("alpha", 0.2)),
+                  "atom_masses": _json_field(data.get("atom_masses", [])),
+                  "atom_positions": _json_field(data.get("atom_positions", [])),
+                  "bond_pairs": _json_field(data.get("bond_pairs", [])),
+                  "bond_stiffness": _json_field(data.get("bond_stiffness", [])),
+                  "bond_rest_lengths": _json_field(data.get("bond_rest_lengths", [])),
+                  "G": _json_field(data.get("G", [0.0, 0.0, 0.0])),
+                  "atom_radii": _fmt_alpha(data.get("atom_radii", [])),
+                  "camera_distance": str(config.get("camera_distance", 40.0)),
+                  "camera_elevation": str(config.get("camera_elevation", 0)),
+                  "camera_azimuth": str(config.get("camera_azimuth", 0)),
+                  "camera_keyframes": _load_camera_kf(config, str(runtime_base))}
+            
+            n_frames = len(indices)
+            compute.save_display_txt(
+                disp_path_new,
+                traj_x[indices], traj_y[indices], traj_z[indices],
+                traj_vx[indices], traj_vy[indices], traj_vz[indices],
+                np.array(data["atom_ids"]), n_frames, n_atoms,
+                header_fields=hf)
+            print(f"[run] 从 trajectory.txt 抽帧生成 display.txt ({n_frames} 帧)")
 
-        # 3. 抽帧 → output/display.txt
-        traj_path = os.path.join(output_dir_abs, "trajectory.txt")
-        data = compute.load_text_data(traj_path)
-
-        NT = int(data["NT"]); DT = float(data["DT"]); NSTEP = int(data["NSTEP"])
-        warmup_steps = int(data.get("warmup_steps", 0))
-        plot_atom_row = int(data["plot_atom_row"]) if "plot_atom_row" in data else 0
-        plot_atom_id = int(data["plot_atom_id"]) if "plot_atom_id" in data else int(data["atom_ids"][plot_atom_row])
-
-        # 抽帧范围控制
-        sample_start = read_optional_index(data, "sample_start", 0)
-        sample_end = read_optional_index(data, "sample_end", NT)
-
-        indices = build_sample_indices(NT, NSTEP, sample_start, sample_end)
-        n_frames = len(indices)
-
-        print(f"[run] 抽帧范围: [{sample_start}, {sample_end}), 共 {n_frames} 帧")
-
-        traj_x = data["traj_x"]
-        traj_y = data["traj_y"]
-        traj_z = data["traj_z"]
-        traj_vx = data["traj_vx"]
-        traj_vy = data["traj_vy"]
-        traj_vz = data["traj_vz"]
-
-        if traj_x.ndim == 1:
-            selected_x = traj_x
-            selected_y = traj_y
-            selected_z = traj_z
-            selected_vx = traj_vx
-            selected_vy = traj_vy
-            selected_vz = traj_vz
-            all_x = traj_x[:, None]
-            all_y = traj_y[:, None]
-            all_z = traj_z[:, None]
-            all_vx = traj_vx[:, None]
-            all_vy = traj_vy[:, None]
-            all_vz = traj_vz[:, None]
-        else:
-            selected_x = traj_x[:, plot_atom_row]
-            selected_y = traj_y[:, plot_atom_row]
-            selected_z = traj_z[:, plot_atom_row]
-            selected_vx = traj_vx[:, plot_atom_row]
-            selected_vy = traj_vy[:, plot_atom_row]
-            selected_vz = traj_vz[:, plot_atom_row]
-            all_x = traj_x
-            all_y = traj_y
-            all_z = traj_z
-            all_vx = traj_vx
-            all_vy = traj_vy
-            all_vz = traj_vz
-
-        if config.get("step_sample", 1):
-            disp_data = {
-                "disp_x": selected_x[indices],
-                "disp_y": selected_y[indices],
-                "disp_z": selected_z[indices],
-                "disp_vx": selected_vx[indices],
-                "disp_vy": selected_vy[indices],
-                "disp_vz": selected_vz[indices],
-                "disp_all_x": all_x[indices],
-                "disp_all_y": all_y[indices],
-                "disp_all_z": all_z[indices],
-                "disp_all_vx": all_vx[indices],
-                "disp_all_vy": all_vy[indices],
-                "disp_all_vz": all_vz[indices],
-                "disp_t": indices * DT,
-                "disp_step": indices,
-                "n_frames": n_frames,
-                "NT": NT, "DT": DT, "NSTEP": NSTEP,
-                "plot_atom_id": plot_atom_id,
-                "plot_atom_row": plot_atom_row,
-                "method": str(data["method"]) if "method" in data else "explicit_euler",
-                "coord_file": str(data["coord_file"]) if "coord_file" in data else os.path.join("input", "coord.txt"),
-                "atom_ids": data["atom_ids"] if "atom_ids" in data else np.array([1]),
-                "atom_masses": data["atom_masses"] if "atom_masses" in data else np.array([float(data["M"])]),
-                "atom_radii": data["atom_radii"] if "atom_radii" in data else np.array([float(data["ball_radius"])]),
-                "atom_positions": data["atom_positions"] if "atom_positions" in data else np.array([[float(data["X0"]), float(data["Y0"]), float(data["Z0"])]]),
-                "atom_velocities": data["atom_velocities"] if "atom_velocities" in data else np.array([[float(data["VX0"]), float(data["VY0"]), float(data["VZ0"])]]),
-                "atom_fixed": data["atom_fixed"] if "atom_fixed" in data else np.array([[0, 0, 0]]),
-                "bond_pairs": data.get("bond_pairs", np.zeros((0, 2), dtype=np.int64)).tolist(),
-                "bond_stiffness": data.get("bond_stiffness", np.zeros(0, dtype=np.float64)).tolist(),
-                "bond_rest_lengths": data.get("bond_rest_lengths", np.zeros(0, dtype=np.float64)).tolist(),
-                "warmup_steps": warmup_steps,
-                "sample_start": sample_start,
-                "sample_end": sample_end,
-                "X_MIN": float(data["X_MIN"]), "X_MAX": float(data["X_MAX"]),
-                "Y_MIN": float(data["Y_MIN"]), "Y_MAX": float(data["Y_MAX"]),
-                "Z_MIN": float(data["Z_MIN"]), "Z_MAX": float(data["Z_MAX"]),
-                "X0": float(data["X0"]), "Y0": float(data["Y0"]), "Z0": float(data["Z0"]),
-                "VX0": float(data["VX0"]), "VY0": float(data["VY0"]), "VZ0": float(data["VZ0"]),
-                "M": float(data["M"]) if "M" in data else 1.0,
-                "alpha": data["alpha"],
-                "ball_radius": float(data["ball_radius"]),
-                "ball_color_r": float(data["ball_color_r"]),
-                "ball_color_g": float(data["ball_color_g"]),
-                "ball_color_b": float(data["ball_color_b"]),
-                "box_color_r": float(data["box_color_r"]),
-                "box_color_g": float(data["box_color_g"]),
-                "box_color_b": float(data["box_color_b"]),
-                "gravity_field": int(data.get("gravity_field", 1)),
-                "gravity_interaction": int(data.get("gravity_interaction", 0)),
-                "elastic_force": int(data.get("elastic_force", 1)),
-                "damping_force": int(data.get("damping_force", 0)),
-                "gravity_strength": float(data.get("gravity_strength", 1.0)),
-                "driving_force": int(config.get("driving_force", 0)),
-                "use_marker": int(config.get("use_marker", 0)),
-            }
-            save_display_txt(disp_data, str(runtime_base))
-            print(f"[run] 抽帧完成: {sample_end - sample_start} 步 -> {n_frames} 帧")
-        else:
-            print("[run] 步骤 [抽帧] 已跳过")
+            # save_trajectory=0 时清理 trajectory.txt
+            if not save_traj:
+                try:
+                    os.remove(traj_path)
+                    print(f"[run] save_trajectory=0，已删除 {traj_path}")
+                except OSError:
+                    pass
 
         # 4. 绘图（可选）
         if not no_plot and config.get("step_plot", 1):
-            try:
-                import matplotlib.pyplot as plt
-
-                # 配置中文字体支持
-                plt.rcParams['font.sans-serif'] = ['SimHei', 'Microsoft YaHei', 'WenQuanYi Micro Hei', 'DejaVu Sans']
-                plt.rcParams['axes.unicode_minus'] = False
-
-                time_arr = np.arange(NT) * DT
-                n_atoms = all_x.shape[1]
-                atom_ids_list = data.get("atom_ids", np.arange(n_atoms) + 1)
-
-                fig, axes = plt.subplots(3, 3, figsize=(15, 13))
-                fig.suptitle("轨迹与能量分析", fontsize=16)
-
-                # ── 位置 / 速度 6 子图（前 2 行，每行 3 列） ──
-                plot_configs = [
-                    (axes[0, 0], all_x, "x - 时间"),
-                    (axes[0, 1], all_y, "y - 时间"),
-                    (axes[0, 2], all_z, "z - 时间"),
-                    (axes[1, 0], all_vx, "vx - 时间"),
-                    (axes[1, 1], all_vy, "vy - 时间"),
-                    (axes[1, 2], all_vz, "vz - 时间"),
-                ]
-
-                colors = plt.cm.tab10(np.linspace(0, 1, n_atoms))
-
-                for ax, data_arr, title in plot_configs:
-                    for i in range(n_atoms):
-                        atom_id = int(atom_ids_list[i])
-                        ax.plot(time_arr, data_arr[:, i], color=colors[i], linewidth=1.5, label=f"原子 {atom_id}")
-                    ax.set_title(title)
-                    ax.set_xlabel("时间 (s)")
-                    ax.grid(True, alpha=0.3)
-                    ax.legend()
-
-                # ── 能量计算 ─────────────────────────────────────
-                masses = np.array(data["atom_masses"])                     # (n_atoms,)
-                G_vec = np.array(data.get("G", [0.0, 0.0, -9.8]))        # [gx, gy, gz]
-                gravity_field_enabled = int(data.get("gravity_field", 1))
-                gravity_interaction_enabled = int(data.get("gravity_interaction", 0))
-                gravity_strength = float(data.get("gravity_strength", 1.0))
-                elastic_force_enabled = int(data.get("elastic_force", 1))
-                damping_force_enabled = int(data.get("damping_force", 0))
-
-                # 动能 Ek = ½ m v²
-                ek = 0.5 * masses[np.newaxis, :] * (all_vx**2 + all_vy**2 + all_vz**2)
-
-                # 均匀重力场势能 Ug = -m G·r
-                ug = np.zeros_like(ek)
-                if gravity_field_enabled:
-                    ug = -masses[np.newaxis, :] * (
-                        G_vec[0] * all_x + G_vec[1] * all_y + G_vec[2] * all_z
-                    )
-
-                # 弹性势能 Us = ½ k (d - d₀)²
-                us = np.zeros_like(ek)
-                bond_pairs = data.get("bond_pairs")
-                bond_stiffness = data.get("bond_stiffness")
-                bond_rest_lengths = data.get("bond_rest_lengths")
-                if elastic_force_enabled and bond_pairs is not None and len(bond_pairs) > 0:
-                    for b_idx in range(len(bond_pairs)):
-                        i, j = bond_pairs[b_idx]
-                        dx = all_x[:, j] - all_x[:, i]
-                        dy = all_y[:, j] - all_y[:, i]
-                        dz = all_z[:, j] - all_z[:, i]
-                        dist = np.sqrt(dx**2 + dy**2 + dz**2)
-                        stretch = dist - bond_rest_lengths[b_idx]
-                        us_each = 0.5 * bond_stiffness[b_idx] * stretch**2
-                        us[:, i] += us_each          # 将整根键的势能记给 i
-
-                # 万有引力势能 Ug_grav = -G_grav * m_i * m_j / r
-                ug_grav = np.zeros_like(ek)
-                if gravity_interaction_enabled:
-                    n_atoms_en = len(masses)
-                    for i in range(n_atoms_en):
-                        for j in range(i + 1, n_atoms_en):
-                            dx = all_x[:, j] - all_x[:, i]
-                            dy = all_y[:, j] - all_y[:, i]
-                            dz = all_z[:, j] - all_z[:, i]
-                            dist = np.sqrt(dx**2 + dy**2 + dz**2)
-                            dist = np.maximum(dist, 1e-12)
-                            pair_pe = -gravity_strength * masses[i] * masses[j] / dist
-                            ug_grav[:, i] += 0.5 * pair_pe
-                            ug_grav[:, j] += 0.5 * pair_pe
-
-                # 各原子总能量
-                e_total = ek + ug + us + ug_grav                           # (NT, n_atoms)
-
-                # 系统能量分量
-                ek_sys = np.sum(ek, axis=1)
-                ug_sys = np.sum(ug, axis=1)
-                us_sys = np.sum(us, axis=1)
-                ug_grav_sys = np.sum(ug_grav, axis=1)
-                e_sys = ek_sys + ug_sys + us_sys + ug_grav_sys
-
-                # ── 第 3 行左：各原子总能量 ──
-                ax_e = axes[2, 0]
-                for i in range(n_atoms):
-                    aid = int(atom_ids_list[i])
-                    ax_e.plot(time_arr, e_total[:, i], color=colors[i], linewidth=1.5, label=f"原子 {aid}")
-                ax_e.set_title("各原子总能量")
-                ax_e.set_xlabel("时间 (s)")
-                ax_e.set_ylabel("能量")
-                ax_e.grid(True, alpha=0.3)
-                ax_e.legend(loc="upper right")
-
-                # ── 第 3 行右：系统总能量 ──
-                ax_sys = axes[2, 1]
-                ax_sys.plot(time_arr, ek_sys, 'b-', linewidth=1.5, label="系统动能")
-                ax_sys.plot(time_arr, ug_sys, 'g-', linewidth=1.5, label="均匀重力势能")
-                if elastic_force_enabled and bond_pairs is not None and len(bond_pairs) > 0:
-                    ax_sys.plot(time_arr, us_sys, color='orange', linewidth=1.5, label="系统弹性势能")
-                if gravity_interaction_enabled:
-                    ax_sys.plot(time_arr, ug_grav_sys, color='purple', linewidth=1.5, label="万有引力势能")
-                ax_sys.plot(time_arr, e_sys, 'r--', linewidth=1.5, label="系统总能量")
-                ax_sys.set_title("系统总能量")
-                ax_sys.set_xlabel("时间 (s)")
-                ax_sys.set_ylabel("能量")
-                ax_sys.grid(True, alpha=0.3)
-                ax_sys.legend(loc="upper right")
-
-                # 隐藏第 3 行第 3 列空子图
-                axes[2, 2].set_visible(False)
-
-                plt.tight_layout(rect=[0, 0.03, 1, 0.95])
-                plot_path = os.path.join(output_dir_abs, "trajectory_plots.png")
-                plt.savefig(plot_path, dpi=300, bbox_inches="tight")
-                print(f"[run] 轨迹图表已保存至: {plot_path}")
-                plt.show()
-            except ImportError:
-                print("[run] 警告: 未安装 matplotlib，跳过绘图")
+            print("[run] 注意: 旧版 step_plot 绘图路径依赖完整轨迹局部变量，当前已暂时跳过。")
+            print("[run] 如需波形/能量动画，请使用 step_plot_wave: 1。")
 
         print(f"[run] 完成！输出目录: {output_dir_abs}")
 
@@ -469,11 +351,13 @@ def run_case(config_path, runtime_base, input_dir="input", output_dir="output",
             if not os.path.exists(draw_script):
                 print(f"[run] 未找到动画脚本: {draw_script}")
             else:
-                # 检查 display.txt 是否存在（step_sample=0 时可能没有）
-                disp_path = os.path.join(output_dir_abs, "display.txt")
+                # 检查 display.npz 或 display.txt 是否存在
+                disp_npz = os.path.join(output_dir_abs, "display.npz")
+                disp_txt = os.path.join(output_dir_abs, "display.txt")
+                disp_path = disp_npz if os.path.exists(disp_npz) else disp_txt
                 if not os.path.exists(disp_path):
-                    print(f"[run] 错误: 找不到 {disp_path}")
-                    print(f"[run] 启动动画需要先运行抽帧（step_sample: 1），或手动保留 output/display.txt")
+                    print(f"[run] 错误: 找不到 display.npz 或 display.txt")
+                    print(f"[run] 启动动画需要先运行模拟（step_simulate: 1）")
                 else:
                     try:
                         print("[run] 正在启动 VisPy 3D 动画窗口…")
@@ -505,14 +389,24 @@ def run_case(config_path, runtime_base, input_dir="input", output_dir="output",
         # 6. 波形能量动画（可选）
         if config.get("step_plot_wave", 0):
             try:
+                _save_gif = int(config.get("plot_wave_save_gif", 0))
+                _save_mp4 = int(config.get("plot_wave_save_mp4", 0))
+                _to_file  = bool(_save_gif or _save_mp4)
+                if _to_file:
+                    import matplotlib
+                    matplotlib.use("Agg")   # 保存文件时用非交互式后端
                 import plot_wave as pw
                 print("[run] 正在绘制波形与能量图…")
-                pw.plot_wave(
+                gif = pw.plot_wave(
                     str(output_dir_abs),
-                    save_gif=int(config.get("plot_wave_save_gif", 0)),
-                    save_mp4=int(config.get("plot_wave_save_mp4", 0)),
+                    save_gif=_save_gif,
+                    save_mp4=_save_mp4,
+                    show=not _to_file,   # 不保存文件时弹出交互窗口
                 )
+                if gif:
+                    print(f"[run] 波形 GIF 已保存: {gif}")
             except Exception as e:
+                import traceback; traceback.print_exc()
                 print(f"[run] 绘制波形图失败: {e}")
 
 

engines/c/Makefile

@@ -1,63 +0,0 @@
-# engines/c/Makefile
-# 跨平台编译：make         → 本地系统编译
-#              make linux  → Linux 交叉编译（需 x86_64-linux-gnu-gcc）
-#              make windows → Windows 交叉编译（需 x86_64-w64-mingw32-gcc）
-#              make macos  → macOS 交叉编译（需 osxcross 工具链）
-
-CC        = gcc
-CFLAGS    = -O3 -march=native -Wall -Wextra
-LDFLAGS   = -lm
-SRCS      = main.c
-
-# 自动检测系统
-UNAME_S  := $(shell uname -s 2>/dev/null || echo Windows)
-
-# 目标文件名：统一使用 .exe 后缀（方便 Python 跨平台调用）
-TARGET    = build/dynamics_c.exe
-
-# ── 本地编译 ─────────────────────────────────
-.PHONY: all clean linux windows macos
-
-all: $(TARGET)
-
-$(TARGET): $(SRCS) | build
-	$(CC) $(CFLAGS) -o $@ $(SRCS) $(LDFLAGS)
-	@echo "  === C engine built: $@ ==="
-
-build:
-	mkdir -p build
-
-# ── 交叉编译 ─────────────────────────────────
-# Linux → Linux (x86_64)
-linux: CROSS_PREFIX = x86_64-linux-gnu-
-linux: CC = $(CROSS_PREFIX)gcc
-linux: CFLAGS = -O3 -march=x86-64 -Wall -Wextra
-linux: $(SRCS) | build
-	$(CC) $(CFLAGS) -o build/dynamics_c_linux.exe $(SRCS) $(LDFLAGS)
-	@echo "  === Linux binary: build/dynamics_c_linux.exe ==="
-
-# 任意平台 → Windows (x86_64)
-# 需要安装 MinGW 交叉编译器：
-#   apt install mingw-w64 (Debian/Ubuntu)
-#   brew install mingw-w64 (macOS)
-windows: CROSS_PREFIX = x86_64-w64-mingw32-
-windows: CC = $(CROSS_PREFIX)gcc
-windows: CFLAGS = -O3 -march=x86-64 -Wall -Wextra
-windows: $(SRCS) | build
-	$(CC) $(CFLAGS) -o build/dynamics_c_win.exe $(SRCS) $(LDFLAGS)
-	@echo "  === Windows binary: build/dynamics_c_win.exe ==="
-
-# 任意平台 → macOS (x86_64)
-# 需要安装 osxcross 工具链
-macos: CROSS_PREFIX = x86_64-apple-darwin-
-macos: CC = $(CROSS_PREFIX)gcc
-macos: CFLAGS = -O3 -march=x86-64 -Wall -Wextra
-macos: $(SRCS) | build
-	$(CC) $(CFLAGS) -o build/dynamics_c_mac.exe $(SRCS) $(LDFLAGS)
-	@echo "  === macOS binary: build/dynamics_c_mac.exe ==="
-
-# ── 编译所有平台 ──────────────────────────────
-all-platforms: linux windows macos
-
-clean:
-	rm -rf build *.o

engines/c/main.c

@@ -1,948 +0,0 @@
-/**
- * engines/c/main.c
- * -----------------
- * C 语言动力学模拟引擎。
- * 与 Python 版 (compute.py) 算法保持一致。
- *
- * 输入:  param.json      数值参数（Python 从 YAML 转换得来）
- *       <input_dir>/coord.txt
- *       <input_dir>/connection.txt
- *       <input_dir>/bond.txt
- * 输出: <output_dir>/trajectory.txt  (JSON 格式，与 Python 版兼容)
- *
- * 编译: cmake --build build --target dynamics_c
- * 用法: ./build/dynamics_c <input_dir> <output_dir> <param_json_path>
- */
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-#include <math.h>
-#include <time.h>
-
-/* ========================================================================
- * 配置参数（从 param.json 读取）
- * ======================================================================== */
-typedef struct {
-    double  box_a;           /* 盒子半边长 */
-    int     NT;              /* 总步数 */
-    double  DT;              /* 时间步长 */
-    int     NSTEP;           /* 抽帧间隔 */
-    int     warmup_steps;    /* 预热步数 */
-    char    method[32];      /* 算法名称 */
-    double  G[3];            /* 重力分量 */
-    double  B[3];            /* 阻尼分量 */
-    int     gravity_field;       /* 均匀重力场开关 */
-    int     gravity_interaction; /* 原子间万有引力开关 */
-    int     elastic_force;       /* 弹簧键力开关 */
-    int     damping_force;       /* 阻尼开关 */
-    double  gravity_strength;    /* 万有引力强度 */
-    int     driving_force;       /* 驱动力开关 */
-} SimParams;
-
-/* ========================================================================
- * 原子数据
- * ======================================================================== */
-typedef struct {
-    int    n_atoms;
-    int    *atom_ids;
-    double *masses;
-    double *radii;
-    double *pos_0;           /* 初始位置 (n_atoms*3) */
-    double *vel_0;           /* 初始速度 (n_atoms*3) */
-    int    *fixed;           /* 固定约束 (n_atoms*3) */
-} AtomData;
-
-/* ========================================================================
- * 成键数据
- * ======================================================================== */
-typedef struct {
-    int    n_bonds;
-    int    *pairs;           /* (n_bonds*2) */
-    double *stiffness;
-    double *rest_lengths;
-} BondData;
-
-/* 前向声明 */
-static void *xmalloc(size_t sz);
-
-/* ========================================================================
- * 驱动力数据
- * ======================================================================== */
-typedef struct {
-    int    n_drivers;
-    int    *atom_idx;
-    double *amp_x, *amp_y, *amp_z;
-    double *freq_x, *freq_y, *freq_z;
-    double *phi_x, *phi_y, *phi_z;   /* radians */
-    int    *has_period;    /* 0=all, 1=limited cycles */
-    double *period_cycles; /* number of cycles */
-    double *freeze_x, *freeze_y, *freeze_z;
-} DriverData;
-
-/* 读取 driver.txt */
-static DriverData read_driver(const char *input_dir, const AtomData *atoms) {
-    DriverData d;
-    memset(&d, 0, sizeof(d));
-
-    char path[512];
-    snprintf(path, sizeof(path), "%s/driver.txt", input_dir);
-    FILE *f = fopen(path, "r");
-    if (!f) return d;
-
-    char line[1024];
-    if (!fgets(line, sizeof(line), f)) { fclose(f); return d; }
-
-    /* 第一遍：统计行数 */
-    int n_lines = 0;
-    while (fgets(line, sizeof(line), f)) {
-        char trimmed[1024];
-        int j = 0;
-        for (int i = 0; line[i]; i++) {
-            if (line[i] != ' ' && line[i] != '\t' && line[i] != '\n' && line[i] != '\r')
-                trimmed[j++] = line[i];
-        }
-        trimmed[j] = '\0';
-        if (strlen(trimmed) > 0 && trimmed[0] != '#') n_lines++;
-    }
-
-    if (n_lines == 0) { fclose(f); return d; }
-
-    /* 分配内存 */
-    d.n_drivers = n_lines;
-    d.atom_idx     = (int*)xmalloc(n_lines * sizeof(int));
-    d.amp_x = (double*)xmalloc(n_lines * sizeof(double));
-    d.amp_y = (double*)xmalloc(n_lines * sizeof(double));
-    d.amp_z = (double*)xmalloc(n_lines * sizeof(double));
-    d.freq_x = (double*)xmalloc(n_lines * sizeof(double));
-    d.freq_y = (double*)xmalloc(n_lines * sizeof(double));
-    d.freq_z = (double*)xmalloc(n_lines * sizeof(double));
-    d.phi_x = (double*)xmalloc(n_lines * sizeof(double));
-    d.phi_y = (double*)xmalloc(n_lines * sizeof(double));
-    d.phi_z = (double*)xmalloc(n_lines * sizeof(double));
-    d.has_period = (int*)xmalloc(n_lines * sizeof(int));
-    d.period_cycles = (double*)xmalloc(n_lines * sizeof(double));
-    d.freeze_x = (double*)xmalloc(n_lines * sizeof(double));
-    d.freeze_y = (double*)xmalloc(n_lines * sizeof(double));
-    d.freeze_z = (double*)xmalloc(n_lines * sizeof(double));
-
-    /* 初始化 freeze 数组 */
-    for (int i = 0; i < n_lines; i++) {
-        d.freeze_x[i] = d.freeze_y[i] = d.freeze_z[i] = 0.0;
-    }
-
-    /* 第二遍：解析 */
-    rewind(f);
-    fgets(line, sizeof(line), f); /* 跳过表头 */
-
-    int idx = 0;
-    while (idx < n_lines && fgets(line, sizeof(line), f)) {
-        char trimmed[1024];
-        int j = 0;
-        for (int i = 0; line[i]; i++) {
-            if (line[i] != ' ' && line[i] != '\t' && line[i] != '\n' && line[i] != '\r')
-                trimmed[j++] = line[i];
-        }
-        trimmed[j] = '\0';
-        if (strlen(trimmed) == 0 || trimmed[0] == '#') continue;
-
-        int atom_id;
-        double amp_x, amp_y, amp_z;
-        double freq_x, freq_y, freq_z;
-        double phi_x, phi_y, phi_z;
-        char period_str[256] = {0};
-
-        int n_parsed = sscanf(line,
-            "%d %lf %lf %lf %lf %lf %lf %lf %lf %lf %255s",
-            &atom_id,
-            &amp_x, &amp_y, &amp_z,
-            &freq_x, &freq_y, &freq_z,
-            &phi_x, &phi_y, &phi_z,
-            period_str);
-
-        if (n_parsed < 11) continue;
-
-        /* 通过原子 ID 匹配内部索引（线性搜索）*/
-        int ii = -1;
-        for (int k = 0; k < atoms->n_atoms; k++) {
-            if (atoms->atom_ids[k] == atom_id) { ii = k; break; }
-        }
-        if (ii < 0) continue;
-
-        d.atom_idx[idx] = ii;
-        d.amp_x[idx] = amp_x;
-        d.amp_y[idx] = amp_y;
-        d.amp_z[idx] = amp_z;
-        d.freq_x[idx] = freq_x;
-        d.freq_y[idx] = freq_y;
-        d.freq_z[idx] = freq_z;
-        /* 角度 → 弧度 */
-        d.phi_x[idx] = phi_x * M_PI / 180.0;
-        d.phi_y[idx] = phi_y * M_PI / 180.0;
-        d.phi_z[idx] = phi_z * M_PI / 180.0;
-
-        if (strcmp(period_str, "all") == 0 || strcmp(period_str, "-1") == 0) {
-            d.has_period[idx] = 0;
-            d.period_cycles[idx] = -1.0;
-        } else {
-            d.has_period[idx] = 1;
-            d.period_cycles[idx] = strtod(period_str, NULL);
-        }
-        idx++;
-    }
-    d.n_drivers = idx;
-
-    fclose(f);
-    return d;
-}
-
-/* ========================================================================
- * 轨迹缓冲区
- * ======================================================================== */
-typedef struct {
-    int    n_steps;
-    int    n_atoms;
-    double *x, *y, *z;
-    double *vx, *vy, *vz;
-} Trajectory;
-
-/* ========================================================================
- * 辅助函数
- * ======================================================================== */
-
-static void die(const char *msg) {
-    fprintf(stderr, "[C-engine] 错误: %s\n", msg);
-    exit(1);
-}
-
-static void *xmalloc(size_t sz) {
-    void *p = malloc(sz);
-    if (!p) die("内存分配失败");
-    return p;
-}
-
-/* 从 JSON 中读取 double 值 */
-static double json_read_double(const char *json, const char *key) {
-    char search[256];
-    snprintf(search, sizeof(search), "\"%s\"", key);
-    const char *p = strstr(json, search);
-    if (!p) return 0.0;
-    p = strchr(p, ':');
-    if (!p) return 0.0;
-    p++;
-    while (*p == ' ' || *p == '\t' || *p == '\n') p++;
-    return strtod(p, NULL);
-}
-
-static int json_read_int(const char *json, const char *key) {
-    return (int)json_read_double(json, key);
-}
-
-/* 从 JSON 中读取字符串值（写入 dst，最多 dst_sz 字节） */
-static void json_read_string(const char *json, const char *key, char *dst, int dst_sz) {
-    char search[256];
-    snprintf(search, sizeof(search), "\"%s\"", key);
-    const char *p = strstr(json, search);
-    if (!p) { dst[0] = '\0'; return; }
-    p = strchr(p, ':');
-    if (!p) { dst[0] = '\0'; return; }
-    p++;
-    while (*p == ' ' || *p == '\t' || *p == '\n') p++;
-    if (*p != '"') { dst[0] = '\0'; return; }
-    p++;
-    int i = 0;
-    while (*p && *p != '"' && i < dst_sz - 1) { dst[i++] = *p++; }
-    dst[i] = '\0';
-}
-
-/* 读取 JSON 数组 (如 "G": [0, 0, -9.8]) 到 double[3] */
-static void json_read_double3(const char *json, const char *key, double out[3]) {
-    char search[256];
-    snprintf(search, sizeof(search), "\"%s\"", key);
-    const char *p = strstr(json, search);
-    if (!p) { out[0]=out[1]=out[2]=0; return; }
-    p = strchr(p, '[');
-    if (!p) { out[0]=out[1]=out[2]=0; return; }
-    p++;
-    for (int i = 0; i < 3; i++) {
-        while (*p == ' ' || *p == '\t' || *p == '\n' || *p == ',') p++;
-        out[i] = strtod(p, (char**)&p);
-    }
-}
-
-/* 读取 param.json */
-static int    g_gravity_field = 1;
-static int    g_gravity_interaction = 0;
-static int    g_elastic_force = 1;
-static int    g_damping_force = 0;
-static double g_gravity_strength = 1.0;
-
-static SimParams read_params(const char *path) {
-    FILE *f = fopen(path, "rb");
-    if (!f) die("无法打开 param.json");
-    fseek(f, 0, SEEK_END);
-    long sz = ftell(f);
-    fseek(f, 0, SEEK_SET);
-    char *buf = (char*)xmalloc(sz + 1);
-    fread(buf, 1, sz, f);
-    buf[sz] = '\0';
-    fclose(f);
-
-    SimParams p;
-    p.box_a       = json_read_double(buf, "box_a");
-    p.NT          = json_read_int(buf, "NT");
-    p.DT          = json_read_double(buf, "DT");
-    p.NSTEP       = json_read_int(buf, "NSTEP");
-    p.warmup_steps = json_read_int(buf, "warmup_steps");
-    strcpy(p.method, "leapfrog"); /* 默认 */
-    json_read_string(buf, "method", p.method, sizeof(p.method));
-    json_read_double3(buf, "G", p.G);
-    json_read_double3(buf, "B", p.B);
-    p.gravity_field       = json_read_int(buf, "gravity_field");
-    p.gravity_interaction = json_read_int(buf, "gravity_interaction");
-    p.elastic_force       = json_read_int(buf, "elastic_force");
-    p.damping_force       = json_read_int(buf, "damping_force");
-    p.gravity_strength    = json_read_double(buf, "gravity_strength");
-    p.driving_force       = json_read_int(buf, "driving_force");
-    g_gravity_field       = p.gravity_field;
-    g_gravity_interaction = p.gravity_interaction;
-    g_elastic_force       = p.elastic_force;
-    g_damping_force       = p.damping_force;
-    g_gravity_strength    = p.gravity_strength;
-
-    free(buf);
-    return p;
-}
-
-/* 读取 coord.txt */
-static AtomData read_coord(const char *input_dir) {
-    char path[512];
-    snprintf(path, sizeof(path), "%s/coord.txt", input_dir);
-    FILE *f = fopen(path, "r");
-    if (!f) die("无法打开 coord.txt");
-
-    /* 跳过第一行表头 */
-    char line[1024];
-    if (!fgets(line, sizeof(line), f)) die("coord.txt 为空");
-
-    int capacity = 16;
-    AtomData a;
-    a.n_atoms = 0;
-    a.atom_ids  = (int*)xmalloc(capacity * sizeof(int));
-    a.masses    = (double*)xmalloc(capacity * sizeof(double));
-    a.radii     = (double*)xmalloc(capacity * sizeof(double));
-    a.pos_0     = (double*)xmalloc(capacity * 3 * sizeof(double));
-    a.vel_0     = (double*)xmalloc(capacity * 3 * sizeof(double));
-    a.fixed     = (int*)xmalloc(capacity * 3 * sizeof(int));
-
-    while (fgets(line, sizeof(line), f)) {
-        if (a.n_atoms >= capacity) {
-            capacity *= 2;
-            a.atom_ids = realloc(a.atom_ids, capacity * sizeof(int));
-            a.masses   = realloc(a.masses,   capacity * sizeof(double));
-            a.radii    = realloc(a.radii,    capacity * sizeof(double));
-            a.pos_0    = realloc(a.pos_0,    capacity * 3 * sizeof(double));
-            a.vel_0    = realloc(a.vel_0,    capacity * 3 * sizeof(double));
-            a.fixed    = realloc(a.fixed,    capacity * 3 * sizeof(int));
-        }
-        int id, fx, fy, fz;
-        double mass, rad, px, py, pz, vx, vy, vz;
-        int n_parsed = sscanf(line, "%d %lf %lf %lf %lf %lf %lf %lf %lf %d %d %d",
-                   &id, &mass, &rad, &px, &py, &pz, &vx, &vy, &vz, &fx, &fy, &fz);
-        if (n_parsed == 9) {
-            fx = fy = fz = 0;
-        } else if (n_parsed != 12) {
-            continue;
-        }
-        int i = a.n_atoms;
-        a.atom_ids[i] = id;
-        a.masses[i]   = mass;
-        a.radii[i]    = rad;
-        a.pos_0[i*3+0] = px; a.pos_0[i*3+1] = py; a.pos_0[i*3+2] = pz;
-        a.vel_0[i*3+0] = vx; a.vel_0[i*3+1] = vy; a.vel_0[i*3+2] = vz;
-        a.fixed[i*3+0] = fx; a.fixed[i*3+1] = fy; a.fixed[i*3+2] = fz;
-        a.n_atoms++;
-    }
-    fclose(f);
-
-    if (a.n_atoms <= 0) die("coord.txt 原子数无效");
-    return a;
-}
-
-/* 读取 connection.txt */
-static BondData read_bonds(const char *input_dir, const AtomData *atoms) {
-    char path[512];
-    BondData b;
-    b.n_bonds = 0;
-    b.pairs = NULL;
-    b.stiffness = NULL;
-    b.rest_lengths = NULL;
-
-    snprintf(path, sizeof(path), "%s/connection.txt", input_dir);
-    FILE *f = fopen(path, "r");
-    if (!f) return b;
-
-    char line[256];
-    if (!fgets(line, sizeof(line), f)) { fclose(f); return b; }
-
-    int n_lines = 0, tmp_a, tmp_b;
-    char bond_name[256];
-    while (fscanf(f, "%d %d %s", &tmp_a, &tmp_b, bond_name) == 3) n_lines++;
-    rewind(f);
-
-    if (n_lines == 0) { fclose(f); return b; }
-
-    b.n_bonds = n_lines;
-    b.pairs = (int*)xmalloc(n_lines * 2 * sizeof(int));
-    b.stiffness = (double*)xmalloc(n_lines * sizeof(double));
-    b.rest_lengths = (double*)xmalloc(n_lines * sizeof(double));
-
-    char bond_path[512];
-    snprintf(bond_path, sizeof(bond_path), "%s/bond.txt", input_dir);
-    FILE *fb = fopen(bond_path, "r");
-
-    for (int i = 0; i < n_lines; i++) {
-        fscanf(f, "%d %d %s", &tmp_a, &tmp_b, bond_name);
-        b.pairs[i*2+0] = tmp_a - 1;
-        b.pairs[i*2+1] = tmp_b - 1;
-        b.stiffness[i] = 1.0;
-        b.rest_lengths[i] = 2.0;
-        if (fb) {
-            char name[256], header[256];
-            double k, r0;
-            rewind(fb);
-            fgets(header, sizeof(header), fb);  // 跳过表头行
-            while (fscanf(fb, "%s %lf %lf", name, &k, &r0) == 3) {
-                if (strcmp(name, bond_name) == 0) {
-                    b.stiffness[i] = k;
-                    b.rest_lengths[i] = r0;
-                    break;
-                }
-            }
-        }
-    }
-    fclose(f);
-    if (fb) fclose(fb);
-    return b;
-}
-
-/* ========================================================================
- * 物理核心（与 Python compute.py 对应）
- * ======================================================================== */
-
-/* 加速度计算（各力独立开关控制） */
-static void compute_acceleration(
-    int n, const double *x, const double *y, const double *z,
-    const double *vx, const double *vy, const double *vz,
-    const double *m, const double G[3], const double B[3],
-    const BondData *bonds,
-    double *ax, double *ay, double *az)
-{
-    /* 先清零 */
-    for (int i = 0; i < n; i++) {
-        ax[i] = 0.0; ay[i] = 0.0; az[i] = 0.0;
-    }
-
-    /* 均匀重力场 */
-    if (g_gravity_field) {
-        for (int i = 0; i < n; i++) {
-            ax[i] += G[0];
-            ay[i] += G[1];
-            az[i] += G[2];
-        }
-    }
-
-    /* 阻尼 */
-    if (g_damping_force) {
-        for (int i = 0; i < n; i++) {
-            ax[i] -= B[0] * vx[i] / m[i];
-            ay[i] -= B[1] * vy[i] / m[i];
-            az[i] -= B[2] * vz[i] / m[i];
-        }
-    }
-
-    /* 弹簧键力 */
-    if (g_elastic_force) {
-        for (int b = 0; b < bonds->n_bonds; b++) {
-            int i = bonds->pairs[b*2+0];
-            int j = bonds->pairs[b*2+1];
-            double dx = x[j] - x[i];
-            double dy = y[j] - y[i];
-            double dz = z[j] - z[i];
-            double dist = sqrt(dx*dx + dy*dy + dz*dz);
-            if (dist < 1e-12) continue;
-            double stretch = dist - bonds->rest_lengths[b];
-            double fmag = bonds->stiffness[b] * stretch;
-            double ux = dx / dist, uy = dy / dist, uz = dz / dist;
-            double fx = fmag * ux, fy = fmag * uy, fz = fmag * uz;
-            ax[i] += fx / m[i];  ay[i] += fy / m[i];  az[i] += fz / m[i];
-            ax[j] -= fx / m[j];  ay[j] -= fy / m[j];  az[j] -= fz / m[j];
-        }
-    }
-
-    /* 万有引力（所有原子对之间） */
-    if (g_gravity_interaction) {
-        for (int i = 0; i < n; i++) {
-            for (int j = i + 1; j < n; j++) {
-                double dx = x[j] - x[i];
-                double dy = y[j] - y[i];
-                double dz = z[j] - z[i];
-                double r2 = dx*dx + dy*dy + dz*dz;
-                if (r2 <= 1e-12) continue;
-                double r = sqrt(r2);
-                double f_mag = g_gravity_strength * m[i] * m[j] / r2;
-                double fx_g = f_mag * dx / r;
-                double fy_g = f_mag * dy / r;
-                double fz_g = f_mag * dz / r;
-                ax[i] += fx_g / m[i]; ay[i] += fy_g / m[i]; az[i] += fz_g / m[i];
-                ax[j] -= fx_g / m[j]; ay[j] -= fy_g / m[j]; az[j] -= fz_g / m[j];
-            }
-        }
-    }
-}
-
-/* 边界条件：clamp 位置 + 速度反转 ——与 Python Limit_in_box 一致 */
-static void limit_in_box(double *pos, double *vel, double lo, double hi) {
-    if (*pos > hi)  { *pos = hi;  *vel = -*vel; }
-    if (*pos < lo)  { *pos = lo;  *vel = -*vel; }
-}
-
-/* ── 显式欧拉法 ──────────── */
-static void explicit_euler_step(
-    int n, double *x, double *y, double *z,
-    double *vx, double *vy, double *vz,
-    const double *m, const double G[3], const double B[3],
-    const BondData *bonds, const int *fixed, double dt)
-{
-    double *ax = (double*)alloca(n * sizeof(double));
-    double *ay = (double*)alloca(n * sizeof(double));
-    double *az = (double*)alloca(n * sizeof(double));
-    compute_acceleration(n, x, y, z, vx, vy, vz, m, G, B, bonds, ax, ay, az);
-
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) continue;
-        x[i]  += vx[i] * dt;
-        y[i]  += vy[i] * dt;
-        z[i]  += vz[i] * dt;
-        vx[i] += ax[i] * dt;
-        vy[i] += ay[i] * dt;
-        vz[i] += az[i] * dt;
-    }
-}
-
-/* ── 隐式欧拉法 ──────────── */
-static void implicit_euler_step(
-    int n, double *x, double *y, double *z,
-    double *vx, double *vy, double *vz,
-    const double *m, const double G[3], const double B[3],
-    const BondData *bonds, const int *fixed, double dt)
-{
-    double *vxn = (double*)alloca(n * sizeof(double));
-    double *vyn = (double*)alloca(n * sizeof(double));
-    double *vzn = (double*)alloca(n * sizeof(double));
-
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) {
-            vxn[i] = 0; vyn[i] = 0; vzn[i] = 0; continue;
-        }
-        double gx = B[0] / m[i], gy = B[1] / m[i], gz = B[2] / m[i];
-        vxn[i] = (vx[i] + G[0] * dt) / (1.0 + gx * dt);
-        vyn[i] = (vy[i] + G[1] * dt) / (1.0 + gy * dt);
-        vzn[i] = (vz[i] + G[2] * dt) / (1.0 + gz * dt);
-    }
-
-    double *ax = (double*)alloca(n * sizeof(double));
-    double *ay = (double*)alloca(n * sizeof(double));
-    double *az = (double*)alloca(n * sizeof(double));
-    compute_acceleration(n, x, y, z, vxn, vyn, vzn, m, G, B, bonds, ax, ay, az);
-
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) continue;
-        vx[i] += ax[i] * dt;
-        vy[i] += ay[i] * dt;
-        vz[i] += az[i] * dt;
-        x[i]  += vx[i] * dt;
-        y[i]  += vy[i] * dt;
-        z[i]  += vz[i] * dt;
-    }
-}
-
-/* ── 中点法 ──────────── */
-static void midpoint_step(
-    int n, double *x, double *y, double *z,
-    double *vx, double *vy, double *vz,
-    const double *m, const double G[3], const double B[3],
-    const BondData *bonds, const int *fixed, double dt)
-{
-    double *ax = (double*)alloca(n * sizeof(double));
-    double *ay = (double*)alloca(n * sizeof(double));
-    double *az = (double*)alloca(n * sizeof(double));
-    compute_acceleration(n, x, y, z, vx, vy, vz, m, G, B, bonds, ax, ay, az);
-
-    double *xm = (double*)alloca(n * sizeof(double));
-    double *ym = (double*)alloca(n * sizeof(double));
-    double *zm = (double*)alloca(n * sizeof(double));
-    double *vxm = (double*)alloca(n * sizeof(double));
-    double *vym = (double*)alloca(n * sizeof(double));
-    double *vzm = (double*)alloca(n * sizeof(double));
-
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) {
-            xm[i]=ym[i]=zm[i]=vxm[i]=vym[i]=vzm[i]=0; continue;
-        }
-        xm[i]  = x[i] + 0.5 * vx[i] * dt;
-        ym[i]  = y[i] + 0.5 * vy[i] * dt;
-        zm[i]  = z[i] + 0.5 * vz[i] * dt;
-        vxm[i] = vx[i] + 0.5 * ax[i] * dt;
-        vym[i] = vy[i] + 0.5 * ay[i] * dt;
-        vzm[i] = vz[i] + 0.5 * az[i] * dt;
-        x[i]   = x[i] + vxm[i] * dt;
-        y[i]   = y[i] + vym[i] * dt;
-        z[i]   = z[i] + vzm[i] * dt;
-    }
-
-    compute_acceleration(n, xm, ym, zm, vxm, vym, vzm, m, G, B, bonds, ax, ay, az);
-
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) continue;
-        vx[i] += ax[i] * dt;
-        vy[i] += ay[i] * dt;
-        vz[i] += az[i] * dt;
-    }
-}
-
-/* ── 蛙跳法（Velocity-Verlet）── */
-static void leapfrog_step(
-    int n, double *x, double *y, double *z,
-    double *vx, double *vy, double *vz,
-    const double *m, const double G[3], const double B[3],
-    const BondData *bonds, const int *fixed, double dt)
-{
-    double *ax = (double*)alloca(n * sizeof(double));
-    double *ay = (double*)alloca(n * sizeof(double));
-    double *az = (double*)alloca(n * sizeof(double));
-    compute_acceleration(n, x, y, z, vx, vy, vz, m, G, B, bonds, ax, ay, az);
-
-    /* 半推速度：v_half = v + 0.5*a*dt */
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) continue;
-        vx[i] += ax[i] * dt * 0.5;
-        vy[i] += ay[i] * dt * 0.5;
-        vz[i] += az[i] * dt * 0.5;
-    }
-
-    /* 全推位置（不含边界）*/
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) continue;
-        x[i] += vx[i] * dt;   /* vx 此时是 v_half */
-        y[i] += vy[i] * dt;
-        z[i] += vz[i] * dt;
-    }
-
-    /* 显式预测器：v_pred = v_half + 0.5*a_old*dt，用第一次加速度外推半步
-       包含重力+阻尼+弹簧的所有贡献（标准 Velocity-Verlet 预测步）*/
-    double *pred_vx = (double*)alloca(n * sizeof(double));
-    double *pred_vy = (double*)alloca(n * sizeof(double));
-    double *pred_vz = (double*)alloca(n * sizeof(double));
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) continue;
-        pred_vx[i] = vx[i] + 0.5 * ax[i] * dt;
-        pred_vy[i] = vy[i] + 0.5 * ay[i] * dt;
-        pred_vz[i] = vz[i] + 0.5 * az[i] * dt;
-    }
-
-    /* 用新位置 + 预测速度重算加速度 */
-    compute_acceleration(n, x, y, z, pred_vx, pred_vy, pred_vz, m, G, B, bonds, ax, ay, az);
-
-    /* 速度后半步：v = v_half + 0.5*a_next*dt
-       vx 仍为 v_half（未被覆盖）*/
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) continue;
-        vx[i] += ax[i] * dt * 0.5;
-        vy[i] += ay[i] * dt * 0.5;
-        vz[i] += az[i] * dt * 0.5;
-    }
-}
-
-/* ── 驱动力（与 Python apply_driving_force 一致）──────────────── */
-static void apply_driving_force(
-    int n, double *x, double *y, double *z,
-    double *vx, double *vy, double *vz,
-    double t, int step, double dt,
-    const DriverData *drivers)
-{
-    if (!drivers || drivers->n_drivers == 0) return;
-    for (int d = 0; d < drivers->n_drivers; d++) {
-        int idx = drivers->atom_idx[d];
-        /* 检查周期限制 */
-        if (drivers->has_period[d]) {
-            double max_freq = fmax(fabs(drivers->freq_x[d]),
-                                   fmax(fabs(drivers->freq_y[d]), fabs(drivers->freq_z[d])));
-            int period_steps = 0;
-            if (max_freq > 1e-12) {
-                period_steps = (int)(drivers->period_cycles[d] / max_freq / dt);
-            }
-            if (step > period_steps) {
-                /* 冻结 */
-                if (drivers->freeze_x) {
-                    x[idx] = drivers->freeze_x[d];
-                    y[idx] = drivers->freeze_y[d];
-                    z[idx] = drivers->freeze_z[d];
-                }
-                vx[idx] = vy[idx] = vz[idx] = 0.0;
-                continue;
-            }
-        }
-
-        double px = drivers->amp_x[d] * cos(2*M_PI*drivers->freq_x[d]*t + drivers->phi_x[d]);
-        double py = drivers->amp_y[d] * cos(2*M_PI*drivers->freq_y[d]*t + drivers->phi_y[d]);
-        double pz = drivers->amp_z[d] * cos(2*M_PI*drivers->freq_z[d]*t + drivers->phi_z[d]);
-        double vpx = -drivers->amp_x[d]*2*M_PI*drivers->freq_x[d]*sin(2*M_PI*drivers->freq_x[d]*t + drivers->phi_x[d]);
-        double vpy = -drivers->amp_y[d]*2*M_PI*drivers->freq_y[d]*sin(2*M_PI*drivers->freq_y[d]*t + drivers->phi_y[d]);
-        double vpz = -drivers->amp_z[d]*2*M_PI*drivers->freq_z[d]*sin(2*M_PI*drivers->freq_z[d]*t + drivers->phi_z[d]);
-
-        x[idx] = px; y[idx] = py; z[idx] = pz;
-        vx[idx] = vpx; vy[idx] = vpy; vz[idx] = vpz;
-
-        /* 记录冻结位置（周期结束时） */
-        if (drivers->has_period[d]) {
-            double max_freq = fmax(fabs(drivers->freq_x[d]),
-                                   fmax(fabs(drivers->freq_y[d]), fabs(drivers->freq_z[d])));
-            int period_steps = 0;
-            if (max_freq > 1e-12) {
-                period_steps = (int)(drivers->period_cycles[d] / max_freq / dt);
-            }
-            if (step == period_steps) {
-                drivers->freeze_x[d] = px;
-                drivers->freeze_y[d] = py;
-                drivers->freeze_z[d] = pz;
-            }
-        }
-    }
-}
-
-/* ── 分发器：调用对应积分方法 + 边界条件 + 自由度约束（与 Python 一致）── */
-static void apply_step(
-    const char *method,
-    int n, double *x, double *y, double *z,
-    double *vx, double *vy, double *vz,
-    const double *m, const double G[3], const double B[3],
-    const BondData *bonds, const int *fixed,
-    const double *pos_0,
-    double box_a, double dt)
-{
-    if (strcmp(method, "explicit_euler") == 0) {
-        explicit_euler_step(n, x, y, z, vx, vy, vz, m, G, B, bonds, fixed, dt);
-    } else if (strcmp(method, "implicit_euler") == 0) {
-        implicit_euler_step(n, x, y, z, vx, vy, vz, m, G, B, bonds, fixed, dt);
-    } else if (strcmp(method, "midpoint") == 0) {
-        midpoint_step(n, x, y, z, vx, vy, vz, m, G, B, bonds, fixed, dt);
-    } else if (strcmp(method, "leapfrog") == 0) {
-        leapfrog_step(n, x, y, z, vx, vy, vz, m, G, B, bonds, fixed, dt);
-    } else {
-        fprintf(stderr, "[C-engine] 未知算法: %s\n", method);
-        exit(1);
-    }
-
-    /* 边界条件（与 Python Limit_in_box 一致） */
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) continue;
-        limit_in_box(&x[i],  &vx[i], -box_a, box_a);
-        limit_in_box(&y[i],  &vy[i], -box_a, box_a);
-        limit_in_box(&z[i],  &vz[i], -box_a, box_a);
-    }
-
-    /* 逐自由度固定约束（与 Python apply_fixed_constraints 一致） */
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0]) { x[i] = pos_0[i*3+0]; vx[i] = 0.0; }
-        if (fixed[i*3+1]) { y[i] = pos_0[i*3+1]; vy[i] = 0.0; }
-        if (fixed[i*3+2]) { z[i] = pos_0[i*3+2]; vz[i] = 0.0; }
-    }
-}
-
-// ========================================================================
-// JSON 输出
-// ========================================================================
-
-static void write_trajectory_json(const char *path, const Trajectory *traj,
-                                  const SimParams *params, const AtomData *atoms,
-                                  const BondData *bonds)
-{
-    FILE *f = fopen(path, "w");
-    if (!f) die("无法写入 trajectory.txt");
-
-    fprintf(f, "{\n");
-
-    const char *names[] = {"traj_x","traj_y","traj_z","traj_vx","traj_vy","traj_vz"};
-    double *arrs[] = {traj->x, traj->y, traj->z, traj->vx, traj->vy, traj->vz};
-
-    for (int a = 0; a < 6; a++) {
-        fprintf(f, "  \"%s\": [\n", names[a]);
-        for (int t = 0; t < traj->n_steps; t++) {
-            fprintf(f, "    [");
-            for (int i = 0; i < traj->n_atoms; i++) {
-                fprintf(f, "%.15g", arrs[a][t * traj->n_atoms + i]);
-                if (i < traj->n_atoms - 1) fputc(',', f);
-            }
-            fprintf(f, "]");
-            if (t < traj->n_steps - 1) fputc(',', f);
-            fputc('\n', f);
-        }
-        fprintf(f, "  ]");
-        fputc(',', f);
-        fputc('\n', f);
-    }
-
-    /* 标量参数 */
-    fprintf(f, "  \"NT\": %d,\n", params->NT);
-    fprintf(f, "  \"DT\": %.15g,\n", params->DT);
-    fprintf(f, "  \"NSTEP\": %d,\n", params->NSTEP);
-    fprintf(f, "  \"method\": \"%s\",\n", params->method);
-    fprintf(f, "  \"warmup_steps\": %d,\n", params->warmup_steps);
-    fprintf(f, "  \"G\": [%.15g, %.15g, %.15g],\n", params->G[0], params->G[1], params->G[2]);
-    fprintf(f, "  \"B\": [%.15g, %.15g, %.15g],\n", params->B[0], params->B[1], params->B[2]);
-
-    fprintf(f, "  \"atom_ids\": [");
-    for (int i = 0; i < atoms->n_atoms; i++) {
-        if (i > 0) fputc(',', f);
-        fprintf(f, "%d", atoms->atom_ids[i]);
-    }
-    fprintf(f, "],\n");
-
-    fprintf(f, "  \"atom_masses\": [");
-    for (int i = 0; i < atoms->n_atoms; i++) {
-        if (i > 0) fputc(',', f);
-        fprintf(f, "%.15g", atoms->masses[i]);
-    }
-    fprintf(f, "],\n");
-
-    fprintf(f, "  \"bond_pairs\": [");
-    for (int b = 0; b < bonds->n_bonds; b++) {
-        if (b > 0) fputc(',', f);
-        fprintf(f, "[%d, %d]", bonds->pairs[b*2], bonds->pairs[b*2+1]);
-    }
-    fprintf(f, "],\n");
-
-    fprintf(f, "  \"bond_stiffness\": [");
-    for (int b = 0; b < bonds->n_bonds; b++) {
-        if (b > 0) fputc(',', f);
-        fprintf(f, "%.15g", bonds->stiffness[b]);
-    }
-    fprintf(f, "],\n");
-
-    fprintf(f, "  \"bond_rest_lengths\": [");
-    for (int b = 0; b < bonds->n_bonds; b++) {
-        if (b > 0) fputc(',', f);
-        fprintf(f, "%.15g", bonds->rest_lengths[b]);
-    }
-    fprintf(f, "],\n");
-    fprintf(f, "  \"driving_force\": %d\n", params->driving_force);
-
-    fprintf(f, "}\n");
-    fclose(f);
-}
-
-// ========================================================================
-// 主函数
-// ========================================================================
-
-int main(int argc, char **argv) {
-    if (argc < 4) {
-        fprintf(stderr, "用法: %s <input_dir> <output_dir> <param_json>\n", argv[0]);
-        return 1;
-    }
-    const char *input_dir  = argv[1];
-    const char *output_dir = argv[2];
-    const char *param_path = argv[3];
-
-    clock_t t0 = clock();
-
-    SimParams params = read_params(param_path);
-    AtomData  atoms  = read_coord(input_dir);
-    BondData  bonds  = read_bonds(input_dir, &atoms);
-
-    DriverData drivers;
-    drivers.n_drivers = 0;
-    if (params.driving_force) {
-        drivers = read_driver(input_dir, &atoms);
-    }
-
-    printf("[C-engine] 原子数=%d, 键数=%d, 驱动=%d, NT=%d, DT=%.6g, method=%s\n",
-           atoms.n_atoms, bonds.n_bonds, drivers.n_drivers, params.NT, params.DT, params.method);
-
-    int n = atoms.n_atoms;
-    double *x  = (double*)xmalloc(n * sizeof(double));
-    double *y  = (double*)xmalloc(n * sizeof(double));
-    double *z  = (double*)xmalloc(n * sizeof(double));
-    double *vx = (double*)xmalloc(n * sizeof(double));
-    double *vy = (double*)xmalloc(n * sizeof(double));
-    double *vz = (double*)xmalloc(n * sizeof(double));
-    for (int i = 0; i < n; i++) {
-        x[i]  = atoms.pos_0[i*3+0];
-        y[i]  = atoms.pos_0[i*3+1];
-        z[i]  = atoms.pos_0[i*3+2];
-        vx[i] = atoms.vel_0[i*3+0];
-        vy[i] = atoms.vel_0[i*3+1];
-        vz[i] = atoms.vel_0[i*3+2];
-    }
-
-    /* 分配轨迹缓冲区：改用 record_steps */
-    int record_steps = params.NT - params.warmup_steps;
-    Trajectory traj;
-    traj.n_steps = record_steps;
-    traj.n_atoms = n;
-    traj.x  = (double*)xmalloc(record_steps * n * sizeof(double) * 6);
-    traj.y  = traj.x  + record_steps * n;
-    traj.z  = traj.y  + record_steps * n;
-    traj.vx = traj.z  + record_steps * n;
-    traj.vy = traj.vx + record_steps * n;
-    traj.vz = traj.vy + record_steps * n;
-
-    /* 预热 */
-    for (int s = 0; s < params.warmup_steps; s++) {
-        double tw = (s + 1) * params.DT;
-        if (params.driving_force) apply_driving_force(n, x, y, z, vx, vy, vz, tw, s, params.DT, &drivers);
-        apply_step(params.method, n, x, y, z, vx, vy, vz,
-                   atoms.masses, params.G, params.B, &bonds, atoms.fixed,
-                   atoms.pos_0,
-                   params.box_a, params.DT);
-    }
-
-    /* 记录 */
-    for (int s = 0; s < record_steps; s++) {
-        double t = (s + params.warmup_steps) * params.DT;
-        if (params.driving_force) apply_driving_force(n, x, y, z, vx, vy, vz, t, s, params.DT, &drivers);
-        for (int i = 0; i < n; i++) {
-            traj.x[ s * n + i]  = x[i];
-            traj.y[ s * n + i]  = y[i];
-            traj.z[ s * n + i]  = z[i];
-            traj.vx[s * n + i]  = vx[i];
-            traj.vy[s * n + i]  = vy[i];
-            traj.vz[s * n + i]  = vz[i];
-        }
-        apply_step(params.method, n, x, y, z, vx, vy, vz,
-                   atoms.masses, params.G, params.B, &bonds, atoms.fixed,
-                   atoms.pos_0,
-                   params.box_a, params.DT);
-    }
-
-    char out_path[512];
-    snprintf(out_path, sizeof(out_path), "%s/trajectory.txt", output_dir);
-    write_trajectory_json(out_path, &traj, &params, &atoms, &bonds);
-
-    clock_t t1 = clock();
-    double elapsed = (double)(t1 - t0) / CLOCKS_PER_SEC;
-    printf("[C-engine] 计算完成: %d 步, %.3f s\n", record_steps, elapsed);
-
-    /* 清理 */
-    free(traj.x);
-    free(x); free(y); free(z);
-    free(vx); free(vy); free(vz);
-    free(atoms.atom_ids);
-    free(atoms.masses); free(atoms.radii);
-    free(atoms.pos_0); free(atoms.vel_0);
-    free(atoms.fixed);
-    if (bonds.pairs) { free(bonds.pairs); free(bonds.stiffness); free(bonds.rest_lengths); }
-
-    return 0;
-}

engines/cpp/main.cpp

@@ -1,863 +0,0 @@
-/**
- * engines/cpp/main.cpp
- * --------------------
- * C++ 动力学模拟引擎。
- * 与 Python 版 (compute.py) 算法保持一致。
- *
- * 输入: param.json, <input_dir>/coord.txt, connection.txt, bond.txt
- * 输出: <output_dir>/trajectory.txt (JSON, 与 Python 版兼容)
- *
- * 编译:
- *   g++ -O3 -march=native -std=c++17 -o build/dynamics_cpp main.cpp
- *
- * 用法:
- *   ./build/dynamics_cpp <input_dir> <output_dir> <param_json>
- */
-
-#include <algorithm>
-#include <chrono>
-#include <cmath>
-#include <cstring>
-#include <fstream>
-#include <iomanip>
-#include <iostream>
-#include <sstream>
-#include <string>
-#include <vector>
-
-// ========================================================================
-// 配置参数（从 param.json 读取）
-// ========================================================================
-struct SimParams {
-    double box_a = 10.0;
-    int NT = 10000;
-    double DT = 0.001;
-    int NSTEP = 100;
-    int warmup_steps = 0;
-    std::string method = "leapfrog";
-    double G[3] = {0, 0, -9.8};
-    double B[3] = {0, 0, 0};
-    int gravity_field = 1;
-    int gravity_interaction = 0;
-    int elastic_force = 1;
-    int damping_force = 0;
-    double gravity_strength = 1.0;
-    int driving_force = 0;
-};
-
-// ========================================================================
-// 原子数据
-// ========================================================================
-struct AtomData {
-    std::vector<int> ids;
-    std::vector<double> masses;
-    std::vector<double> radii;
-    std::vector<double> pos_0;   // (n_atoms * 3)
-    std::vector<double> vel_0;   // (n_atoms * 3)
-    std::vector<int> fixed;      // (n_atoms * 3), 0/1 flags
-};
-
-// ========================================================================
-// 成键数据
-// ========================================================================
-struct BondData {
-    std::vector<int> pairs;          // (n_bonds * 2)
-    std::vector<double> stiffness;
-    std::vector<double> rest_lengths;
-};
-
-// ========================================================================
-// 驱动力数据
-// ========================================================================
-struct DriverData {
-    int n_drivers = 0;
-    std::vector<int> atom_idx;       // internal atom indices
-    std::vector<double> amp_x, amp_y, amp_z;
-    std::vector<double> freq_x, freq_y, freq_z;
-    std::vector<double> phi_x, phi_y, phi_z;  // radians
-    std::vector<int> has_period;     // 0=all, 1=limited
-    std::vector<double> period_cycles;
-    std::vector<double> freeze_x, freeze_y, freeze_z;
-};
-
-// ========================================================================
-// 辅助函数
-// ========================================================================
-
-static void die(const std::string &msg) {
-    std::cerr << "[C++-engine] 错误: " << msg << std::endl;
-    exit(1);
-}
-
-/* 读整个文件为字符串 */
-static std::string read_file(const std::string &path) {
-    std::ifstream f(path, std::ios::binary);
-    if (!f) die("无法打开 " + path);
-    std::ostringstream ss;
-    ss << f.rdbuf();
-    return ss.str();
-}
-
-/* 从 JSON 中查找 key，返回冒号后的数值 */
-static double json_read_double(const std::string &json, const std::string &key) {
-    auto pos = json.find("\"" + key + "\"");
-    if (pos == std::string::npos) return 0.0;
-    pos = json.find(':', pos);
-    if (pos == std::string::npos) return 0.0;
-    while (pos < json.size() && (json[pos] == ':' || json[pos] == ' ' || json[pos] == '\t' || json[pos] == '\n')) pos++;
-    return std::stod(json.substr(pos));
-}
-
-static int json_read_int(const std::string &json, const std::string &key) {
-    return static_cast<int>(json_read_double(json, key));
-}
-
-/* 从 JSON 中读取字符串值 */
-static std::string json_read_string(const std::string &json, const std::string &key) {
-    auto pos = json.find("\"" + key + "\"");
-    if (pos == std::string::npos) return "";
-    pos = json.find(':', pos);
-    if (pos == std::string::npos) return "";
-    while (pos < json.size() && (json[pos] == ':' || json[pos] == ' ' || json[pos] == '\t' || json[pos] == '\n')) pos++;
-    if (pos >= json.size()) return "";
-    // 找到引号
-    if (json[pos] != '"') return "";
-    pos++;
-    std::string result;
-    while (pos < json.size() && json[pos] != '"') {
-        result += json[pos];
-        pos++;
-    }
-    return result;
-}
-
-/* 读取 JSON 数组 (如 "G": [0, 0, -9.8]) 到 double[3] */
-static void json_read_double3(const std::string &json, const std::string &key, double out[3]) {
-    auto pos = json.find("\"" + key + "\"");
-    if (pos == std::string::npos) { out[0] = out[1] = out[2] = 0; return; }
-    pos = json.find('[', pos);
-    if (pos == std::string::npos) { out[0] = out[1] = out[2] = 0; return; }
-    pos++;
-    for (int i = 0; i < 3; i++) {
-        while (pos < json.size() && (json[pos] == ' ' || json[pos] == '\t' || json[pos] == '\n' || json[pos] == ',')) pos++;
-        char *end;
-        out[i] = std::strtod(json.c_str() + pos, &end);
-        pos = end - json.c_str();
-    }
-}
-
-/* 解析 param.json */
-static SimParams read_params(const std::string &path) {
-    std::string buf = read_file(path);
-    SimParams p;
-    p.box_a        = json_read_double(buf, "box_a");
-    p.NT           = json_read_int(buf, "NT");
-    p.DT           = json_read_double(buf, "DT");
-    p.NSTEP        = json_read_int(buf, "NSTEP");
-    p.warmup_steps = json_read_int(buf, "warmup_steps");
-    std::string m  = json_read_string(buf, "method");
-    if (!m.empty()) p.method = m;
-    json_read_double3(buf, "G", p.G);
-    json_read_double3(buf, "B", p.B);
-    p.gravity_field       = json_read_int(buf, "gravity_field");
-    p.gravity_interaction = json_read_int(buf, "gravity_interaction");
-    p.elastic_force       = json_read_int(buf, "elastic_force");
-    p.damping_force       = json_read_int(buf, "damping_force");
-    p.gravity_strength    = json_read_double(buf, "gravity_strength");
-    p.driving_force       = json_read_int(buf, "driving_force");
-    return p;
-}
-
-/* 读取 coord.txt */
-static AtomData read_coord(const std::string &input_dir) {
-    std::string path = input_dir + "/coord.txt";
-    std::ifstream f(path);
-    if (!f) die("无法打开 " + path);
-
-    std::string header;
-    std::getline(f, header);  // 跳过表头
-
-    AtomData a;
-    int id, fx, fy, fz;
-    double mass, rad, px, py, pz, vx, vy, vz;
-    std::string line;
-
-    while (std::getline(f, line)) {
-        if (line.empty() || line[0] == '#') continue;
-        int n_parsed = std::sscanf(line.c_str(), "%d %lf %lf %lf %lf %lf %lf %lf %lf %d %d %d",
-                                    &id, &mass, &rad, &px, &py, &pz, &vx, &vy, &vz, &fx, &fy, &fz);
-        if (n_parsed == 9) {
-            fx = fy = fz = 0;
-        } else if (n_parsed != 12) {
-            continue;
-        }
-        a.ids.push_back(id);
-        a.masses.push_back(mass);
-        a.radii.push_back(rad);
-        a.pos_0.push_back(px); a.pos_0.push_back(py); a.pos_0.push_back(pz);
-        a.vel_0.push_back(vx); a.vel_0.push_back(vy); a.vel_0.push_back(vz);
-        a.fixed.push_back(fx); a.fixed.push_back(fy); a.fixed.push_back(fz);
-    }
-
-    if (a.ids.empty()) die("coord.txt 中没有原子数据");
-    return a;
-}
-
-/* 读取 connection.txt 和 bond.txt */
-static BondData read_bonds(const std::string &input_dir) {
-    BondData b;
-    std::string conn_path = input_dir + "/connection.txt";
-    std::ifstream f(conn_path);
-    if (!f) return b;  // 无成键
-
-    std::string header;
-    std::getline(f, header);  // 跳过表头
-
-    // 先读取 bond.txt 获得键参数映射
-    std::string bond_path = input_dir + "/bond.txt";
-    std::ifstream fb(bond_path);
-
-    int a1, a2;
-    std::string bond_name;
-    std::vector<std::tuple<int, int, std::string>> conn_lines;
-    while (f >> a1 >> a2 >> bond_name) {
-        conn_lines.emplace_back(a1 - 1, a2 - 1, bond_name);
-    }
-
-    for (auto &[i, j, name] : conn_lines) {
-        double k = 1.0, r0 = 2.0;
-        if (fb) {
-            fb.clear();
-            fb.seekg(0);
-            std::string bn, header;
-            double bk, br;
-            std::getline(fb, header);  // 跳过表头行
-            while (fb >> bn >> bk >> br) {
-                if (bn == name) {
-                    k = bk;
-                    r0 = br;
-                    break;
-                }
-            }
-        }
-        b.pairs.push_back(i);
-        b.pairs.push_back(j);
-        b.stiffness.push_back(k);
-        b.rest_lengths.push_back(r0);
-    }
-
-    return b;
-}
-
-/* 读取 driver.txt */
-static DriverData read_driver(const std::string &input_dir, const AtomData &atoms) {
-    DriverData d;
-    std::string path = input_dir + "/driver.txt";
-    std::ifstream f(path);
-    if (!f) { std::cerr << "[C++-engine] 警告: 无法打开 " << path << std::endl; return d; }
-
-    std::string header;
-    std::getline(f, header);  // skip header
-
-    int n;
-    double ax, ay, az, fx, fy, fz, px, py, pz;
-    std::string period_str;
-
-    while (f >> n >> ax >> ay >> az >> fx >> fy >> fz >> px >> py >> pz >> period_str) {
-        // Find atom index by id
-        int idx = -1;
-        for (size_t i = 0; i < atoms.ids.size(); i++) {
-            if (atoms.ids[i] == n) { idx = i; break; }
-        }
-        if (idx < 0) {
-            std::cerr << "[C++-engine] 警告: driver.txt 原子 " << n << " 不在 coord.txt 中" << std::endl;
-            continue;
-        }
-        d.atom_idx.push_back(idx);
-        d.amp_x.push_back(ax); d.amp_y.push_back(ay); d.amp_z.push_back(az);
-        d.freq_x.push_back(fx); d.freq_y.push_back(fy); d.freq_z.push_back(fz);
-        // Convert degrees to radians
-        const double DEG2RAD = M_PI / 180.0;
-        d.phi_x.push_back(px * DEG2RAD);
-        d.phi_y.push_back(py * DEG2RAD);
-        d.phi_z.push_back(pz * DEG2RAD);
-
-        if (period_str == "all") {
-            d.has_period.push_back(0);
-            d.period_cycles.push_back(-1.0);
-        } else {
-            d.has_period.push_back(1);
-            d.period_cycles.push_back(std::stod(period_str));
-        }
-        d.freeze_x.push_back(0.0);
-        d.freeze_y.push_back(0.0);
-        d.freeze_z.push_back(0.0);
-        d.n_drivers++;
-    }
-
-    if (d.n_drivers > 0)
-        std::cout << "[C++-engine] 已加载驱动力: " << d.n_drivers << " 条定义" << std::endl;
-    return d;
-}
-
-// ========================================================================
-// 物理核心
-// ========================================================================
-
-/* 加速度计算（各力独立开关控制）——与 Python compute_acceleration 一致 */
-static void compute_acceleration(
-    int n,
-    const double *x, const double *y, const double *z,
-    const double *vx, const double *vy, const double *vz,
-    const double *m, const double G[3], const double B[3],
-    const BondData &bonds,
-    int gravity_field, int gravity_interaction,
-    int elastic_force, int damping_force,
-    double gravity_strength,
-    double *ax, double *ay, double *az)
-{
-    // 清零
-    std::fill(ax, ax + n, 0.0);
-    std::fill(ay, ay + n, 0.0);
-    std::fill(az, az + n, 0.0);
-
-    // 均匀重力场
-    if (gravity_field) {
-        for (int i = 0; i < n; i++) {
-            ax[i] += G[0];
-            ay[i] += G[1];
-            az[i] += G[2];
-        }
-    }
-
-    // 阻尼
-    if (damping_force) {
-        for (int i = 0; i < n; i++) {
-            ax[i] -= B[0] * vx[i] / m[i];
-            ay[i] -= B[1] * vy[i] / m[i];
-            az[i] -= B[2] * vz[i] / m[i];
-        }
-    }
-
-    // 弹簧力
-    if (elastic_force) {
-        int nb = static_cast<int>(bonds.stiffness.size());
-        for (int b = 0; b < nb; b++) {
-            int i = bonds.pairs[b * 2];
-            int j = bonds.pairs[b * 2 + 1];
-            double dx = x[j] - x[i];
-            double dy = y[j] - y[i];
-            double dz = z[j] - z[i];
-            double dist = std::sqrt(dx * dx + dy * dy + dz * dz);
-            if (dist < 1e-12) continue;
-            double stretch = dist - bonds.rest_lengths[b];
-            double fmag = bonds.stiffness[b] * stretch;
-            double ux = dx / dist, uy = dy / dist, uz = dz / dist;
-            double fx = fmag * ux, fy = fmag * uy, fz = fmag * uz;
-            ax[i] += fx / m[i];  ay[i] += fy / m[i];  az[i] += fz / m[i];
-            ax[j] -= fx / m[j];  ay[j] -= fy / m[j];  az[j] -= fz / m[j];
-        }
-    }
-
-    // 万有引力（所有原子对之间）
-    if (gravity_interaction) {
-        for (int i = 0; i < n; i++) {
-            for (int j = i + 1; j < n; j++) {
-                double dx = x[j] - x[i];
-                double dy = y[j] - y[i];
-                double dz = z[j] - z[i];
-                double r2 = dx * dx + dy * dy + dz * dz;
-                if (r2 <= 1e-12) continue;
-                double r = std::sqrt(r2);
-                double f_mag = gravity_strength * m[i] * m[j] / r2;
-                double fx_g = f_mag * dx / r;
-                double fy_g = f_mag * dy / r;
-                double fz_g = f_mag * dz / r;
-                ax[i] += fx_g / m[i]; ay[i] += fy_g / m[i]; az[i] += fz_g / m[i];
-                ax[j] -= fx_g / m[j]; ay[j] -= fy_g / m[j]; az[j] -= fz_g / m[j];
-            }
-        }
-    }
-}
-
-/* 边界条件：clamp 位置 + 速度反转 ——与 Python Limit_in_box 一致 */
-static void limit_in_box(double &pos, double &vel, double lo, double hi) {
-    if (pos > hi)  { pos = hi;  vel = -vel; }
-    if (pos < lo)  { pos = lo;  vel = -vel; }
-}
-
-// ========================================================================
-// 四种积分方法（只做位置/速度更新，不含边界条件）
-// 与 Python: Explicit_Euler_Method / Implicit_Euler_Method /
-//            Midpoint_Method / Leapfrog_Method 保持一致
-// ========================================================================
-
-/* ── 显式欧拉法 ──────────── */
-static void explicit_euler_step(
-    int n, double *x, double *y, double *z,
-    double *vx, double *vy, double *vz,
-    const double *m, const double G[3], const double B[3],
-    const BondData &bonds, const int *fixed, double dt,
-    int gravity_field, int gravity_interaction,
-    int elastic_force, int damping_force,
-    double gravity_strength)
-{
-    std::vector<double> ax(n), ay(n), az(n);
-    compute_acceleration(n, x, y, z, vx, vy, vz, m, G, B, bonds,
-                         gravity_field, gravity_interaction,
-                         elastic_force, damping_force, gravity_strength,
-                         ax.data(), ay.data(), az.data());
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) continue;
-        x[i]  += vx[i] * dt;
-        y[i]  += vy[i] * dt;
-        z[i]  += vz[i] * dt;
-        vx[i] += ax[i] * dt;
-        vy[i] += ay[i] * dt;
-        vz[i] += az[i] * dt;
-    }
-}
-
-/* ── 隐式欧拉法 ──────────── */
-static void implicit_euler_step(
-    int n, double *x, double *y, double *z,
-    double *vx, double *vy, double *vz,
-    const double *m, const double G[3], const double B[3],
-    const BondData &bonds, const int *fixed, double dt,
-    int gravity_field, int gravity_interaction,
-    int elastic_force, int damping_force,
-    double gravity_strength)
-{
-    std::vector<double> ax(n), ay(n), az(n);
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) {
-            ax[i] = ay[i] = az[i] = 0;
-            continue;
-        }
-        double gamma_x = B[0] / m[i];
-        double gamma_y = B[1] / m[i];
-        double gamma_z = B[2] / m[i];
-        // 隐式更新速度（重力 + 阻尼）
-        double vxn = (vx[i] + G[0] * dt) / (1.0 + gamma_x * dt);
-        double vyn = (vy[i] + G[1] * dt) / (1.0 + gamma_y * dt);
-        double vzn = (vz[i] + G[2] * dt) / (1.0 + gamma_z * dt);
-        // 用隐式速度 + 当前位置算加速度（包含各力开关）
-        // 注意：Python 中 compute_acceleration(x, y, z, vx_next, ...) 用新速度+旧位置
-        double tpx = x[i], tpy = y[i], tpz = z[i];
-        compute_acceleration(1, &tpx, &tpy, &tpz, &vxn, &vyn, &vzn,
-                             &m[i], G, B, bonds,
-                             gravity_field, gravity_interaction,
-                             elastic_force, damping_force, gravity_strength,
-                             &ax[i], &ay[i], &az[i]);
-        vx[i] += ax[i] * dt;
-        vy[i] += ay[i] * dt;
-        vz[i] += az[i] * dt;
-        x[i]  += vx[i] * dt;
-        y[i]  += vy[i] * dt;
-        z[i]  += vz[i] * dt;
-    }
-}
-
-/* ── 中点法 ──────────── */
-static void midpoint_step(
-    int n, double *x, double *y, double *z,
-    double *vx, double *vy, double *vz,
-    const double *m, const double G[3], const double B[3],
-    const BondData &bonds, const int *fixed, double dt,
-    int gravity_field, int gravity_interaction,
-    int elastic_force, int damping_force,
-    double gravity_strength)
-{
-    std::vector<double> ax(n), ay(n), az(n);
-    compute_acceleration(n, x, y, z, vx, vy, vz, m, G, B, bonds,
-                         gravity_field, gravity_interaction,
-                         elastic_force, damping_force, gravity_strength,
-                         ax.data(), ay.data(), az.data());
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) continue;
-        double x_mid = x[i] + 0.5 * vx[i] * dt;
-        double y_mid = y[i] + 0.5 * vy[i] * dt;
-        double z_mid = z[i] + 0.5 * vz[i] * dt;
-        double vx_mid = vx[i] + 0.5 * ax[i] * dt;
-        double vy_mid = vy[i] + 0.5 * ay[i] * dt;
-        double vz_mid = vz[i] + 0.5 * az[i] * dt;
-        x[i] += vx_mid * dt;
-        y[i] += vy_mid * dt;
-        z[i] += vz_mid * dt;
-        double ax_mid, ay_mid, az_mid;
-        compute_acceleration(1, &x_mid, &y_mid, &z_mid, &vx_mid, &vy_mid, &vz_mid,
-                             &m[i], G, B, bonds,
-                             gravity_field, gravity_interaction,
-                             elastic_force, damping_force, gravity_strength,
-                             &ax_mid, &ay_mid, &az_mid);
-        vx[i] += ax_mid * dt;
-        vy[i] += ay_mid * dt;
-        vz[i] += az_mid * dt;
-    }
-}
-
-/* ── 蛙跳法（Velocity-Verlet）——与 Python Leapfrog_Method 一致 ── */
-static void leapfrog_full_step(
-    int n, double *x, double *y, double *z,
-    double *vx, double *vy, double *vz,
-    const double *m, const double G[3], const double B[3],
-    const BondData &bonds, const int *fixed, double dt,
-    int gravity_field, int gravity_interaction,
-    int elastic_force, int damping_force,
-    double gravity_strength)
-{
-    // 第一次加速度
-    std::vector<double> ax(n), ay(n), az(n);
-    compute_acceleration(n, x, y, z, vx, vy, vz, m, G, B, bonds,
-                         gravity_field, gravity_interaction,
-                         elastic_force, damping_force, gravity_strength,
-                         ax.data(), ay.data(), az.data());
-
-    // 半推速度：v_half = v + 0.5*a*dt  (存入 vx, vy, vz)
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) continue;
-        vx[i] += ax[i] * dt * 0.5;
-        vy[i] += ay[i] * dt * 0.5;
-        vz[i] += az[i] * dt * 0.5;
-    }
-
-    // 全推位置（不含边界，边界在外层统一处理）
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) continue;
-        x[i] += vx[i] * dt;   // vx 此时是 v_half
-        y[i] += vy[i] * dt;
-        z[i] += vz[i] * dt;
-    }
-
-    // 显式预测器：v_pred = v_half + 0.5*a_old*dt，用第一次加速度外推半步
-    // 包含所有力的贡献（标准 Velocity-Verlet 预测步）
-    std::vector<double> pred_vx(n), pred_vy(n), pred_vz(n);
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) continue;
-        pred_vx[i] = vx[i] + 0.5 * ax[i] * dt;
-        pred_vy[i] = vy[i] + 0.5 * ay[i] * dt;
-        pred_vz[i] = vz[i] + 0.5 * az[i] * dt;
-    }
-
-    // 用新位置 + 预测速度重算加速度
-    compute_acceleration(n, x, y, z, pred_vx.data(), pred_vy.data(), pred_vz.data(),
-                         m, G, B, bonds,
-                         gravity_field, gravity_interaction,
-                         elastic_force, damping_force, gravity_strength,
-                         ax.data(), ay.data(), az.data());
-
-    // 速度后半步：v = v_half + 0.5*a_next*dt
-    // vx 仍为 v_half（未被覆盖），直接加上 0.5*a_next*dt
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) continue;
-        vx[i] += ax[i] * dt * 0.5;
-        vy[i] += ay[i] * dt * 0.5;
-        vz[i] += az[i] * dt * 0.5;
-    }
-}
-
-/* ── 分发器：调用对应积分方法 + 边界条件（与 Python apply_motion_update 一致）── */
-static void apply_step(
-    const std::string &method,
-    int n, double *x, double *y, double *z,
-    double *vx, double *vy, double *vz,
-    const double *m, const double G[3], const double B[3],
-    const BondData &bonds, const int *fixed,
-    const double *pos_0,
-    double box_a, double dt,
-    int gravity_field, int gravity_interaction,
-    int elastic_force, int damping_force,
-    double gravity_strength)
-{
-    // 积分
-    if (method == "explicit_euler") {
-        explicit_euler_step(n, x, y, z, vx, vy, vz, m, G, B, bonds, fixed, dt,
-                            gravity_field, gravity_interaction,
-                            elastic_force, damping_force, gravity_strength);
-    } else if (method == "implicit_euler") {
-        implicit_euler_step(n, x, y, z, vx, vy, vz, m, G, B, bonds, fixed, dt,
-                            gravity_field, gravity_interaction,
-                            elastic_force, damping_force, gravity_strength);
-    } else if (method == "midpoint") {
-        midpoint_step(n, x, y, z, vx, vy, vz, m, G, B, bonds, fixed, dt,
-                      gravity_field, gravity_interaction,
-                      elastic_force, damping_force, gravity_strength);
-    } else if (method == "leapfrog") {
-        leapfrog_full_step(n, x, y, z, vx, vy, vz, m, G, B, bonds, fixed, dt,
-                           gravity_field, gravity_interaction,
-                           elastic_force, damping_force, gravity_strength);
-    } else {
-        die("未知算法: " + method);
-    }
-
-    // 边界条件（与 Python Limit_in_box 一致）
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0] && fixed[i*3+1] && fixed[i*3+2]) continue;
-        limit_in_box(x[i],  vx[i], -box_a, box_a);
-        limit_in_box(y[i],  vy[i], -box_a, box_a);
-        limit_in_box(z[i],  vz[i], -box_a, box_a);
-    }
-
-    // 逐自由度固定约束（与 Python apply_fixed_constraints 一致）
-    for (int i = 0; i < n; i++) {
-        if (fixed[i*3+0]) { x[i] = pos_0[i*3];   vx[i] = 0.0; }
-        if (fixed[i*3+1]) { y[i] = pos_0[i*3+1]; vy[i] = 0.0; }
-        if (fixed[i*3+2]) { z[i] = pos_0[i*3+2]; vz[i] = 0.0; }
-    }
-}
-
-// ========================================================================
-// 驱动力应用
-// ========================================================================
-
-static void apply_driving_force(
-    int n, double *x, double *y, double *z,
-    double *vx, double *vy, double *vz,
-    double t, int step, double dt,
-    DriverData &drivers)
-{
-    if (drivers.n_drivers == 0) return;
-    for (int d = 0; d < drivers.n_drivers; d++) {
-        int idx = drivers.atom_idx[d];
-
-        // Check period limits
-        if (drivers.has_period[d]) {
-            double max_freq = std::max({std::fabs(drivers.freq_x[d]),
-                                        std::fabs(drivers.freq_y[d]),
-                                        std::fabs(drivers.freq_z[d])});
-            int period_steps = 0;
-            if (max_freq > 1e-12) {
-                period_steps = static_cast<int>(drivers.period_cycles[d] / max_freq / dt);
-            }
-            if (step > period_steps) {
-                // Frozen: keep last position, zero velocity
-                x[idx] = drivers.freeze_x[d];
-                y[idx] = drivers.freeze_y[d];
-                z[idx] = drivers.freeze_z[d];
-                vx[idx] = vy[idx] = vz[idx] = 0.0;
-                continue;
-            }
-        }
-
-        const double TWO_PI = 2.0 * M_PI;
-        double px = drivers.amp_x[d] * std::cos(TWO_PI * drivers.freq_x[d] * t + drivers.phi_x[d]);
-        double py = drivers.amp_y[d] * std::cos(TWO_PI * drivers.freq_y[d] * t + drivers.phi_y[d]);
-        double pz = drivers.amp_z[d] * std::cos(TWO_PI * drivers.freq_z[d] * t + drivers.phi_z[d]);
-        double vpx = -drivers.amp_x[d] * TWO_PI * drivers.freq_x[d] * std::sin(TWO_PI * drivers.freq_x[d] * t + drivers.phi_x[d]);
-        double vpy = -drivers.amp_y[d] * TWO_PI * drivers.freq_y[d] * std::sin(TWO_PI * drivers.freq_y[d] * t + drivers.phi_y[d]);
-        double vpz = -drivers.amp_z[d] * TWO_PI * drivers.freq_z[d] * std::sin(TWO_PI * drivers.freq_z[d] * t + drivers.phi_z[d]);
-
-        x[idx] = px; y[idx] = py; z[idx] = pz;
-        vx[idx] = vpx; vy[idx] = vpy; vz[idx] = vpz;
-
-        // Record freeze position at the last driving step
-        if (drivers.has_period[d]) {
-            double max_freq = std::max({std::fabs(drivers.freq_x[d]),
-                                        std::fabs(drivers.freq_y[d]),
-                                        std::fabs(drivers.freq_z[d])});
-            int period_steps = 0;
-            if (max_freq > 1e-12) {
-                period_steps = static_cast<int>(drivers.period_cycles[d] / max_freq / dt);
-            }
-            if (step == period_steps) {
-                drivers.freeze_x[d] = px;
-                drivers.freeze_y[d] = py;
-                drivers.freeze_z[d] = pz;
-            }
-        }
-    }
-}
-
-// ========================================================================
-// JSON 输出
-// ========================================================================
-
-static void write_trajectory_json(
-    const std::string &path,
-    const std::vector<double> &x, const std::vector<double> &y,
-    const std::vector<double> &z, const std::vector<double> &vx,
-    const std::vector<double> &vy, const std::vector<double> &vz,
-    int n_steps, int n_atoms,
-    const SimParams &params, const AtomData &atoms, const BondData &bonds)
-{
-    std::ofstream f(path);
-    if (!f) die("无法写入 " + path);
-    f << std::setprecision(15);
-
-    f << "{\n";
-
-    // 轨迹数组
-    const std::string names[] = {"traj_x","traj_y","traj_z","traj_vx","traj_vy","traj_vz"};
-    const std::vector<double> *arrs[] = {&x, &y, &z, &vx, &vy, &vz};
-
-    for (int a = 0; a < 6; a++) {
-        f << "  \"" << names[a] << "\": [\n";
-        const auto &data = *arrs[a];
-        for (int t = 0; t < n_steps; t++) {
-            f << "    [";
-            for (int i = 0; i < n_atoms; i++) {
-                f << data[t * n_atoms + i];
-                if (i < n_atoms - 1) f << ',';
-            }
-            f << ']';
-            if (t < n_steps - 1) f << ',';
-            f << '\n';
-        }
-        f << "  ],\n";
-    }
-
-    // 标量参数
-    f << "  \"NT\": " << params.NT << ",\n";
-    f << "  \"DT\": " << params.DT << ",\n";
-    f << "  \"NSTEP\": " << params.NSTEP << ",\n";
-    f << "  \"method\": \"" << params.method << "\",\n";
-    f << "  \"warmup_steps\": " << params.warmup_steps << ",\n";
-    f << "  \"G\": [" << params.G[0] << ", " << params.G[1] << ", " << params.G[2] << "],\n";
-    f << "  \"B\": [" << params.B[0] << ", " << params.B[1] << ", " << params.B[2] << "],\n";
-
-    // 原子信息
-    f << "  \"atom_ids\": [";
-    for (size_t i = 0; i < atoms.ids.size(); i++) {
-        if (i > 0) f << ',';
-        f << atoms.ids[i];
-    }
-    f << "],\n";
-
-    f << "  \"atom_masses\": [";
-    for (size_t i = 0; i < atoms.masses.size(); i++) {
-        if (i > 0) f << ',';
-        f << atoms.masses[i];
-    }
-    f << "],\n";
-
-    // 成键
-    f << "  \"bond_pairs\": [";
-    for (size_t b = 0; b < bonds.stiffness.size(); b++) {
-        if (b > 0) f << ',';
-        f << "[" << bonds.pairs[b * 2] << ", " << bonds.pairs[b * 2 + 1] << "]";
-    }
-    f << "],\n";
-
-    f << "  \"bond_stiffness\": [";
-    for (size_t b = 0; b < bonds.stiffness.size(); b++) {
-        if (b > 0) f << ',';
-        f << bonds.stiffness[b];
-    }
-    f << "],\n";
-
-    f << "  \"bond_rest_lengths\": [";
-    for (size_t b = 0; b < bonds.rest_lengths.size(); b++) {
-        if (b > 0) f << ',';
-        f << bonds.rest_lengths[b];
-    }
-    f << "],\n";
-
-    f << "  \"driving_force\": " << params.driving_force << "\n";
-
-    f << "}\n";
-}
-
-// ========================================================================
-// 主函数
-// ========================================================================
-
-int main(int argc, char **argv) {
-    if (argc < 4) {
-        std::cerr << "用法: " << argv[0] << " <input_dir> <output_dir> <param_json>" << std::endl;
-        return 1;
-    }
-
-    std::string input_dir  = argv[1];
-    std::string output_dir = argv[2];
-    std::string param_path = argv[3];
-
-    auto t0 = std::chrono::high_resolution_clock::now();
-
-    // 读取参数和输入
-    SimParams params = read_params(param_path);
-    AtomData  atoms  = read_coord(input_dir);
-    BondData  bonds  = read_bonds(input_dir);
-
-    DriverData drivers;
-    if (params.driving_force) {
-        drivers = read_driver(input_dir, atoms);
-    }
-
-    std::cout << "[C++-engine] 原子数=" << atoms.ids.size()
-              << ", 键数=" << bonds.stiffness.size()
-              << ", NT=" << params.NT << ", DT=" << params.DT
-              << ", method=" << params.method << std::endl;
-
-    int n = static_cast<int>(atoms.ids.size());
-
-    // 初始化位置/速度
-    std::vector<double> x(n), y(n), z(n), vx(n), vy(n), vz(n);
-    for (int i = 0; i < n; i++) {
-        x[i]  = atoms.pos_0[i * 3];
-        y[i]  = atoms.pos_0[i * 3 + 1];
-        z[i]  = atoms.pos_0[i * 3 + 2];
-        vx[i] = atoms.vel_0[i * 3];
-        vy[i] = atoms.vel_0[i * 3 + 1];
-        vz[i] = atoms.vel_0[i * 3 + 2];
-    }
-
-    // 分配轨迹缓冲区
-    int record_steps = params.NT - params.warmup_steps;
-    std::vector<double> traj_x(record_steps * n);
-    std::vector<double> traj_y(record_steps * n);
-    std::vector<double> traj_z(record_steps * n);
-    std::vector<double> traj_vx(record_steps * n);
-    std::vector<double> traj_vy(record_steps * n);
-    std::vector<double> traj_vz(record_steps * n);
-
-    // 预热
-    for (int s = 0; s < params.warmup_steps; s++) {
-        double tw = (s + 1) * params.DT;
-        if (params.driving_force)
-            apply_driving_force(n, x.data(), y.data(), z.data(), vx.data(), vy.data(), vz.data(), tw, s, params.DT, drivers);
-        apply_step(params.method, n, x.data(), y.data(), z.data(),
-                   vx.data(), vy.data(), vz.data(),
-                   atoms.masses.data(), params.G, params.B,
-                   bonds, atoms.fixed.data(),
-                   atoms.pos_0.data(),
-                   params.box_a, params.DT,
-                   params.gravity_field, params.gravity_interaction,
-                   params.elastic_force, params.damping_force, params.gravity_strength);
-    }
-
-    // 记录
-    for (int s = 0; s < record_steps; s++) {
-        double t = (s + params.warmup_steps) * params.DT;
-        if (params.driving_force)
-            apply_driving_force(n, x.data(), y.data(), z.data(), vx.data(), vy.data(), vz.data(), t, s, params.DT, drivers);
-        // 保存当前帧
-        for (int i = 0; i < n; i++) {
-            traj_x[s * n + i]  = x[i];
-            traj_y[s * n + i]  = y[i];
-            traj_z[s * n + i]  = z[i];
-            traj_vx[s * n + i] = vx[i];
-            traj_vy[s * n + i] = vy[i];
-            traj_vz[s * n + i] = vz[i];
-        }
-
-        apply_step(params.method, n, x.data(), y.data(), z.data(),
-                   vx.data(), vy.data(), vz.data(),
-                   atoms.masses.data(), params.G, params.B,
-                   bonds, atoms.fixed.data(),
-                   atoms.pos_0.data(),
-                   params.box_a, params.DT,
-                   params.gravity_field, params.gravity_interaction,
-                   params.elastic_force, params.damping_force, params.gravity_strength);
-    }
-
-    // 输出轨迹
-    std::string out_path = output_dir + "/trajectory.txt";
-    write_trajectory_json(out_path, traj_x, traj_y, traj_z, traj_vx, traj_vy, traj_vz,
-                          record_steps, n, params, atoms, bonds);
-
-    auto t1 = std::chrono::high_resolution_clock::now();
-    double elapsed = std::chrono::duration<double>(t1 - t0).count();
-    std::cout << "[C++-engine] 计算完成: " << record_steps << " 步, " << elapsed << " s" << std::endl;
-
-    return 0;
-}

engines/engine_dll.py

@@ -0,0 +1,426 @@
+"""
+engines/engine_dll.py
+---------------------
+Python ctypes 包装器：加载 C/C++/Fortran 动态链接库并调用 run_dynamics()。
+
+用法（由 compute.py 内部调用，不直接运行）：
+
+    from engines.engine_dll import load_dll, run_dynamics_dll
+
+    dll = load_dll("c")          # 自动查找 engines/c/build/dynamics_c.dll/.so/.dylib
+    arrays = run_dynamics_dll(dll, config, atom_data, bond_data, driver_data)
+    # arrays: dict with keys x, y, z, vx, vy, vz  shape=(n_frames, n_atoms)
+
+DLL 编译（C 版本）：
+  Windows:  gcc -O3 -shared -o engines/release/dynamics_c.dll engines/src/c/dynamics_lib.c -lm
+  Linux:    gcc -O3 -shared -fPIC -o engines/release/dynamics_c.so  engines/src/c/dynamics_lib.c -lm
+  macOS:    gcc -O3 -dynamiclib -o engines/release/dynamics_c.dylib engines/src/c/dynamics_lib.c -lm
+或用 make dll 一键编译：
+  cd engines/src/c && make dll
+"""
+
+import ctypes
+import os
+import platform
+import numpy as np
+
+# ── DLL 文件名后缀 ─────────────────────────────────────────────
+_SUFFIX = {
+    "windows": ".dll",
+    "linux":   ".so",
+    "darwin":  ".dylib",
+}
+
+# ── method 字符串 → 整数 ID ────────────────────────────────────
+_METHOD_ID = {
+    "explicit_euler": 0,
+    "euler":          0,
+    "implicit_euler": 1,
+    "midpoint":       2,
+    "leapfrog":       3,
+}
+
+_HERE = os.path.dirname(os.path.abspath(__file__))
+
+
+_DLL_NAME = {
+    "c":       "dynamics_c",
+    "cpp":     "dynamics_cpp",
+    "c++":     "dynamics_cpp",
+    "fortran": "dynamics_f90",
+    "f90":     "dynamics_f90",
+    # "python" 引擎通过直接 import 调用，不使用 DLL
+}
+
+# 引擎名规范化：将别名统一为目录名
+_ENGINE_DIR = {
+    "c":       "c",
+    "cpp":     "cpp",
+    "c++":     "cpp",
+    "fortran": "fortran",
+    "f90":     "fortran",
+    "python":  "python",
+}
+
+
+def _dll_candidates(engine: str) -> list[str]:
+    """返回 DLL 候选路径列表（按优先级）。"""
+    sys = platform.system().lower()
+    ext = _SUFFIX.get(sys, ".so")
+    eng_dir = _ENGINE_DIR.get(engine, engine)
+    name    = _DLL_NAME.get(engine, f"dynamics_{engine}")
+    base = os.path.join(_HERE, "release", name)
+    return [
+        base + ext,
+        base + ".dll",
+        base + ".so",
+        base + ".dylib",
+    ]
+
+
+def load_dll(engine: str = "c"):
+    """加载指定引擎。
+
+    - C/C++/Fortran: 返回 ctypes.CDLL 对象
+    - Python: 返回模块对象（直接 import，无需编译）
+
+    Args:
+        engine: "c", "cpp", "fortran", 或 "python"
+    Raises:
+        FileNotFoundError: DLL/模块文件不存在
+    """
+    if _ENGINE_DIR.get(engine, engine) == "python":
+        import importlib.util, sys as _sys
+        mod_path = os.path.join(_HERE, "python", "dynamics_lib.py")
+        if not os.path.exists(mod_path):
+            raise FileNotFoundError(f"Python 引擎未找到: {mod_path}")
+        spec = importlib.util.spec_from_file_location(
+            "engines.python.dynamics_lib", mod_path)
+        mod = importlib.util.module_from_spec(spec)
+        spec.loader.exec_module(mod)
+        return mod  # 返回模块，不是 CDLL
+
+    for p in _dll_candidates(engine):
+        if os.path.exists(p):
+            lib = ctypes.CDLL(p)
+            _setup_prototype(lib)
+            return lib
+    raise FileNotFoundError(
+        f"DLL 未找到（引擎 {engine}），候选路径：\n" +
+        "\n".join(f"  {p}" for p in _dll_candidates(engine)) +
+        f"\n请先编译：cd engines/{engine} && make dll"
+    )
+
+
+def _setup_prototype(lib: ctypes.CDLL) -> None:
+    """配置 run_dynamics 的参数类型和返回类型。"""
+    c_dbl_p = ctypes.POINTER(ctypes.c_double)
+    c_int_p = ctypes.POINTER(ctypes.c_int)
+    cb_type  = ctypes.CFUNCTYPE(None, ctypes.c_int, ctypes.c_int)
+
+    lib.run_dynamics.restype = ctypes.c_int
+    lib.run_dynamics.argtypes = [
+        ctypes.c_int,    # n_atoms
+        c_dbl_p,         # pos_init    [n_atoms*3]
+        c_dbl_p,         # vel_init    [n_atoms*3]
+        c_dbl_p,         # masses      [n_atoms]
+        c_int_p,         # fixed       [n_atoms*3]
+        ctypes.c_int,    # n_bonds
+        c_int_p,         # bond_pairs  [n_bonds*2]
+        c_dbl_p,         # bond_k      [n_bonds]
+        c_dbl_p,         # bond_r0     [n_bonds]
+        ctypes.c_double, # box_a
+        ctypes.c_double, # dt
+        ctypes.c_int,    # NT
+        ctypes.c_int,    # NSTEP
+        ctypes.c_int,    # warmup_steps
+        ctypes.c_int,    # method_id
+        ctypes.c_double, # Gx
+        ctypes.c_double, # Gy
+        ctypes.c_double, # Gz
+        ctypes.c_double, # Bx
+        ctypes.c_double, # By
+        ctypes.c_double, # Bz
+        ctypes.c_int,    # gravity_field
+        ctypes.c_int,    # elastic_force
+        ctypes.c_int,    # damping_force
+        ctypes.c_double, # gravity_strength
+        ctypes.c_int,    # n_drivers
+        c_int_p,         # drv_idx     [n_drivers]
+        c_dbl_p,         # drv_amp     [n_drivers*3]
+        c_dbl_p,         # drv_freq    [n_drivers*3]
+        c_dbl_p,         # drv_phi     [n_drivers*3]
+        c_dbl_p,         # drv_eq      [n_drivers*3]
+        c_dbl_p,         # drv_ncycles [n_drivers]
+        c_int_p,         # drv_has_period [n_drivers]
+        ctypes.c_int,    # n_frames
+        c_dbl_p,         # out_x
+        c_dbl_p,         # out_y
+        c_dbl_p,         # out_z
+        c_dbl_p,         # out_vx
+        c_dbl_p,         # out_vy
+        c_dbl_p,         # out_vz
+        cb_type,         # progress_cb (可为 NULL)
+    ]
+
+
+def _c_dbl(arr: np.ndarray):
+    """返回 float64 C 连续数组的 ctypes 指针。"""
+    a = np.ascontiguousarray(arr, dtype=np.float64)
+    return a.ctypes.data_as(ctypes.POINTER(ctypes.c_double)), a
+
+
+def _c_int(arr: np.ndarray):
+    """返回 int32 C 连续数组的 ctypes 指针。"""
+    a = np.ascontiguousarray(arr, dtype=np.int32)
+    return a.ctypes.data_as(ctypes.POINTER(ctypes.c_int)), a
+
+
+def _is_python_module(lib) -> bool:
+    """判断 lib 是否为 Python 引擎模块（而非 ctypes.CDLL）。"""
+    return not isinstance(lib, ctypes.CDLL)
+
+
+def _run_dynamics_python(lib, config, atom_positions, atom_velocities, atom_masses,
+                          atom_fixed, bond_pairs, bond_stiffness, bond_rest_lengths,
+                          driver_data, atom_ids, progress_cb=None) -> dict:
+    """调用 Python 引擎的 run_dynamics()，参数/返回值格式与 ctypes 版相同。"""
+    n = len(atom_masses)
+    NT          = int(config["NT"])
+    NSTEP       = int(config.get("NSTEP", 1))
+    warmup      = int(config.get("warmup_steps", 0))
+    dt          = float(config["DT"])
+    box_a       = float(config.get("box_a", 300.0))
+    method_str  = str(config.get("method", "leapfrog")).lower().replace(" ", "_")
+    method_id   = _METHOD_ID.get(method_str, 3)
+
+    G = config.get("G", [0.0, 0.0, 0.0])
+    B = config.get("B", [0.0, 0.0, 0.0])
+    if hasattr(G, "tolist"): G = G.tolist()
+    if hasattr(B, "tolist"): B = B.tolist()
+
+    gravity_field    = int(config.get("gravity_field", 0))
+    elastic_force    = int(config.get("elastic_force", 1))
+    damping_force    = int(config.get("damping_force", 0))
+    gravity_strength = float(config.get("gravity_strength", 1.0))
+
+    record_steps = NT - warmup
+    n_frames = max(1, record_steps // NSTEP)
+
+    nd = len(driver_data) if driver_data else 0
+    if nd > 0:
+        drv_idx  = np.array([d["local_idx"] for d in driver_data], dtype=np.int64)
+        drv_amp  = np.array([d["amp"]       for d in driver_data], dtype=np.float64)
+        drv_freq = np.array([d["freq"]      for d in driver_data], dtype=np.float64)
+        drv_phi  = np.array([d["phi"]       for d in driver_data], dtype=np.float64)
+        drv_eq   = np.array([d["eq_pos"]    for d in driver_data], dtype=np.float64)
+        drv_nc   = np.array([d["n_cycles"]  for d in driver_data], dtype=np.float64)
+        drv_hp   = np.array([d["has_period"]for d in driver_data], dtype=np.int32)
+    else:
+        drv_idx = drv_amp = drv_freq = drv_phi = drv_eq = drv_nc = drv_hp = \
+            np.zeros(0, dtype=np.int64)
+
+    out_x, out_y, out_z, out_vx, out_vy, out_vz = lib.run_dynamics(
+        n_atoms=n,
+        pos_init=atom_positions,
+        vel_init=atom_velocities,
+        masses=atom_masses,
+        fixed=atom_fixed,
+        n_bonds=len(bond_pairs),
+        bond_pairs=bond_pairs,
+        bond_k=bond_stiffness,
+        bond_r0=bond_rest_lengths,
+        box_a=box_a,
+        dt=dt,
+        NT=NT,
+        NSTEP=NSTEP,
+        warmup_steps=warmup,
+        method_id=method_id,
+        Gx=float(G[0]), Gy=float(G[1]), Gz=float(G[2]),
+        Bx=float(B[0]), By=float(B[1]), Bz=float(B[2]),
+        gravity_field=gravity_field,
+        elastic_force=elastic_force,
+        damping_force=damping_force,
+        gravity_strength=gravity_strength,
+        n_drivers=nd,
+        drv_idx=drv_idx,
+        drv_amp=drv_amp,
+        drv_freq=drv_freq,
+        drv_phi=drv_phi,
+        drv_eq=drv_eq,
+        drv_ncycles=drv_nc,
+        drv_has_period=drv_hp,
+        n_frames=n_frames,
+        progress_cb=progress_cb,
+    )
+
+    shape = (n_frames, n)
+    t_arr = np.arange(n_frames) * NSTEP * dt + warmup * dt
+    return {
+        "x":  out_x.reshape(shape), "y":  out_y.reshape(shape),
+        "z":  out_z.reshape(shape), "vx": out_vx.reshape(shape),
+        "vy": out_vy.reshape(shape), "vz": out_vz.reshape(shape),
+        "t":  t_arr,
+    }
+
+
+def run_dynamics_dll(
+    lib,
+    config: dict,
+    atom_positions: np.ndarray,   # (n_atoms, 3)
+    atom_velocities: np.ndarray,  # (n_atoms, 3)
+    atom_masses: np.ndarray,      # (n_atoms,)
+    atom_fixed: np.ndarray,       # (n_atoms, 3) int, 1=固定
+    bond_pairs: np.ndarray,       # (n_bonds, 2) int 0-based 局部索引
+    bond_stiffness: np.ndarray,   # (n_bonds,)
+    bond_rest_lengths: np.ndarray,# (n_bonds,)
+    driver_data: list,            # 驱动原子列表（见下文）
+    atom_ids: np.ndarray,         # (n_atoms,) 全局 atom id（用于驱动原子查找）
+    progress_cb=None,
+) -> dict:
+    """调用 DLL 的 run_dynamics()，返回抽帧后的轨迹数组。
+
+    driver_data 格式（每个元素对应一个驱动原子）：
+        {
+          "atom_id":    int,          # 全局 atom id
+          "local_idx":  int,          # 在 atom_ids 数组中的位置（0-based）
+          "amp":        [ax, ay, az],
+          "freq":       [fx, fy, fz],
+          "phi":        [px, py, pz],
+          "eq_pos":     [ex, ey, ez],
+          "n_cycles":   float,        # 0=不限
+          "has_period": int,          # 0/1
+        }
+
+    返回：
+        {
+          "x":  np.ndarray (n_frames, n_atoms),
+          "y":  ...,
+          "z":  ...,
+          "vx": ..., "vy": ..., "vz": ...,
+          "t":  np.ndarray (n_frames,),   # 时间轴
+        }
+    """
+    # Python 引擎：直接调用模块函数，不走 ctypes
+    if _is_python_module(lib):
+        return _run_dynamics_python(
+            lib, config, atom_positions, atom_velocities, atom_masses,
+            atom_fixed, bond_pairs, bond_stiffness, bond_rest_lengths,
+            driver_data, atom_ids, progress_cb)
+
+    n = len(atom_masses)
+    NT          = int(config["NT"])
+    NSTEP       = int(config.get("NSTEP", 1))
+    warmup      = int(config.get("warmup_steps", 0))
+    dt          = float(config["DT"])
+    box_a       = float(config.get("box_a", 300.0))
+    method_str  = str(config.get("method", "leapfrog")).lower().replace(" ", "_")
+    method_id   = _METHOD_ID.get(method_str, 3)
+
+    G = config.get("G", [0.0, 0.0, 0.0])
+    B = config.get("B", [0.0, 0.0, 0.0])
+    if hasattr(G, "tolist"): G = G.tolist()
+    if hasattr(B, "tolist"): B = B.tolist()
+
+    gravity_field    = int(config.get("gravity_field", 0))
+    elastic_force    = int(config.get("elastic_force", 1))
+    damping_force    = int(config.get("damping_force", 0))
+    gravity_strength = float(config.get("gravity_strength", 1.0))
+
+    # ── 计算帧数 ──────────────────────────────────────────────
+    record_steps = NT - warmup
+    n_frames = max(1, record_steps // NSTEP)
+
+    # ── 驱动原子数据 ──────────────────────────────────────────
+    nd = len(driver_data) if driver_data else 0
+    if nd > 0:
+        drv_idx_arr  = np.array([d["local_idx"]  for d in driver_data], dtype=np.int32)
+        drv_amp_arr  = np.array([d["amp"]         for d in driver_data], dtype=np.float64).ravel()
+        drv_freq_arr = np.array([d["freq"]        for d in driver_data], dtype=np.float64).ravel()
+        drv_phi_arr  = np.array([d["phi"]         for d in driver_data], dtype=np.float64).ravel()
+        drv_eq_arr   = np.array([d["eq_pos"]      for d in driver_data], dtype=np.float64).ravel()
+        drv_nc_arr   = np.array([d["n_cycles"]    for d in driver_data], dtype=np.float64)
+        drv_hp_arr   = np.array([d["has_period"]  for d in driver_data], dtype=np.int32)
+    else:
+        drv_idx_arr  = np.zeros(1, dtype=np.int32)
+        drv_amp_arr  = np.zeros(3, dtype=np.float64)
+        drv_freq_arr = np.zeros(3, dtype=np.float64)
+        drv_phi_arr  = np.zeros(3, dtype=np.float64)
+        drv_eq_arr   = np.zeros(3, dtype=np.float64)
+        drv_nc_arr   = np.zeros(1, dtype=np.float64)
+        drv_hp_arr   = np.zeros(1, dtype=np.int32)
+
+    # ── 输出缓冲区 ────────────────────────────────────────────
+    out_x  = np.zeros(n_frames * n, dtype=np.float64)
+    out_y  = np.zeros(n_frames * n, dtype=np.float64)
+    out_z  = np.zeros(n_frames * n, dtype=np.float64)
+    out_vx = np.zeros(n_frames * n, dtype=np.float64)
+    out_vy = np.zeros(n_frames * n, dtype=np.float64)
+    out_vz = np.zeros(n_frames * n, dtype=np.float64)
+
+    # ── ctypes 指针（保留 arr 引用防止 GC） ──────────────────
+    p_pos,   _pos   = _c_dbl(atom_positions.ravel())
+    p_vel,   _vel   = _c_dbl(atom_velocities.ravel())
+    p_mass,  _mass  = _c_dbl(atom_masses)
+    p_fixed, _fixed = _c_int(atom_fixed.ravel())
+    p_bp,    _bp    = _c_int(bond_pairs.ravel() if len(bond_pairs) else np.zeros(2, dtype=np.int32))
+    p_bk,    _bk    = _c_dbl(bond_stiffness if len(bond_stiffness) else np.zeros(1))
+    p_br0,   _br0   = _c_dbl(bond_rest_lengths if len(bond_rest_lengths) else np.zeros(1))
+    p_didx,  _didx  = _c_int(drv_idx_arr)
+    p_damp,  _damp  = _c_dbl(drv_amp_arr)
+    p_dfrq,  _dfrq  = _c_dbl(drv_freq_arr)
+    p_dphi,  _dphi  = _c_dbl(drv_phi_arr)
+    p_deq,   _deq   = _c_dbl(drv_eq_arr)
+    p_dnc,   _dnc   = _c_dbl(drv_nc_arr)
+    p_dhp,   _dhp   = _c_int(drv_hp_arr)
+
+    p_ox  = out_x.ctypes.data_as(ctypes.POINTER(ctypes.c_double))
+    p_oy  = out_y.ctypes.data_as(ctypes.POINTER(ctypes.c_double))
+    p_oz  = out_z.ctypes.data_as(ctypes.POINTER(ctypes.c_double))
+    p_ovx = out_vx.ctypes.data_as(ctypes.POINTER(ctypes.c_double))
+    p_ovy = out_vy.ctypes.data_as(ctypes.POINTER(ctypes.c_double))
+    p_ovz = out_vz.ctypes.data_as(ctypes.POINTER(ctypes.c_double))
+
+    # 进度回调
+    cb_type = ctypes.CFUNCTYPE(None, ctypes.c_int, ctypes.c_int)
+    if progress_cb is not None:
+        cb = cb_type(progress_cb)
+    else:
+        cb = ctypes.cast(None, cb_type)
+
+    ret = lib.run_dynamics(
+        n,
+        p_pos, p_vel, p_mass, p_fixed,
+        len(bond_pairs), p_bp, p_bk, p_br0,
+        box_a, dt, NT, NSTEP, warmup, method_id,
+        float(G[0]), float(G[1]), float(G[2]),
+        float(B[0]), float(B[1]), float(B[2]),
+        gravity_field, elastic_force, damping_force, gravity_strength,
+        nd, p_didx, p_damp, p_dfrq, p_dphi, p_deq, p_dnc, p_dhp,
+        n_frames,
+        p_ox, p_oy, p_oz, p_ovx, p_ovy, p_ovz,
+        cb,
+    )
+
+    if ret != 0:
+        raise RuntimeError(f"run_dynamics() returned error code {ret}")
+
+    shape = (n_frames, n)
+    t_arr = np.arange(n_frames) * NSTEP * dt + warmup * dt
+
+    return {
+        "x":  out_x.reshape(shape),
+        "y":  out_y.reshape(shape),
+        "z":  out_z.reshape(shape),
+        "vx": out_vx.reshape(shape),
+        "vy": out_vy.reshape(shape),
+        "vz": out_vz.reshape(shape),
+        "t":  t_arr,
+    }
+
+
+def is_dll_available(engine: str = "c") -> bool:
+    """检查指定引擎是否可用（DLL 已编译或 Python 模块存在）。"""
+    if _ENGINE_DIR.get(engine, engine) == "python":
+        return os.path.exists(os.path.join(_HERE, "python", "dynamics_lib.py"))
+    return any(os.path.exists(p) for p in _dll_candidates(engine))

engines/python/dynamics_lib.py

@@ -0,0 +1,404 @@
+"""
+engines/python/dynamics_lib.py
+-------------------------------
+纯 NumPy 计算引擎：无文件 I/O，所有数据以 NumPy 数组传入，
+结果作为 NumPy 数组返回。
+
+接口与 C/C++/Fortran DLL 的 run_dynamics() 完全一致，
+算法与 compute.py 的 run_simulation() 保持一致。
+
+用法（由 engine_dll.py 内部调用）：
+    from engines.python.dynamics_lib import run_dynamics
+    out_x, out_y, out_z, out_vx, out_vy, out_vz = run_dynamics(...)
+"""
+
+import numpy as np
+
+TWO_PI = 2.0 * np.pi
+
+# ── method_id 映射 ──────────────────────────────────────────
+# 0=euler  1=implicit_euler  2=midpoint  3=leapfrog
+
+
+# ── 保守加速度（弹簧键 + 均匀重力场，不含阻尼）──────────────
+def _accel_conservative(x, y, z, m, Gx, Gy, Gz,
+                         gravity_field, elastic_force,
+                         bond_pairs, bond_k, bond_r0):
+    ax = np.full_like(x, Gx) if gravity_field else np.zeros_like(x)
+    ay = np.full_like(y, Gy) if gravity_field else np.zeros_like(y)
+    az = np.full_like(z, Gz) if gravity_field else np.zeros_like(z)
+
+    if elastic_force and len(bond_pairs) > 0:
+        i1 = bond_pairs[:, 0]
+        i2 = bond_pairs[:, 1]
+        dx = x[i2] - x[i1]
+        dy = y[i2] - y[i1]
+        dz = z[i2] - z[i1]
+        dist = np.sqrt(dx*dx + dy*dy + dz*dz)
+        valid = dist > 1e-12
+        fac = np.where(valid, bond_k * (dist - bond_r0) / dist, 0.0)
+        fx = fac * dx
+        fy = fac * dy
+        fz_b = fac * dz
+        np.add.at(ax, i1, fx / m[i1]);   np.add.at(ax, i2, -fx / m[i2])
+        np.add.at(ay, i1, fy / m[i1]);   np.add.at(ay, i2, -fy / m[i2])
+        np.add.at(az, i1, fz_b / m[i1]); np.add.at(az, i2, -fz_b / m[i2])
+
+    return ax, ay, az
+
+
+# ── 完整加速度（含阻尼）──────────────────────────────────────
+def _accel_full(x, y, z, vx, vy, vz, m, Gx, Gy, Gz, Bx, By, Bz,
+                gravity_field, elastic_force, damping_force,
+                bond_pairs, bond_k, bond_r0):
+    ax, ay, az = _accel_conservative(x, y, z, m, Gx, Gy, Gz,
+                                      gravity_field, elastic_force,
+                                      bond_pairs, bond_k, bond_r0)
+    if damping_force:
+        ax -= Bx * vx / m
+        ay -= By * vy / m
+        az -= Bz * vz / m
+    return ax, ay, az
+
+
+# ── 蛙跳法（半隐式阻尼，与 compute.py leapfrog_staggered_step 一致）─
+def _leapfrog_step(x, y, z, vx, vy, vz, fixed, m,
+                    Gx, Gy, Gz, Bx, By, Bz,
+                    gravity_field, elastic_force, damping_force,
+                    bond_pairs, bond_k, bond_r0, dt):
+    ax, ay, az = _accel_conservative(x, y, z, m, Gx, Gy, Gz,
+                                      gravity_field, elastic_force,
+                                      bond_pairs, bond_k, bond_r0)
+    has_damp = damping_force and (Bx != 0.0 or By != 0.0 or Bz != 0.0)
+    if has_damp:
+        alpha_x = Bx * dt / (2.0 * m)
+        alpha_y = By * dt / (2.0 * m)
+        alpha_z = Bz * dt / (2.0 * m)
+        vx_new = (vx * (1.0 - alpha_x) + ax * dt) / (1.0 + alpha_x)
+        vy_new = (vy * (1.0 - alpha_y) + ay * dt) / (1.0 + alpha_y)
+        vz_new = (vz * (1.0 - alpha_z) + az * dt) / (1.0 + alpha_z)
+    else:
+        vx_new = vx + ax * dt
+        vy_new = vy + ay * dt
+        vz_new = vz + az * dt
+    # 全固定原子保持不变
+    all_fixed = np.all(fixed, axis=1)
+    vx_new = np.where(all_fixed, vx, vx_new)
+    vy_new = np.where(all_fixed, vy, vy_new)
+    vz_new = np.where(all_fixed, vz, vz_new)
+    x_new = x + vx_new * dt
+    y_new = y + vy_new * dt
+    z_new = z + vz_new * dt
+    return x_new, y_new, z_new, vx_new, vy_new, vz_new
+
+
+# ── 显式欧拉法 ───────────────────────────────────────────────
+def _euler_step(x, y, z, vx, vy, vz, fixed, m,
+                 Gx, Gy, Gz, Bx, By, Bz,
+                 gravity_field, elastic_force, damping_force,
+                 bond_pairs, bond_k, bond_r0, dt):
+    ax, ay, az = _accel_full(x, y, z, vx, vy, vz, m, Gx, Gy, Gz, Bx, By, Bz,
+                              gravity_field, elastic_force, damping_force,
+                              bond_pairs, bond_k, bond_r0)
+    all_fixed = np.all(fixed, axis=1)
+    mask = ~all_fixed
+    x_new  = np.where(mask, x  + vx * dt, x)
+    y_new  = np.where(mask, y  + vy * dt, y)
+    z_new  = np.where(mask, z  + vz * dt, z)
+    vx_new = np.where(mask, vx + ax * dt, vx)
+    vy_new = np.where(mask, vy + ay * dt, vy)
+    vz_new = np.where(mask, vz + az * dt, vz)
+    return x_new, y_new, z_new, vx_new, vy_new, vz_new
+
+
+# ── 隐式欧拉法（与 compute.py Implicit_Euler_Method 一致）──────
+def _implicit_euler_step(x, y, z, vx, vy, vz, fixed, m,
+                          Gx, Gy, Gz, Bx, By, Bz,
+                          gravity_field, elastic_force, damping_force,
+                          bond_pairs, bond_k, bond_r0, dt):
+    gamma_x = Bx / m
+    gamma_y = By / m
+    gamma_z = Bz / m
+    vx_next = (vx + Gx * dt) / (1.0 + gamma_x * dt)
+    vy_next = (vy + Gy * dt) / (1.0 + gamma_y * dt)
+    vz_next = (vz + Gz * dt) / (1.0 + gamma_z * dt)
+    ax, ay, az = _accel_full(x, y, z, vx_next, vy_next, vz_next, m,
+                              Gx, Gy, Gz, Bx, By, Bz,
+                              gravity_field, elastic_force, damping_force,
+                              bond_pairs, bond_k, bond_r0)
+    all_fixed = np.all(fixed, axis=1)
+    mask = ~all_fixed
+    vx_new = np.where(mask, vx + ax * dt, vx)
+    vy_new = np.where(mask, vy + ay * dt, vy)
+    vz_new = np.where(mask, vz + az * dt, vz)
+    x_new  = np.where(mask, x  + vx_new * dt, x)
+    y_new  = np.where(mask, y  + vy_new * dt, y)
+    z_new  = np.where(mask, z  + vz_new * dt, z)
+    return x_new, y_new, z_new, vx_new, vy_new, vz_new
+
+
+# ── 中点法（与 compute.py Midpoint_Method 一致）────────────────
+def _midpoint_step(x, y, z, vx, vy, vz, fixed, m,
+                    Gx, Gy, Gz, Bx, By, Bz,
+                    gravity_field, elastic_force, damping_force,
+                    bond_pairs, bond_k, bond_r0, dt):
+    ax, ay, az = _accel_full(x, y, z, vx, vy, vz, m, Gx, Gy, Gz, Bx, By, Bz,
+                              gravity_field, elastic_force, damping_force,
+                              bond_pairs, bond_k, bond_r0)
+    all_fixed = np.all(fixed, axis=1)
+    mask = ~all_fixed
+    xm  = np.where(mask, x  + 0.5*vx*dt, x)
+    ym  = np.where(mask, y  + 0.5*vy*dt, y)
+    zm  = np.where(mask, z  + 0.5*vz*dt, z)
+    vxm = np.where(mask, vx + 0.5*ax*dt, 0.0)
+    vym = np.where(mask, vy + 0.5*ay*dt, 0.0)
+    vzm = np.where(mask, vz + 0.5*az*dt, 0.0)
+    x_new = np.where(mask, x + vxm * dt, x)
+    y_new = np.where(mask, y + vym * dt, y)
+    z_new = np.where(mask, z + vzm * dt, z)
+    axm, aym, azm = _accel_full(xm, ym, zm, vxm, vym, vzm, m, Gx, Gy, Gz, Bx, By, Bz,
+                                 gravity_field, elastic_force, damping_force,
+                                 bond_pairs, bond_k, bond_r0)
+    vx_new = np.where(mask, vx + axm * dt, vx)
+    vy_new = np.where(mask, vy + aym * dt, vy)
+    vz_new = np.where(mask, vz + azm * dt, vz)
+    return x_new, y_new, z_new, vx_new, vy_new, vz_new
+
+
+# ── 边界：反弹 + 回绕 + 逐自由度固定约束 ───────────────────────
+def _apply_bc(x, y, z, vx, vy, vz, fixed, pos_init, box_a):
+    lo, hi = -box_a, box_a
+
+    # 反弹（全固定原子跳过）
+    all_fixed = np.all(fixed, axis=1)
+    do_bc = ~all_fixed
+    over_x  = do_bc & (x > hi); under_x = do_bc & (x < lo)
+    over_y  = do_bc & (y > hi); under_y = do_bc & (y < lo)
+    over_z  = do_bc & (z > hi); under_z = do_bc & (z < lo)
+    x  = np.where(over_x, hi, np.where(under_x, lo, x))
+    y  = np.where(over_y, hi, np.where(under_y, lo, y))
+    z  = np.where(over_z, hi, np.where(under_z, lo, z))
+    vx = np.where(over_x | under_x, -np.abs(vx)*np.sign(np.where(over_x, 1, -1)), vx)
+    vy = np.where(over_y | under_y, -np.abs(vy)*np.sign(np.where(over_y, 1, -1)), vy)
+    vz = np.where(over_z | under_z, -np.abs(vz)*np.sign(np.where(over_z, 1, -1)), vz)
+    # 反弹速度简化：越界则取反绝对值（与 C 版 _limit1 一致）
+    vx = np.where(over_x, -np.abs(vx), np.where(under_x, np.abs(vx), vx))
+    vy = np.where(over_y, -np.abs(vy), np.where(under_y, np.abs(vy), vy))
+    vz = np.where(over_z, -np.abs(vz), np.where(under_z, np.abs(vz), vz))
+
+    # 回绕
+    x = np.where(x > hi, lo, np.where(x < lo, hi, x))
+    y = np.where(y > hi, lo, np.where(y < lo, hi, y))
+    z = np.where(z > hi, lo, np.where(z < lo, hi, z))
+
+    # 逐自由度固定约束
+    fx = fixed[:, 0].astype(bool)
+    fy = fixed[:, 1].astype(bool)
+    fz = fixed[:, 2].astype(bool)
+    x  = np.where(fx, pos_init[:, 0], x);  vx = np.where(fx, 0.0, vx)
+    y  = np.where(fy, pos_init[:, 1], y);  vy = np.where(fy, 0.0, vy)
+    z  = np.where(fz, pos_init[:, 2], z);  vz = np.where(fz, 0.0, vz)
+    return x, y, z, vx, vy, vz
+
+
+# ── 驱动力（与 compute.py apply_driving_force 逻辑一致）─────────
+def _apply_driving(x, y, z, vx, vy, vz, t, step, dt,
+                    drv_idx, drv_amp, drv_freq, drv_phi, drv_eq,
+                    drv_ncycles, drv_has_period, freeze):
+    """freeze: (n_drivers, 3) mutable array for frozen positions."""
+    nd = len(drv_idx)
+    for d in range(nd):
+        idx = drv_idx[d]
+        fx_ = drv_freq[d, 0]; fy_ = drv_freq[d, 1]; fz_ = drv_freq[d, 2]
+
+        if drv_has_period[d]:
+            mf = max(abs(fx_), abs(fy_), abs(fz_))
+            ps = int(drv_ncycles[d] / mf / dt) if mf > 1e-12 else 0
+            if step > ps:
+                x[idx] = freeze[d, 0]; y[idx] = freeze[d, 1]; z[idx] = freeze[d, 2]
+                vx[idx] = vy[idx] = vz[idx] = 0.0
+                continue
+            px = drv_eq[d,0] + drv_amp[d,0]*np.cos(TWO_PI*fx_*t + drv_phi[d,0])
+            py = drv_eq[d,1] + drv_amp[d,1]*np.cos(TWO_PI*fy_*t + drv_phi[d,1])
+            pz = drv_eq[d,2] + drv_amp[d,2]*np.cos(TWO_PI*fz_*t + drv_phi[d,2])
+            if step == ps:
+                freeze[d, 0] = px; freeze[d, 1] = py; freeze[d, 2] = pz
+
+        x[idx]  = drv_eq[d,0] + drv_amp[d,0]*np.cos(TWO_PI*fx_*t + drv_phi[d,0])
+        y[idx]  = drv_eq[d,1] + drv_amp[d,1]*np.cos(TWO_PI*fy_*t + drv_phi[d,1])
+        z[idx]  = drv_eq[d,2] + drv_amp[d,2]*np.cos(TWO_PI*fz_*t + drv_phi[d,2])
+        vx[idx] = -drv_amp[d,0]*TWO_PI*fx_*np.sin(TWO_PI*fx_*t + drv_phi[d,0])
+        vy[idx] = -drv_amp[d,1]*TWO_PI*fy_*np.sin(TWO_PI*fy_*t + drv_phi[d,1])
+        vz[idx] = -drv_amp[d,2]*TWO_PI*fz_*np.sin(TWO_PI*fz_*t + drv_phi[d,2])
+
+
+def _do_step(x, y, z, vx, vy, vz, fixed, masses, method_id,
+              Gx, Gy, Gz, Bx, By, Bz,
+              gravity_field, elastic_force, damping_force,
+              bond_pairs, bond_k, bond_r0, dt, pos_init, box_a):
+    if method_id == 0:
+        x, y, z, vx, vy, vz = _euler_step(
+            x, y, z, vx, vy, vz, fixed, masses,
+            Gx, Gy, Gz, Bx, By, Bz,
+            gravity_field, elastic_force, damping_force,
+            bond_pairs, bond_k, bond_r0, dt)
+    elif method_id == 1:
+        x, y, z, vx, vy, vz = _implicit_euler_step(
+            x, y, z, vx, vy, vz, fixed, masses,
+            Gx, Gy, Gz, Bx, By, Bz,
+            gravity_field, elastic_force, damping_force,
+            bond_pairs, bond_k, bond_r0, dt)
+    elif method_id == 2:
+        x, y, z, vx, vy, vz = _midpoint_step(
+            x, y, z, vx, vy, vz, fixed, masses,
+            Gx, Gy, Gz, Bx, By, Bz,
+            gravity_field, elastic_force, damping_force,
+            bond_pairs, bond_k, bond_r0, dt)
+    else:
+        x, y, z, vx, vy, vz = _leapfrog_step(
+            x, y, z, vx, vy, vz, fixed, masses,
+            Gx, Gy, Gz, Bx, By, Bz,
+            gravity_field, elastic_force, damping_force,
+            bond_pairs, bond_k, bond_r0, dt)
+    x, y, z, vx, vy, vz = _apply_bc(x, y, z, vx, vy, vz, fixed, pos_init, box_a)
+    return x, y, z, vx, vy, vz
+
+
+# ══════════════════════════════════════════════════════════════
+# 主函数：run_dynamics
+# 接口与 C/C++/Fortran DLL 的 run_dynamics() 对应，
+# 参数格式：numpy 数组（替代 ctypes 指针）。
+#
+# method_id: 0=euler 1=implicit_euler 2=midpoint 3=leapfrog
+# drv_amp/freq/phi/eq: (n_drivers, 3) float64
+# drv_ncycles: (n_drivers,) float64   0=不限
+# drv_has_period: (n_drivers,) int
+#
+# 返回：(out_x, out_y, out_z, out_vx, out_vy, out_vz)
+#       各 shape=(n_frames, n_atoms)
+# ══════════════════════════════════════════════════════════════
+def run_dynamics(
+    n_atoms, pos_init, vel_init, masses, fixed,
+    n_bonds, bond_pairs, bond_k, bond_r0,
+    box_a, dt,
+    NT, NSTEP, warmup_steps, method_id,
+    Gx, Gy, Gz, Bx, By, Bz,
+    gravity_field, elastic_force, damping_force, gravity_strength,
+    n_drivers, drv_idx, drv_amp, drv_freq, drv_phi, drv_eq,
+    drv_ncycles, drv_has_period,
+    n_frames,
+    progress_cb=None,
+):
+    """运行动力学模拟，返回抽帧轨迹数组。
+
+    Args:
+        pos_init:   (n_atoms, 3) float64
+        vel_init:   (n_atoms, 3) float64
+        masses:     (n_atoms,)   float64
+        fixed:      (n_atoms, 3) int  — 1=固定
+        bond_pairs: (n_bonds, 2) int  — 0-based 局部索引
+        bond_k:     (n_bonds,)   float64
+        bond_r0:    (n_bonds,)   float64
+        drv_idx:    (n_drivers,) int  — 0-based
+        drv_amp/freq/phi/eq: (n_drivers, 3) float64
+        drv_ncycles:  (n_drivers,) float64
+        drv_has_period: (n_drivers,) int
+        n_frames:   预分配的输出帧数
+
+    Returns:
+        out_x, out_y, out_z, out_vx, out_vy, out_vz — 各 (n_frames, n_atoms)
+    """
+    pos_init  = np.asarray(pos_init,  dtype=np.float64)
+    vel_init  = np.asarray(vel_init,  dtype=np.float64)
+    masses    = np.asarray(masses,    dtype=np.float64)
+    fixed     = np.asarray(fixed,     dtype=np.int32)
+    bond_pairs = np.asarray(bond_pairs, dtype=np.int64).reshape(-1, 2) if n_bonds else np.zeros((0,2), dtype=np.int64)
+    bond_k    = np.asarray(bond_k,    dtype=np.float64) if n_bonds else np.zeros(0)
+    bond_r0   = np.asarray(bond_r0,   dtype=np.float64) if n_bonds else np.zeros(0)
+
+    n = n_atoms
+    x  = pos_init[:, 0].copy()
+    y  = pos_init[:, 1].copy()
+    z  = pos_init[:, 2].copy()
+    vx = vel_init[:, 0].copy()
+    vy = vel_init[:, 1].copy()
+    vz = vel_init[:, 2].copy()
+
+    # 驱动力数据（保证正确形状）
+    nd = n_drivers
+    if nd > 0:
+        drv_idx   = np.asarray(drv_idx,        dtype=np.int64)
+        drv_amp   = np.asarray(drv_amp,         dtype=np.float64).reshape(nd, 3)
+        drv_freq  = np.asarray(drv_freq,        dtype=np.float64).reshape(nd, 3)
+        drv_phi   = np.asarray(drv_phi,         dtype=np.float64).reshape(nd, 3)
+        drv_eq    = np.asarray(drv_eq,          dtype=np.float64).reshape(nd, 3)
+        drv_nc    = np.asarray(drv_ncycles,     dtype=np.float64)
+        drv_hp    = np.asarray(drv_has_period,  dtype=np.int32)
+        freeze    = np.zeros((nd, 3), dtype=np.float64)
+    else:
+        drv_idx = drv_amp = drv_freq = drv_phi = drv_eq = drv_nc = drv_hp = freeze = None
+
+    def _drive(t_, step_):
+        if nd > 0:
+            _apply_driving(x, y, z, vx, vy, vz, t_, step_, dt,
+                           drv_idx, drv_amp, drv_freq, drv_phi, drv_eq,
+                           drv_nc, drv_hp, freeze)
+
+    # ── 蛙跳法：初始化 v(-dt/2) ─────────────────────────────
+    if method_id == 3:
+        ax0, ay0, az0 = _accel_conservative(x, y, z, masses, Gx, Gy, Gz,
+                                             gravity_field, elastic_force,
+                                             bond_pairs, bond_k, bond_r0)
+        all_fixed = np.all(fixed, axis=1)
+        vx = np.where(all_fixed, vx, vx - 0.5 * ax0 * dt)
+        vy = np.where(all_fixed, vy, vy - 0.5 * ay0 * dt)
+        vz = np.where(all_fixed, vz, vz - 0.5 * az0 * dt)
+
+    # ── 初始驱动 t=0 ─────────────────────────────────────────
+    _drive(0.0, 0)
+
+    # ── 预热 ─────────────────────────────────────────────────
+    for s in range(warmup_steps):
+        tw = (s + 1) * dt
+        _drive(tw, s)
+        x, y, z, vx, vy, vz = _do_step(
+            x, y, z, vx, vy, vz, fixed, masses, method_id,
+            Gx, Gy, Gz, Bx, By, Bz,
+            gravity_field, elastic_force, damping_force,
+            bond_pairs, bond_k, bond_r0, dt, pos_init, box_a)
+
+    # ── 记录循环 ─────────────────────────────────────────────
+    record_steps = NT - warmup_steps
+    prog_interval = max(1, record_steps // 100)
+
+    out_x  = np.zeros((n_frames, n), dtype=np.float64)
+    out_y  = np.zeros((n_frames, n), dtype=np.float64)
+    out_z  = np.zeros((n_frames, n), dtype=np.float64)
+    out_vx = np.zeros((n_frames, n), dtype=np.float64)
+    out_vy = np.zeros((n_frames, n), dtype=np.float64)
+    out_vz = np.zeros((n_frames, n), dtype=np.float64)
+    frame_idx = 0
+
+    for s in range(record_steps):
+        if progress_cb is not None and s % prog_interval == 0 and s > 0:
+            progress_cb(s, record_steps)
+
+        t = (s + warmup_steps) * dt
+        _drive(t, s)
+
+        if s % NSTEP == 0 and frame_idx < n_frames:
+            out_x[frame_idx]  = x
+            out_y[frame_idx]  = y
+            out_z[frame_idx]  = z
+            out_vx[frame_idx] = vx
+            out_vy[frame_idx] = vy
+            out_vz[frame_idx] = vz
+            frame_idx += 1
+
+        x, y, z, vx, vy, vz = _do_step(
+            x, y, z, vx, vy, vz, fixed, masses, method_id,
+            Gx, Gy, Gz, Bx, By, Bz,
+            gravity_field, elastic_force, damping_force,
+            bond_pairs, bond_k, bond_r0, dt, pos_init, box_a)
+
+    return out_x, out_y, out_z, out_vx, out_vy, out_vz

engines/python/main.py

@@ -0,0 +1,287 @@
+"""
+engines/python/main.py
+-----------------------
+独立 Python 计算引擎。
+
+与 main.c / main.cpp / main.f90 结构一致：
+  输入: <input_dir>/coord.txt, connection.txt, bond.txt, [driver.txt]
+        <param_json> (同 engines/c/param.json 格式)
+  输出: <output_dir>/display.txt  (+ display.npz)
+        <output_dir>/trajectory.txt (若 save_trajectory=1)
+
+用法:
+  python main.py <input_dir> <output_dir> <param_json>
+
+内部调用 dynamics_lib.run_dynamics()，算法与 compute.py 完全一致。
+"""
+
+import json
+import os
+import sys
+import time
+import numpy as np
+
+# 将父目录（engines/python 的上级 engines）加入 sys.path，
+# 以便在独立运行时也能找到 dynamics_lib
+_HERE = os.path.dirname(os.path.abspath(__file__))
+sys.path.insert(0, _HERE)
+
+from dynamics_lib import run_dynamics
+
+# 为读取 coord/bond/display，复用 compute.py 中的 I/O 函数
+_COMPUTE = os.path.join(_HERE, "..", "..")
+sys.path.insert(0, _COMPUTE)
+import compute as _c
+
+_METHOD_ID = {
+    "explicit_euler": 0,
+    "euler":          0,
+    "implicit_euler": 1,
+    "midpoint":       2,
+    "leapfrog":       3,
+}
+
+
+def _load_params(param_path):
+    """读取 param.json（与 C 引擎格式相同）."""
+    with open(param_path, "r", encoding="utf-8") as f:
+        p = json.load(f)
+    return p
+
+
+def main():
+    if len(sys.argv) < 4:
+        print("用法: python main.py <input_dir> <output_dir> <param_json>")
+        sys.exit(1)
+
+    input_dir  = sys.argv[1]
+    output_dir = sys.argv[2]
+    param_path = sys.argv[3]
+
+    os.makedirs(output_dir, exist_ok=True)
+
+    # ── 读取参数 ─────────────────────────────────────────────
+    p = _load_params(param_path)
+    box_a         = float(p.get("box_a", 10.0))
+    NT            = int(p.get("NT", 10000))
+    dt            = float(p.get("DT", 0.001))
+    NSTEP         = int(p.get("NSTEP", 100))
+    warmup_steps  = int(p.get("warmup_steps", 0))
+    method_str    = str(p.get("method", "leapfrog")).lower().replace(" ", "_")
+    method_id     = _METHOD_ID.get(method_str, 3)
+    G             = p.get("G", [0.0, 0.0, -9.8])
+    B             = p.get("B", [0.0, 0.0,  0.0])
+    gravity_field    = int(p.get("gravity_field", 1))
+    elastic_force    = int(p.get("elastic_force", 1))
+    damping_force    = int(p.get("damping_force", 0))
+    gravity_strength = float(p.get("gravity_strength", 1.0))
+    driving_force    = int(p.get("driving_force", 0))
+    save_traj        = int(p.get("save_trajectory", 0))
+
+    # ── 读取原子数据 ──────────────────────────────────────────
+    coord_path = os.path.join(input_dir, "coord.txt")
+    atom_ids, masses, radii, positions, velocities, fixed = _c.load_coord_file(coord_path)
+
+    # ── 读取键数据 ────────────────────────────────────────────
+    conn_path = os.path.join(input_dir, "connection.txt")
+    bond_path = os.path.join(input_dir, "bond.txt")
+    bond_map  = _c.load_bond_parameters(bond_path)
+    bond_pairs, bond_names, bond_stiffness, bond_rest_lengths = \
+        _c.load_bond_connections(conn_path, atom_ids, positions, bond_map)
+    n_bonds = len(bond_pairs)
+
+    # ── 读取驱动力 ────────────────────────────────────────────
+    drv_list = []
+    if driving_force:
+        driver_path = os.path.join(input_dir, "driver.txt")
+        raw_drivers = _c.load_driver_file(driver_path, atom_ids)
+        if raw_drivers:
+            atom_id_map = {int(aid): i for i, aid in enumerate(atom_ids)}
+            for d in raw_drivers:
+                aid = int(d["atom_id"])
+                if aid not in atom_id_map:
+                    continue
+                lidx = atom_id_map[aid]
+                eq   = positions[lidx].tolist()
+                d["eq_pos"] = np.array(eq)
+                pc   = d.get("period_cycles")
+                nc   = float(pc) if pc is not None else 0.0
+                hp   = 1 if nc > 0 else 0
+                drv_list.append({
+                    "local_idx": lidx,
+                    "amp":  d["amp"].tolist(),
+                    "freq": d["freq"].tolist(),
+                    "phi":  d["phi"].tolist(),   # radians
+                    "eq":   eq,
+                    "nc":   nc,
+                    "hp":   hp,
+                })
+
+    nd = len(drv_list)
+    if nd > 0:
+        drv_idx   = np.array([d["local_idx"] for d in drv_list], dtype=np.int64)
+        drv_amp   = np.array([d["amp"]  for d in drv_list], dtype=np.float64)
+        drv_freq  = np.array([d["freq"] for d in drv_list], dtype=np.float64)
+        drv_phi   = np.array([d["phi"]  for d in drv_list], dtype=np.float64)
+        drv_eq    = np.array([d["eq"]   for d in drv_list], dtype=np.float64)
+        drv_nc    = np.array([d["nc"]   for d in drv_list], dtype=np.float64)
+        drv_hp    = np.array([d["hp"]   for d in drv_list], dtype=np.int32)
+    else:
+        drv_idx = drv_amp = drv_freq = drv_phi = drv_eq = drv_nc = drv_hp = \
+            np.zeros(0, dtype=np.int64)
+
+    # ── 计算帧数 ──────────────────────────────────────────────
+    record_steps = NT - warmup_steps
+    n_frames = max(1, record_steps // NSTEP)
+
+    # ── 进度回调 ──────────────────────────────────────────────
+    def _progress(step, total):
+        pct = step * 100 // total
+        print(f"[python-engine] progress: {step}/{total} ({pct}%)", flush=True)
+
+    # ── 运行计算 ──────────────────────────────────────────────
+    t0 = time.time()
+    print(f"[python-engine] NT={NT}  NSTEP={NSTEP}  method={method_str}  "
+          f"n_atoms={len(atom_ids)}  n_bonds={n_bonds}")
+
+    out_x, out_y, out_z, out_vx, out_vy, out_vz = run_dynamics(
+        n_atoms=len(atom_ids),
+        pos_init=positions,
+        vel_init=velocities,
+        masses=masses,
+        fixed=fixed,
+        n_bonds=n_bonds,
+        bond_pairs=bond_pairs,
+        bond_k=bond_stiffness,
+        bond_r0=bond_rest_lengths,
+        box_a=box_a,
+        dt=dt,
+        NT=NT,
+        NSTEP=NSTEP,
+        warmup_steps=warmup_steps,
+        method_id=method_id,
+        Gx=float(G[0]), Gy=float(G[1]), Gz=float(G[2]),
+        Bx=float(B[0]), By=float(B[1]), Bz=float(B[2]),
+        gravity_field=gravity_field,
+        elastic_force=elastic_force,
+        damping_force=damping_force,
+        gravity_strength=gravity_strength,
+        n_drivers=nd,
+        drv_idx=drv_idx,
+        drv_amp=drv_amp,
+        drv_freq=drv_freq,
+        drv_phi=drv_phi,
+        drv_eq=drv_eq,
+        drv_ncycles=drv_nc,
+        drv_has_period=drv_hp,
+        n_frames=n_frames,
+        progress_cb=_progress,
+    )
+    elapsed = time.time() - t0
+    print(f"[python-engine] 完成: {n_frames} 帧  {elapsed:.3f} s")
+
+    # ── 构建 display header ───────────────────────────────────
+    ball_radius    = float(p.get("ball_radius",  0.5))
+    ball_color     = p.get("ball_color",   [0.9, 0.2, 0.2])
+    box_color      = p.get("box_color",    [0.8, 0.8, 0.85])
+    use_marker     = int(p.get("use_marker",     0))
+    alpha_val      = p.get("alpha",        0.2)
+    cam_dist       = float(p.get("camera_distance",   40.0))
+    cam_elev       = float(p.get("camera_elevation",   0.0))
+    cam_azim       = float(p.get("camera_azimuth",     0.0))
+    cam_cx         = float(p.get("camera_center_x",    0.0))
+    cam_cy         = float(p.get("camera_center_y",    0.0))
+    cam_cz         = float(p.get("camera_center_z",    0.0))
+
+    header = {
+        "DT":                  str(dt),
+        "NSTEP":               str(NSTEP),
+        "method":              method_str,
+        "NT":                  str(NT),
+        "warmup_steps":        str(warmup_steps),
+        "dynamic_steps":       str(record_steps),
+        "T_total":             str(NT * dt),
+        "box_a":               str(box_a),
+        "gravity_field":       str(gravity_field),
+        "elastic_force":       str(elastic_force),
+        "damping_force":       str(damping_force),
+        "driving_force":       str(driving_force),
+        "gravity_strength":    str(gravity_strength),
+        "G":                   json.dumps([float(v) for v in G]),
+        "B":                   json.dumps([float(v) for v in B]),
+        "number_of_frames":    str(n_frames),
+        "number_of_particles": str(len(atom_ids)),
+        "use_marker":          str(use_marker),
+        "display_color":       json.dumps(p.get("display_color",
+            {"x":[0,[1.0,0.0,0.0]],"y":[0,[0.0,1.0,0.0]],"z":[0,[0.0,0.0,1.0]],
+             "xy":[0,[1.0,1.0,0.0]],"yz":[0,[0.0,1.0,1.0]],"zx":[0,[1.0,0.0,1.0]],
+             "xyz":[1,[1.0,1.0,1.0]]})),
+        "ball_radius":         str(ball_radius),
+        "ball_color_r":        str(ball_color[0]),
+        "ball_color_g":        str(ball_color[1]),
+        "ball_color_b":        str(ball_color[2]),
+        "box_color_r":         str(box_color[0]),
+        "box_color_g":         str(box_color[1]),
+        "box_color_b":         str(box_color[2]),
+        "alpha":               str(alpha_val) if not isinstance(alpha_val, list)
+                               else ",".join(str(a) for a in alpha_val),
+        "atom_radii":          ",".join(str(r) for r in radii),
+        "atom_masses":         json.dumps([float(m) for m in masses]),
+        "atom_positions":      json.dumps(positions.tolist()),
+        "bond_pairs":          json.dumps(bond_pairs.tolist() if n_bonds else []),
+        "bond_stiffness":      json.dumps(bond_stiffness.tolist() if n_bonds else []),
+        "bond_rest_lengths":   json.dumps(bond_rest_lengths.tolist() if n_bonds else []),
+        "X_MIN": str(-box_a), "X_MAX": str(box_a),
+        "Y_MIN": str(-box_a), "Y_MAX": str(box_a),
+        "Z_MIN": str(-box_a), "Z_MAX": str(box_a),
+        "camera_distance":  str(cam_dist),
+        "camera_elevation": str(cam_elev),
+        "camera_azimuth":   str(cam_azim),
+        "camera_center_x":  str(cam_cx),
+        "camera_center_y":  str(cam_cy),
+        "camera_center_z":  str(cam_cz),
+        "camera_keyframes": "",
+    }
+
+    # ── 保存 display.txt + display.npz ───────────────────────
+    disp_txt = os.path.join(output_dir, "display.txt")
+    _c.save_display_txt(
+        disp_txt,
+        out_x, out_y, out_z, out_vx, out_vy, out_vz,
+        atom_ids, record_steps, len(atom_ids),
+        header_fields=header,
+    )
+    print(f"[python-engine] display.txt 已保存: {disp_txt}")
+
+    disp_npz = os.path.join(output_dir, "display.npz")
+    _c.save_display_npz(
+        disp_npz,
+        out_x, out_y, out_z, out_vx, out_vy, out_vz,
+        atom_ids, header_fields=header,
+    )
+    print(f"[python-engine] display.npz 已保存: {disp_npz}")
+
+    # ── 可选：保存 trajectory.txt ─────────────────────────────
+    if save_traj:
+        traj_payload = {
+            "traj_x":  out_x, "traj_y":  out_y, "traj_z":  out_z,
+            "traj_vx": out_vx, "traj_vy": out_vy, "traj_vz": out_vz,
+            "NT": record_steps, "DT": dt, "NSTEP": NSTEP,
+            "method": method_str,
+            "atom_ids": atom_ids,
+            "atom_masses": masses,
+            "atom_radii": radii,
+            "atom_positions": positions,
+            "bond_pairs": bond_pairs,
+            "bond_stiffness": bond_stiffness,
+            "bond_rest_lengths": bond_rest_lengths,
+            "G": [float(v) for v in G],
+            "B": [float(v) for v in B],
+        }
+        traj_path = os.path.join(output_dir, "trajectory.txt")
+        _c.save_text_data(traj_path, traj_payload)
+        print(f"[python-engine] trajectory.txt 已保存: {traj_path}")
+
+
+if __name__ == "__main__":
+    main()

engines/src/c/Makefile

@@ -0,0 +1,51 @@
+# engines/src/c/Makefile
+# 编译 DLL 到 engines/release/（主程序通过 ctypes 直接调用）
+
+CC        = gcc
+CFLAGS    = -O3 -march=native -Wall -Wextra
+LDFLAGS   = -lm
+LIB_SRC   = dynamics_lib.c
+
+# 自动检测系统
+UNAME_S  := $(shell uname -s 2>/dev/null || echo Windows)
+
+# Windows 检测：Msys2/MINGW 也视为 Windows
+IS_WINDOWS := $(findstring MINGW,$(UNAME_S))
+ifneq ($(IS_WINDOWS),)
+  UNAME_S := Windows
+endif
+IS_WINDOWS := $(findstring MSYS,$(UNAME_S))
+ifneq ($(IS_WINDOWS),)
+  UNAME_S := Windows
+endif
+
+# DLL 输出到 engines/release/
+DLL_DIR = ../../release
+
+ifeq ($(UNAME_S),Linux)
+  DLL_TARGET = $(DLL_DIR)/dynamics_c.so
+  DLL_FLAGS  = -shared -fPIC
+else ifeq ($(UNAME_S),Darwin)
+  DLL_TARGET = $(DLL_DIR)/dynamics_c.dylib
+  DLL_FLAGS  = -dynamiclib
+else
+  # Windows: 静态链接运行时，避免依赖 libgcc_s_seh-1.dll
+  DLL_TARGET = $(DLL_DIR)/dynamics_c.dll
+  DLL_FLAGS  = -shared -static
+endif
+
+.PHONY: all dll clean
+
+all: dll
+
+dll: $(DLL_TARGET)
+
+$(DLL_TARGET): $(LIB_SRC) | $(DLL_DIR)
+	$(CC) $(CFLAGS) $(DLL_FLAGS) -o $@ $(LIB_SRC) $(LDFLAGS)
+	@echo "  === C DLL built: $@ ==="
+
+$(DLL_DIR):
+	mkdir -p $(DLL_DIR)
+
+clean:
+	rm -f $(DLL_TARGET)

engines/src/c/dynamics_lib.c

@@ -0,0 +1,554 @@
+/**
+ * engines/c/dynamics_lib.c
+ * -------------------------
+ * 纯计算 DLL：无文件 I/O，所有数据由 Python 以 NumPy 数组传入，
+ * 结果直接写入 Python 预分配的输出数组。
+ * 算法与 main.c 和 compute.py 保持完全一致。
+ *
+ * 编译（Windows DLL）:
+ *   gcc -O3 -march=native -shared -o build/dynamics_c.dll dynamics_lib.c -lm
+ * 编译（Linux .so）:
+ *   gcc -O3 -march=native -shared -fPIC -o build/dynamics_c.so dynamics_lib.c -lm
+ * 编译（macOS .dylib）:
+ *   gcc -O3 -march=native -dynamiclib -o build/dynamics_c.dylib dynamics_lib.c -lm
+ */
+
+#ifdef _WIN32
+#  define EXPORT __declspec(dllexport)
+#else
+#  define EXPORT __attribute__((visibility("default")))
+#endif
+
+#include <math.h>
+#include <stdlib.h>
+#include <string.h>
+#include <stdio.h>
+
+/* ── 驱动力结构体 ─────────────────────────────────────────── */
+typedef struct {
+    int     n_drivers;
+    const int    *idx;         /* [n_drivers] 0-based local atom index */
+    const double *amp;         /* [n_drivers*3] (ax,ay,az) interleaved */
+    const double *freq;        /* [n_drivers*3] */
+    const double *phi;         /* [n_drivers*3] radians */
+    const double *eq;          /* [n_drivers*3] equilibrium positions */
+    const double *ncycles;     /* [n_drivers] 0=unlimited */
+    const int    *has_period;  /* [n_drivers] */
+    /* mutable freeze positions (allocated internally) */
+    double *freeze;            /* [n_drivers*3] */
+} Drivers;
+
+/* ── 加速度：保守力（弹簧键 + 均匀重力场）────────────────── */
+static void accel_conservative(
+    int n, const double *x, const double *y, const double *z,
+    const double *m,
+    double Gx, double Gy, double Gz,
+    int gravity_field, int elastic_force,
+    int n_bonds, const int *bond_pairs,
+    const double *bond_k, const double *bond_r0,
+    double *ax, double *ay, double *az)
+{
+    for (int i = 0; i < n; i++) {
+        ax[i] = gravity_field ? Gx : 0.0;
+        ay[i] = gravity_field ? Gy : 0.0;
+        az[i] = gravity_field ? Gz : 0.0;
+    }
+
+    if (!elastic_force || n_bonds == 0) return;
+
+    for (int b = 0; b < n_bonds; b++) {
+        int  ii = bond_pairs[b*2];
+        int  jj = bond_pairs[b*2+1];
+        double dx = x[jj] - x[ii];
+        double dy = y[jj] - y[ii];
+        double dz = z[jj] - z[ii];
+        double dist = sqrt(dx*dx + dy*dy + dz*dz);
+        if (dist < 1e-12) continue;
+        double k  = bond_k[b];
+        double r0 = bond_r0[b];
+        double fac = k * (dist - r0) / dist;
+        double fx = fac * dx, fy = fac * dy, fz_b = fac * dz;
+        ax[ii] += fx / m[ii];  ay[ii] += fy / m[ii];  az[ii] += fz_b / m[ii];
+        ax[jj] -= fx / m[jj];  ay[jj] -= fy / m[jj];  az[jj] -= fz_b / m[jj];
+    }
+}
+
+/* ── 完整加速度（含阻尼）────────────────────────────────── */
+static void accel_full(
+    int n, const double *x, const double *y, const double *z,
+    const double *vx, const double *vy, const double *vz,
+    const double *m,
+    double Gx, double Gy, double Gz,
+    double Bx, double By, double Bz,
+    int gravity_field, int elastic_force, int damping_force,
+    int n_bonds, const int *bond_pairs,
+    const double *bond_k, const double *bond_r0,
+    double *ax, double *ay, double *az)
+{
+    accel_conservative(n, x, y, z, m, Gx, Gy, Gz,
+                       gravity_field, elastic_force,
+                       n_bonds, bond_pairs, bond_k, bond_r0,
+                       ax, ay, az);
+    if (damping_force) {
+        for (int i = 0; i < n; i++) {
+            ax[i] -= Bx * vx[i] / m[i];
+            ay[i] -= By * vy[i] / m[i];
+            az[i] -= Bz * vz[i] / m[i];
+        }
+    }
+}
+
+/* ── 边界：反弹（与 main.c limit_in_box 一致）────────────── */
+static inline void _limit1(double *p, double *v, double lo, double hi) {
+    if (*p > hi) { *p = hi; *v = -fabs(*v); }
+    if (*p < lo) { *p = lo; *v =  fabs(*v); }
+}
+
+/* ── 边界：回绕（与 main.c wrap_position 一致）──────────── */
+static inline void _wrap1(double *p, double lo, double hi) {
+    if (*p > hi) *p = lo;
+    if (*p < lo) *p = hi;
+}
+
+/* ── 边界 + 固定约束（与 main.c apply_step 末尾一致）──────── */
+static void apply_boundary_and_constraints(
+    int n, double *x, double *y, double *z,
+    double *vx, double *vy, double *vz,
+    const int *fixed, const double *pos_init,
+    double box_a)
+{
+    double lo = -box_a, hi = box_a;
+
+    /* 反弹 */
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) continue;
+        _limit1(&x[i], &vx[i], lo, hi);
+        _limit1(&y[i], &vy[i], lo, hi);
+        _limit1(&z[i], &vz[i], lo, hi);
+    }
+
+    /* 回绕 */
+    for (int i = 0; i < n; i++) {
+        _wrap1(&x[i], lo, hi);
+        _wrap1(&y[i], lo, hi);
+        _wrap1(&z[i], lo, hi);
+    }
+
+    /* 逐自由度固定约束：与 main.c 和 Python apply_fixed_constraints 一致 */
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3+0]) { x[i] = pos_init[i*3+0]; vx[i] = 0.0; }
+        if (fixed[i*3+1]) { y[i] = pos_init[i*3+1]; vy[i] = 0.0; }
+        if (fixed[i*3+2]) { z[i] = pos_init[i*3+2]; vz[i] = 0.0; }
+    }
+}
+
+/* ══════════════════════════════════════════════════════════
+ * 蛙跳法（与 main.c leapfrog_step 完全一致）
+ * x(t), v(t-dt/2) → x(t+dt), v(t+dt/2)
+ * 无阻尼：纯辛积分。有阻尼：半隐式处理 α = B·dt/(2m)
+ * ══════════════════════════════════════════════════════════ */
+static void leapfrog_step(
+    int n, double *x, double *y, double *z,
+    double *vx, double *vy, double *vz,
+    const double *m, const int *fixed,
+    double Gx, double Gy, double Gz,
+    double Bx, double By, double Bz,
+    int gravity_field, int elastic_force, int damping_force,
+    int n_bonds, const int *bp, const double *bk, const double *br0,
+    double dt)
+{
+    double *ax = (double*)alloca(n*sizeof(double)*3);
+    double *ay = ax+n; double *az = ay+n;
+
+    accel_conservative(n, x, y, z, m, Gx, Gy, Gz,
+                       gravity_field, elastic_force,
+                       n_bonds, bp, bk, br0, ax, ay, az);
+
+    int has_damp = damping_force && (Bx != 0.0 || By != 0.0 || Bz != 0.0);
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) continue;
+        if (has_damp) {
+            double ax_ = Bx*dt/(2.0*m[i]);
+            double ay_ = By*dt/(2.0*m[i]);
+            double az_ = Bz*dt/(2.0*m[i]);
+            vx[i] = (vx[i]*(1.0-ax_) + ax[i]*dt) / (1.0+ax_);
+            vy[i] = (vy[i]*(1.0-ay_) + ay[i]*dt) / (1.0+ay_);
+            vz[i] = (vz[i]*(1.0-az_) + az[i]*dt) / (1.0+az_);
+        } else {
+            vx[i] += ax[i]*dt;
+            vy[i] += ay[i]*dt;
+            vz[i] += az[i]*dt;
+        }
+        x[i] += vx[i]*dt;
+        y[i] += vy[i]*dt;
+        z[i] += vz[i]*dt;
+    }
+}
+
+/* ══════════════════════════════════════════════════════════
+ * 显式欧拉法（与 main.c explicit_euler_step 一致）
+ * ══════════════════════════════════════════════════════════ */
+static void euler_step(
+    int n, double *x, double *y, double *z,
+    double *vx, double *vy, double *vz,
+    const double *m, const int *fixed,
+    double Gx, double Gy, double Gz,
+    double Bx, double By, double Bz,
+    int gravity_field, int elastic_force, int damping_force,
+    int n_bonds, const int *bp, const double *bk, const double *br0,
+    double dt)
+{
+    double *ax = (double*)alloca(n*sizeof(double)*3);
+    double *ay = ax+n; double *az = ay+n;
+    accel_full(n, x, y, z, vx, vy, vz, m, Gx, Gy, Gz, Bx, By, Bz,
+               gravity_field, elastic_force, damping_force,
+               n_bonds, bp, bk, br0, ax, ay, az);
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) continue;
+        x[i] += vx[i]*dt;  y[i] += vy[i]*dt;  z[i] += vz[i]*dt;
+        vx[i]+= ax[i]*dt;  vy[i]+= ay[i]*dt;  vz[i]+= az[i]*dt;
+    }
+}
+
+/* ══════════════════════════════════════════════════════════
+ * 隐式欧拉法（与 main.c implicit_euler_step 完全一致）
+ *
+ * main.c 逻辑：
+ *   1. 用 v_next ≈ (v + G·dt)/(1 + γ·dt) 预测（只含重力+阻尼，不含弹簧）
+ *   2. 用 (x, v_next) 计算完整加速度 a_next
+ *   3. v += a_next·dt;  x += v·dt
+ * ══════════════════════════════════════════════════════════ */
+static void implicit_euler_step(
+    int n, double *x, double *y, double *z,
+    double *vx, double *vy, double *vz,
+    const double *m, const int *fixed,
+    double Gx, double Gy, double Gz,
+    double Bx, double By, double Bz,
+    int gravity_field, int elastic_force, int damping_force,
+    int n_bonds, const int *bp, const double *bk, const double *br0,
+    double dt)
+{
+    double *vxn = (double*)alloca(n*sizeof(double)*3);
+    double *vyn = vxn+n; double *vzn = vyn+n;
+
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) {
+            vxn[i] = vyn[i] = vzn[i] = 0.0; continue;
+        }
+        double gx = Bx / m[i], gy = By / m[i], gz = Bz / m[i];
+        vxn[i] = (vx[i] + Gx*dt) / (1.0 + gx*dt);
+        vyn[i] = (vy[i] + Gy*dt) / (1.0 + gy*dt);
+        vzn[i] = (vz[i] + Gz*dt) / (1.0 + gz*dt);
+    }
+
+    double *ax = (double*)alloca(n*sizeof(double)*3);
+    double *ay = ax+n; double *az = ay+n;
+    accel_full(n, x, y, z, vxn, vyn, vzn, m, Gx, Gy, Gz, Bx, By, Bz,
+               gravity_field, elastic_force, damping_force,
+               n_bonds, bp, bk, br0, ax, ay, az);
+
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) continue;
+        vx[i] += ax[i]*dt;
+        vy[i] += ay[i]*dt;
+        vz[i] += az[i]*dt;
+        x[i]  += vx[i]*dt;
+        y[i]  += vy[i]*dt;
+        z[i]  += vz[i]*dt;
+    }
+}
+
+/* ══════════════════════════════════════════════════════════
+ * 中点法（与 main.c midpoint_step 完全一致）
+ *
+ * main.c 逻辑：
+ *   1. a = accel(x, v)
+ *   2. xm = x + 0.5·v·dt;  vm = v + 0.5·a·dt
+ *   3. x  = x + vm·dt      (位置更新用 vm，即中点速度)
+ *   4. am = accel(xm, vm)
+ *   5. v  = v + am·dt
+ * ══════════════════════════════════════════════════════════ */
+static void midpoint_step(
+    int n, double *x, double *y, double *z,
+    double *vx, double *vy, double *vz,
+    const double *m, const int *fixed,
+    double Gx, double Gy, double Gz,
+    double Bx, double By, double Bz,
+    int gravity_field, int elastic_force, int damping_force,
+    int n_bonds, const int *bp, const double *bk, const double *br0,
+    double dt)
+{
+    /* Allocate in one block for cache locality */
+    double *buf = (double*)alloca(n*sizeof(double)*9);
+    double *ax  = buf;
+    double *ay  = ax+n; double *az  = ay+n;
+    double *xm  = az+n; double *ym  = xm+n; double *zm  = ym+n;
+    double *vxm = zm+n; double *vym = vxm+n; double *vzm = vym+n;
+
+    accel_full(n, x, y, z, vx, vy, vz, m, Gx, Gy, Gz, Bx, By, Bz,
+               gravity_field, elastic_force, damping_force,
+               n_bonds, bp, bk, br0, ax, ay, az);
+
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) {
+            xm[i]=x[i]; ym[i]=y[i]; zm[i]=z[i];
+            vxm[i]=vym[i]=vzm[i]=0.0; continue;
+        }
+        xm[i]  = x[i]  + 0.5*vx[i]*dt;
+        ym[i]  = y[i]  + 0.5*vy[i]*dt;
+        zm[i]  = z[i]  + 0.5*vz[i]*dt;
+        vxm[i] = vx[i] + 0.5*ax[i]*dt;
+        vym[i] = vy[i] + 0.5*ay[i]*dt;
+        vzm[i] = vz[i] + 0.5*az[i]*dt;
+        /* position updated with midpoint velocity (same as main.c) */
+        x[i]   = x[i]  + vxm[i]*dt;
+        y[i]   = y[i]  + vym[i]*dt;
+        z[i]   = z[i]  + vzm[i]*dt;
+    }
+
+    double *axm = (double*)alloca(n*sizeof(double)*3);
+    double *aym = axm+n; double *azm = aym+n;
+    accel_full(n, xm, ym, zm, vxm, vym, vzm, m, Gx, Gy, Gz, Bx, By, Bz,
+               gravity_field, elastic_force, damping_force,
+               n_bonds, bp, bk, br0, axm, aym, azm);
+
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) continue;
+        vx[i] += axm[i]*dt;
+        vy[i] += aym[i]*dt;
+        vz[i] += azm[i]*dt;
+    }
+}
+
+/* ── 驱动力（与 main.c apply_driving_force 一致）────────── */
+static void apply_driving(
+    int n, double *x, double *y, double *z,
+    double *vx, double *vy, double *vz,
+    double t, int step, double dt, Drivers *drv)
+{
+    (void)n;
+    if (!drv || drv->n_drivers == 0) return;
+    const double TWO_PI = 2.0 * 3.14159265358979323846;
+
+    for (int d = 0; d < drv->n_drivers; d++) {
+        int idx = drv->idx[d];
+        double fx = drv->freq[d*3+0];
+        double fy = drv->freq[d*3+1];
+        double fz = drv->freq[d*3+2];
+
+        if (drv->has_period[d]) {
+            double mf = fabs(fx) > fabs(fy) ? fabs(fx) : fabs(fy);
+            if (fabs(fz) > mf) mf = fabs(fz);
+            int period_steps = 0;
+            if (mf > 1e-12)
+                period_steps = (int)(drv->ncycles[d] / mf / dt);
+            if (step > period_steps) {
+                x[idx] = drv->freeze[d*3+0];
+                y[idx] = drv->freeze[d*3+1];
+                z[idx] = drv->freeze[d*3+2];
+                vx[idx] = vy[idx] = vz[idx] = 0.0;
+                continue;
+            }
+
+            double px = drv->eq[d*3+0] + drv->amp[d*3+0]*cos(TWO_PI*fx*t + drv->phi[d*3+0]);
+            double py = drv->eq[d*3+1] + drv->amp[d*3+1]*cos(TWO_PI*fy*t + drv->phi[d*3+1]);
+            double pz = drv->eq[d*3+2] + drv->amp[d*3+2]*cos(TWO_PI*fz*t + drv->phi[d*3+2]);
+            if (step == period_steps) {
+                drv->freeze[d*3+0] = px;
+                drv->freeze[d*3+1] = py;
+                drv->freeze[d*3+2] = pz;
+            }
+        }
+
+        x[idx]  = drv->eq[d*3+0] + drv->amp[d*3+0]*cos(TWO_PI*fx*t + drv->phi[d*3+0]);
+        y[idx]  = drv->eq[d*3+1] + drv->amp[d*3+1]*cos(TWO_PI*fy*t + drv->phi[d*3+1]);
+        z[idx]  = drv->eq[d*3+2] + drv->amp[d*3+2]*cos(TWO_PI*fz*t + drv->phi[d*3+2]);
+        vx[idx] = -drv->amp[d*3+0]*TWO_PI*fx*sin(TWO_PI*fx*t + drv->phi[d*3+0]);
+        vy[idx] = -drv->amp[d*3+1]*TWO_PI*fy*sin(TWO_PI*fy*t + drv->phi[d*3+1]);
+        vz[idx] = -drv->amp[d*3+2]*TWO_PI*fz*sin(TWO_PI*fz*t + drv->phi[d*3+2]);
+    }
+}
+
+/* ══════════════════════════════════════════════════════════
+ * 导出函数：run_dynamics
+ *
+ * 与 main.c 的计算顺序完全一致：
+ *   1. leapfrog 初始化 v(-dt/2)
+ *   2. 初始驱动 t=0
+ *   3. 预热循环（不记录）
+ *   4. 记录循环：drive → record → step → boundary → constraints
+ *
+ * 参数说明（所有数组均为 C-contiguous 行优先 float64/int32）：
+ *   n_atoms     原子数
+ *   pos_init    初始位置 [n_atoms*3]  x0,y0,z0, x1,y1,z1, ...
+ *   vel_init    初始速度 [n_atoms*3]
+ *   masses      质量     [n_atoms]
+ *   fixed       自由度约束 [n_atoms*3]  int32, 1=固定
+ *   n_bonds     键数
+ *   bond_pairs  键对     [n_bonds*2]  int32, 0-based local index
+ *   bond_k      刚度     [n_bonds]
+ *   bond_r0     平衡键长 [n_bonds]
+ *   box_a       盒子半边长
+ *   dt          时间步长
+ *   NT          总步数（含预热）
+ *   NSTEP       抽帧间隔
+ *   warmup_steps 预热步数
+ *   method_id   0=euler 1=implicit 2=midpoint 3=leapfrog
+ *   Gx/Gy/Gz    均匀重力场加速度分量
+ *   Bx/By/Bz    阻尼系数分量
+ *   gravity_field / elastic_force / damping_force  力开关
+ *   gravity_strength  原子间引力强度（暂未实现，留接口）
+ *   n_drivers   驱动原子数
+ *   drv_idx     驱动原子局部索引  [n_drivers]  int32
+ *   drv_amp     振幅 [n_drivers*3]
+ *   drv_freq    频率 [n_drivers*3]
+ *   drv_phi     初相（弧度）[n_drivers*3]
+ *   drv_eq      平衡位置 [n_drivers*3]
+ *   drv_ncycles 周期数  [n_drivers]  0=不限
+ *   drv_has_period  [n_drivers]  int32
+ *   n_frames    输出帧数（Python 预计算：(NT-warmup)/NSTEP 向上取整）
+ *   out_x/y/z/vx/vy/vz  输出数组 [n_frames*n_atoms]  由 Python 预分配
+ *   progress_cb 进度回调（可为 NULL）
+ *
+ * 返回：0=成功，负数=错误
+ * ══════════════════════════════════════════════════════════ */
+EXPORT int run_dynamics(
+    int n_atoms,
+    const double *pos_init,
+    const double *vel_init,
+    const double *masses,
+    const int    *fixed,
+    int n_bonds,
+    const int    *bond_pairs,
+    const double *bond_k,
+    const double *bond_r0,
+    double box_a, double dt,
+    int NT, int NSTEP, int warmup_steps, int method_id,
+    double Gx, double Gy, double Gz,
+    double Bx, double By, double Bz,
+    int gravity_field, int elastic_force, int damping_force,
+    double gravity_strength,
+    int n_drivers,
+    const int    *drv_idx,
+    const double *drv_amp,
+    const double *drv_freq,
+    const double *drv_phi,
+    const double *drv_eq,
+    const double *drv_ncycles,
+    const int    *drv_has_period,
+    int n_frames,
+    double *out_x, double *out_y, double *out_z,
+    double *out_vx, double *out_vy, double *out_vz,
+    void (*progress_cb)(int step, int total))
+{
+    (void)gravity_strength;   /* 原子间引力暂未实现 */
+
+    int n = n_atoms;
+
+    /* ── 工作数组 ── */
+    double *x  = (double*)malloc(n*sizeof(double));
+    double *y  = (double*)malloc(n*sizeof(double));
+    double *z  = (double*)malloc(n*sizeof(double));
+    double *vx = (double*)malloc(n*sizeof(double));
+    double *vy = (double*)malloc(n*sizeof(double));
+    double *vz = (double*)malloc(n*sizeof(double));
+    if (!x||!y||!z||!vx||!vy||!vz) return -1;
+
+    for (int i = 0; i < n; i++) {
+        x[i]=pos_init[i*3+0]; y[i]=pos_init[i*3+1]; z[i]=pos_init[i*3+2];
+        vx[i]=vel_init[i*3+0]; vy[i]=vel_init[i*3+1]; vz[i]=vel_init[i*3+2];
+    }
+
+    /* ── 驱动结构 ── */
+    Drivers drv;
+    drv.n_drivers  = n_drivers;
+    drv.idx        = drv_idx;
+    drv.amp        = drv_amp;
+    drv.freq       = drv_freq;
+    drv.phi        = drv_phi;
+    drv.eq         = drv_eq;
+    drv.ncycles    = drv_ncycles;
+    drv.has_period = drv_has_period;
+    drv.freeze     = NULL;
+    if (n_drivers > 0) {
+        drv.freeze = (double*)calloc(n_drivers*3, sizeof(double));
+        if (!drv.freeze) { free(x);free(y);free(z);free(vx);free(vy);free(vz); return -2; }
+    }
+
+    /* ── 内联步进宏 ── */
+#define DO_STEP() do { \
+    switch (method_id) { \
+    case 0: euler_step(n,x,y,z,vx,vy,vz,masses,fixed,Gx,Gy,Gz,Bx,By,Bz, \
+                       gravity_field,elastic_force,damping_force, \
+                       n_bonds,bond_pairs,bond_k,bond_r0,dt); break; \
+    case 1: implicit_euler_step(n,x,y,z,vx,vy,vz,masses,fixed,Gx,Gy,Gz,Bx,By,Bz, \
+                       gravity_field,elastic_force,damping_force, \
+                       n_bonds,bond_pairs,bond_k,bond_r0,dt); break; \
+    case 2: midpoint_step(n,x,y,z,vx,vy,vz,masses,fixed,Gx,Gy,Gz,Bx,By,Bz, \
+                       gravity_field,elastic_force,damping_force, \
+                       n_bonds,bond_pairs,bond_k,bond_r0,dt); break; \
+    default: leapfrog_step(n,x,y,z,vx,vy,vz,masses,fixed,Gx,Gy,Gz,Bx,By,Bz, \
+                       gravity_field,elastic_force,damping_force, \
+                       n_bonds,bond_pairs,bond_k,bond_r0,dt); break; \
+    } \
+    apply_boundary_and_constraints(n,x,y,z,vx,vy,vz,fixed,pos_init,box_a); \
+} while(0)
+
+    /* ── 蛙跳法：初始化 v(-dt/2) = v(0) - 0.5·a_c(0)·dt ── */
+    if (method_id == 3) {
+        double *ax0 = (double*)alloca(n*sizeof(double)*3);
+        double *ay0 = ax0+n; double *az0 = ay0+n;
+        accel_conservative(n, x, y, z, masses, Gx, Gy, Gz,
+                           gravity_field, elastic_force,
+                           n_bonds, bond_pairs, bond_k, bond_r0,
+                           ax0, ay0, az0);
+        for (int i = 0; i < n; i++) {
+            if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) continue;
+            vx[i] -= 0.5*ax0[i]*dt;
+            vy[i] -= 0.5*ay0[i]*dt;
+            vz[i] -= 0.5*az0[i]*dt;
+        }
+    }
+
+    /* ── 初始驱动 t=0（与 main.c 一致：leapfrog init 之后施加）── */
+    if (n_drivers > 0) apply_driving(n, x, y, z, vx, vy, vz, 0.0, 0, dt, &drv);
+
+    /* ── 预热（不记录）── */
+    for (int s = 0; s < warmup_steps; s++) {
+        double tw = (s + 1) * dt;
+        if (n_drivers > 0) apply_driving(n, x, y, z, vx, vy, vz, tw, s, dt, &drv);
+        DO_STEP();
+    }
+
+    /* ── 记录循环 ── */
+    int record_steps = NT - warmup_steps;
+    int prog_interval = record_steps / 100;
+    if (prog_interval < 1) prog_interval = 1;
+    int frame_idx = 0;
+
+    for (int s = 0; s < record_steps; s++) {
+        if (progress_cb && s % prog_interval == 0 && s > 0)
+            progress_cb(s, record_steps);
+
+        double t = (s + warmup_steps) * dt;
+        if (n_drivers > 0) apply_driving(n, x, y, z, vx, vy, vz, t, s, dt, &drv);
+
+        /* 抽帧记录（drive 之后，step 之前，与 main.c 一致）*/
+        if (s % NSTEP == 0 && frame_idx < n_frames) {
+            int base = frame_idx * n;
+            for (int i = 0; i < n; i++) {
+                out_x [base+i] = x[i];   out_y [base+i] = y[i];   out_z [base+i] = z[i];
+                out_vx[base+i] = vx[i];  out_vy[base+i] = vy[i];  out_vz[base+i] = vz[i];
+            }
+            frame_idx++;
+        }
+        DO_STEP();
+    }
+
+#undef DO_STEP
+
+    free(x); free(y); free(z);
+    free(vx); free(vy); free(vz);
+    if (drv.freeze) free(drv.freeze);
+    return 0;
+}

engines/src/cpp/Makefile

@@ -0,0 +1,50 @@
+# engines/src/cpp/Makefile
+# 编译 DLL 到 engines/release/（主程序通过 ctypes 直接调用）
+
+CXX     = g++
+LIB_SRC = dynamics_lib.cpp
+
+UNAME_S := $(shell uname -s 2>/dev/null || echo Windows)
+
+# Windows 检测：Msys2/MINGW 也视为 Windows
+IS_WINDOWS := $(findstring MINGW,$(UNAME_S))
+ifneq ($(IS_WINDOWS),)
+  UNAME_S := Windows
+endif
+IS_WINDOWS := $(findstring MSYS,$(UNAME_S))
+ifneq ($(IS_WINDOWS),)
+  UNAME_S := Windows
+endif
+
+CXXFLAGS = -O3 -march=native -std=c++17 -Wall -Wextra -D_USE_MATH_DEFINES
+
+# DLL 输出到 engines/release/
+DLL_DIR = ../../release
+
+ifeq ($(UNAME_S),Linux)
+  DLL_TARGET = $(DLL_DIR)/dynamics_cpp.so
+  DLL_FLAGS  = -shared -fPIC
+else ifeq ($(UNAME_S),Darwin)
+  DLL_TARGET = $(DLL_DIR)/dynamics_cpp.dylib
+  DLL_FLAGS  = -dynamiclib
+else
+  # Windows: 完全静态链接，避免依赖运行时 DLL
+  DLL_TARGET = $(DLL_DIR)/dynamics_cpp.dll
+  DLL_FLAGS  = -shared -static
+endif
+
+.PHONY: all dll clean
+
+all: dll
+
+dll: $(DLL_TARGET)
+
+$(DLL_TARGET): $(LIB_SRC) | $(DLL_DIR)
+	$(CXX) $(CXXFLAGS) $(DLL_FLAGS) -o $@ $(LIB_SRC)
+	@echo "  === C++ DLL built: $@ ==="
+
+$(DLL_DIR):
+	mkdir -p $(DLL_DIR)
+
+clean:
+	rm -f $(DLL_TARGET)

engines/src/cpp/dynamics_lib.cpp

@@ -0,0 +1,450 @@
+/**
+ * engines/cpp/dynamics_lib.cpp
+ * -----------------------------
+ * 纯计算 DLL（C++ 版）：无文件 I/O，所有数据由 Python 以 NumPy 数组传入。
+ * 算法与 main.cpp / compute.py 保持完全一致。
+ *
+ * 编译（Windows）:
+ *   g++ -O3 -march=native -std=c++17 -shared -o build/dynamics_cpp.dll dynamics_lib.cpp
+ * 编译（Linux）:
+ *   g++ -O3 -march=native -std=c++17 -shared -fPIC -o build/dynamics_cpp.so dynamics_lib.cpp
+ * 编译（macOS）:
+ *   g++ -O3 -march=native -std=c++17 -dynamiclib -o build/dynamics_cpp.dylib dynamics_lib.cpp
+ */
+
+#ifdef _WIN32
+#  define EXPORT extern "C" __declspec(dllexport)
+#else
+#  define EXPORT extern "C" __attribute__((visibility("default")))
+#endif
+
+#include <cmath>
+#include <cstring>
+#include <cstdlib>
+#include <vector>
+
+/* ── 驱动力结构体 ─────────────────────────────────────────── */
+struct Drivers {
+    int           n_drivers  = 0;
+    const int    *idx        = nullptr;
+    const double *amp        = nullptr;
+    const double *freq       = nullptr;
+    const double *phi        = nullptr;
+    const double *eq         = nullptr;
+    const double *ncycles    = nullptr;
+    const int    *has_period = nullptr;
+    std::vector<double> freeze;   /* [n_drivers*3] 冻结位置（period 结束时锁定）*/
+};
+
+/* ── 加速度：保守力（弹簧键 + 均匀重力场）────────────────── */
+static void accel_conservative(
+    int n, const double *x, const double *y, const double *z,
+    const double *m,
+    double Gx, double Gy, double Gz,
+    int gravity_field, int elastic_force,
+    int n_bonds, const int *bond_pairs,
+    const double *bond_k, const double *bond_r0,
+    double *ax, double *ay, double *az)
+{
+    for (int i = 0; i < n; i++) {
+        ax[i] = gravity_field ? Gx : 0.0;
+        ay[i] = gravity_field ? Gy : 0.0;
+        az[i] = gravity_field ? Gz : 0.0;
+    }
+    if (!elastic_force || n_bonds == 0) return;
+    for (int b = 0; b < n_bonds; b++) {
+        int ii = bond_pairs[b*2];
+        int jj = bond_pairs[b*2+1];
+        double dx = x[jj]-x[ii], dy = y[jj]-y[ii], dz = z[jj]-z[ii];
+        double dist = std::sqrt(dx*dx + dy*dy + dz*dz);
+        if (dist < 1e-12) continue;
+        double fac = bond_k[b] * (dist - bond_r0[b]) / dist;
+        double fx = fac*dx, fy = fac*dy, fz_b = fac*dz;
+        ax[ii] += fx/m[ii];  ay[ii] += fy/m[ii];  az[ii] += fz_b/m[ii];
+        ax[jj] -= fx/m[jj];  ay[jj] -= fy/m[jj];  az[jj] -= fz_b/m[jj];
+    }
+}
+
+/* ── 完整加速度（含阻尼）────────────────────────────────── */
+static void accel_full(
+    int n, const double *x, const double *y, const double *z,
+    const double *vx, const double *vy, const double *vz,
+    const double *m,
+    double Gx, double Gy, double Gz,
+    double Bx, double By, double Bz,
+    int gravity_field, int elastic_force, int damping_force,
+    int n_bonds, const int *bond_pairs,
+    const double *bond_k, const double *bond_r0,
+    double *ax, double *ay, double *az)
+{
+    accel_conservative(n, x, y, z, m, Gx, Gy, Gz,
+                       gravity_field, elastic_force,
+                       n_bonds, bond_pairs, bond_k, bond_r0,
+                       ax, ay, az);
+    if (damping_force) {
+        for (int i = 0; i < n; i++) {
+            ax[i] -= Bx * vx[i] / m[i];
+            ay[i] -= By * vy[i] / m[i];
+            az[i] -= Bz * vz[i] / m[i];
+        }
+    }
+}
+
+/* ── 边界：反弹 ──────────────────────────────────────────── */
+static inline void _limit1(double &p, double &v, double lo, double hi) {
+    if (p > hi) { p = hi; v = -std::fabs(v); }
+    if (p < lo) { p = lo; v =  std::fabs(v); }
+}
+
+/* ── 边界：回绕 ──────────────────────────────────────────── */
+static inline void _wrap1(double &p, double lo, double hi) {
+    if (p > hi) p = lo;
+    if (p < lo) p = hi;
+}
+
+/* ── 边界 + 固定约束 ────────────────────────────────────── */
+static void apply_boundary_and_constraints(
+    int n, double *x, double *y, double *z,
+    double *vx, double *vy, double *vz,
+    const int *fixed, const double *pos_init, double box_a)
+{
+    double lo = -box_a, hi = box_a;
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) continue;
+        _limit1(x[i], vx[i], lo, hi);
+        _limit1(y[i], vy[i], lo, hi);
+        _limit1(z[i], vz[i], lo, hi);
+    }
+    for (int i = 0; i < n; i++) {
+        _wrap1(x[i], lo, hi);
+        _wrap1(y[i], lo, hi);
+        _wrap1(z[i], lo, hi);
+    }
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3+0]) { x[i]  = pos_init[i*3+0]; vx[i] = 0.0; }
+        if (fixed[i*3+1]) { y[i]  = pos_init[i*3+1]; vy[i] = 0.0; }
+        if (fixed[i*3+2]) { z[i]  = pos_init[i*3+2]; vz[i] = 0.0; }
+    }
+}
+
+/* ══════════════════════════════════════════════════════════
+ * 蛙跳法（与 main.cpp leapfrog_step 完全一致）
+ * ══════════════════════════════════════════════════════════ */
+static void leapfrog_step(
+    int n, double *x, double *y, double *z,
+    double *vx, double *vy, double *vz,
+    const double *m, const int *fixed,
+    double Gx, double Gy, double Gz,
+    double Bx, double By, double Bz,
+    int gravity_field, int elastic_force, int damping_force,
+    int n_bonds, const int *bp, const double *bk, const double *br0, double dt)
+{
+    std::vector<double> buf(n * 3);
+    double *ax = buf.data(), *ay = ax+n, *az = ay+n;
+    accel_conservative(n, x, y, z, m, Gx, Gy, Gz,
+                       gravity_field, elastic_force,
+                       n_bonds, bp, bk, br0, ax, ay, az);
+    bool has_damp = damping_force && (Bx != 0.0 || By != 0.0 || Bz != 0.0);
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) continue;
+        if (has_damp) {
+            double ax_ = Bx*dt/(2.0*m[i]);
+            double ay_ = By*dt/(2.0*m[i]);
+            double az_ = Bz*dt/(2.0*m[i]);
+            vx[i] = (vx[i]*(1.0-ax_) + ax[i]*dt) / (1.0+ax_);
+            vy[i] = (vy[i]*(1.0-ay_) + ay[i]*dt) / (1.0+ay_);
+            vz[i] = (vz[i]*(1.0-az_) + az[i]*dt) / (1.0+az_);
+        } else {
+            vx[i] += ax[i]*dt;
+            vy[i] += ay[i]*dt;
+            vz[i] += az[i]*dt;
+        }
+        x[i] += vx[i]*dt;
+        y[i] += vy[i]*dt;
+        z[i] += vz[i]*dt;
+    }
+}
+
+/* ══════════════════════════════════════════════════════════
+ * 显式欧拉法
+ * ══════════════════════════════════════════════════════════ */
+static void euler_step(
+    int n, double *x, double *y, double *z,
+    double *vx, double *vy, double *vz,
+    const double *m, const int *fixed,
+    double Gx, double Gy, double Gz,
+    double Bx, double By, double Bz,
+    int gravity_field, int elastic_force, int damping_force,
+    int n_bonds, const int *bp, const double *bk, const double *br0, double dt)
+{
+    std::vector<double> buf(n * 3);
+    double *ax = buf.data(), *ay = ax+n, *az = ay+n;
+    accel_full(n, x, y, z, vx, vy, vz, m, Gx, Gy, Gz, Bx, By, Bz,
+               gravity_field, elastic_force, damping_force,
+               n_bonds, bp, bk, br0, ax, ay, az);
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) continue;
+        x[i] += vx[i]*dt;  y[i] += vy[i]*dt;  z[i] += vz[i]*dt;
+        vx[i]+= ax[i]*dt;  vy[i]+= ay[i]*dt;  vz[i]+= az[i]*dt;
+    }
+}
+
+/* ══════════════════════════════════════════════════════════
+ * 隐式欧拉法（与 main.cpp implicit_euler_step 完全一致）
+ * ══════════════════════════════════════════════════════════ */
+static void implicit_euler_step(
+    int n, double *x, double *y, double *z,
+    double *vx, double *vy, double *vz,
+    const double *m, const int *fixed,
+    double Gx, double Gy, double Gz,
+    double Bx, double By, double Bz,
+    int gravity_field, int elastic_force, int damping_force,
+    int n_bonds, const int *bp, const double *bk, const double *br0, double dt)
+{
+    std::vector<double> vbuf(n * 3), abuf(n * 3);
+    double *vxn = vbuf.data(), *vyn = vxn+n, *vzn = vyn+n;
+    double *ax  = abuf.data(), *ay  = ax+n,  *az  = ay+n;
+
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) {
+            vxn[i] = vyn[i] = vzn[i] = 0.0; continue;
+        }
+        double gx = Bx/m[i], gy = By/m[i], gz = Bz/m[i];
+        vxn[i] = (vx[i] + Gx*dt) / (1.0 + gx*dt);
+        vyn[i] = (vy[i] + Gy*dt) / (1.0 + gy*dt);
+        vzn[i] = (vz[i] + Gz*dt) / (1.0 + gz*dt);
+    }
+    accel_full(n, x, y, z, vxn, vyn, vzn, m, Gx, Gy, Gz, Bx, By, Bz,
+               gravity_field, elastic_force, damping_force,
+               n_bonds, bp, bk, br0, ax, ay, az);
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) continue;
+        vx[i] += ax[i]*dt;  vy[i] += ay[i]*dt;  vz[i] += az[i]*dt;
+        x[i]  += vx[i]*dt; y[i]  += vy[i]*dt;  z[i]  += vz[i]*dt;
+    }
+}
+
+/* ══════════════════════════════════════════════════════════
+ * 中点法（与 main.cpp midpoint_step 完全一致）
+ * ══════════════════════════════════════════════════════════ */
+static void midpoint_step(
+    int n, double *x, double *y, double *z,
+    double *vx, double *vy, double *vz,
+    const double *m, const int *fixed,
+    double Gx, double Gy, double Gz,
+    double Bx, double By, double Bz,
+    int gravity_field, int elastic_force, int damping_force,
+    int n_bonds, const int *bp, const double *bk, const double *br0, double dt)
+{
+    std::vector<double> buf(n * 9);
+    double *ax  = buf.data();
+    double *ay  = ax+n;  double *az  = ay+n;
+    double *xm  = az+n;  double *ym  = xm+n; double *zm  = ym+n;
+    double *vxm = zm+n;  double *vym = vxm+n; double *vzm = vym+n;
+
+    accel_full(n, x, y, z, vx, vy, vz, m, Gx, Gy, Gz, Bx, By, Bz,
+               gravity_field, elastic_force, damping_force,
+               n_bonds, bp, bk, br0, ax, ay, az);
+
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) {
+            xm[i]=x[i]; ym[i]=y[i]; zm[i]=z[i];
+            vxm[i]=vym[i]=vzm[i]=0.0; continue;
+        }
+        xm[i]  = x[i]  + 0.5*vx[i]*dt;
+        ym[i]  = y[i]  + 0.5*vy[i]*dt;
+        zm[i]  = z[i]  + 0.5*vz[i]*dt;
+        vxm[i] = vx[i] + 0.5*ax[i]*dt;
+        vym[i] = vy[i] + 0.5*ay[i]*dt;
+        vzm[i] = vz[i] + 0.5*az[i]*dt;
+        x[i]   = x[i]  + vxm[i]*dt;
+        y[i]   = y[i]  + vym[i]*dt;
+        z[i]   = z[i]  + vzm[i]*dt;
+    }
+
+    std::vector<double> abuf(n * 3);
+    double *axm = abuf.data(), *aym = axm+n, *azm = aym+n;
+    accel_full(n, xm, ym, zm, vxm, vym, vzm, m, Gx, Gy, Gz, Bx, By, Bz,
+               gravity_field, elastic_force, damping_force,
+               n_bonds, bp, bk, br0, axm, aym, azm);
+    for (int i = 0; i < n; i++) {
+        if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) continue;
+        vx[i] += axm[i]*dt;
+        vy[i] += aym[i]*dt;
+        vz[i] += azm[i]*dt;
+    }
+}
+
+/* ── 驱动力 ─────────────────────────────────────────────── */
+static void apply_driving(
+    int n, double *x, double *y, double *z,
+    double *vx, double *vy, double *vz,
+    double t, int step, double dt, Drivers &drv)
+{
+    (void)n;
+    if (drv.n_drivers == 0) return;
+    constexpr double TWO_PI = 2.0 * 3.14159265358979323846;
+
+    for (int d = 0; d < drv.n_drivers; d++) {
+        int idx = drv.idx[d];
+        double fx = drv.freq[d*3+0];
+        double fy = drv.freq[d*3+1];
+        double fz = drv.freq[d*3+2];
+
+        if (drv.has_period[d]) {
+            double mf = std::fabs(fx) > std::fabs(fy) ? std::fabs(fx) : std::fabs(fy);
+            if (std::fabs(fz) > mf) mf = std::fabs(fz);
+            int period_steps = 0;
+            if (mf > 1e-12)
+                period_steps = (int)(drv.ncycles[d] / mf / dt);
+            if (step > period_steps) {
+                x[idx] = drv.freeze[d*3+0];
+                y[idx] = drv.freeze[d*3+1];
+                z[idx] = drv.freeze[d*3+2];
+                vx[idx] = vy[idx] = vz[idx] = 0.0;
+                continue;
+            }
+            double px = drv.eq[d*3+0] + drv.amp[d*3+0]*std::cos(TWO_PI*fx*t + drv.phi[d*3+0]);
+            double py = drv.eq[d*3+1] + drv.amp[d*3+1]*std::cos(TWO_PI*fy*t + drv.phi[d*3+1]);
+            double pz = drv.eq[d*3+2] + drv.amp[d*3+2]*std::cos(TWO_PI*fz*t + drv.phi[d*3+2]);
+            if (step == period_steps) {
+                drv.freeze[d*3+0] = px;
+                drv.freeze[d*3+1] = py;
+                drv.freeze[d*3+2] = pz;
+            }
+        }
+        x[idx]  = drv.eq[d*3+0] + drv.amp[d*3+0]*std::cos(TWO_PI*fx*t + drv.phi[d*3+0]);
+        y[idx]  = drv.eq[d*3+1] + drv.amp[d*3+1]*std::cos(TWO_PI*fy*t + drv.phi[d*3+1]);
+        z[idx]  = drv.eq[d*3+2] + drv.amp[d*3+2]*std::cos(TWO_PI*fz*t + drv.phi[d*3+2]);
+        vx[idx] = -drv.amp[d*3+0]*TWO_PI*fx*std::sin(TWO_PI*fx*t + drv.phi[d*3+0]);
+        vy[idx] = -drv.amp[d*3+1]*TWO_PI*fy*std::sin(TWO_PI*fy*t + drv.phi[d*3+1]);
+        vz[idx] = -drv.amp[d*3+2]*TWO_PI*fz*std::sin(TWO_PI*fz*t + drv.phi[d*3+2]);
+    }
+}
+
+/* ══════════════════════════════════════════════════════════
+ * 导出函数：run_dynamics（接口与 C 版完全相同）
+ * ══════════════════════════════════════════════════════════ */
+EXPORT int run_dynamics(
+    int n_atoms,
+    const double *pos_init,
+    const double *vel_init,
+    const double *masses,
+    const int    *fixed,
+    int n_bonds,
+    const int    *bond_pairs,
+    const double *bond_k,
+    const double *bond_r0,
+    double box_a, double dt,
+    int NT, int NSTEP, int warmup_steps, int method_id,
+    double Gx, double Gy, double Gz,
+    double Bx, double By, double Bz,
+    int gravity_field, int elastic_force, int damping_force,
+    double gravity_strength,
+    int n_drivers,
+    const int    *drv_idx,
+    const double *drv_amp,
+    const double *drv_freq,
+    const double *drv_phi,
+    const double *drv_eq,
+    const double *drv_ncycles,
+    const int    *drv_has_period,
+    int n_frames,
+    double *out_x, double *out_y, double *out_z,
+    double *out_vx, double *out_vy, double *out_vz,
+    void (*progress_cb)(int step, int total))
+{
+    (void)gravity_strength;
+    int n = n_atoms;
+
+    std::vector<double> xv(n), yv(n), zv(n);
+    std::vector<double> vxv(n), vyv(n), vzv(n);
+    for (int i = 0; i < n; i++) {
+        xv[i]=pos_init[i*3+0]; yv[i]=pos_init[i*3+1]; zv[i]=pos_init[i*3+2];
+        vxv[i]=vel_init[i*3+0]; vyv[i]=vel_init[i*3+1]; vzv[i]=vel_init[i*3+2];
+    }
+    double *x=xv.data(), *y=yv.data(), *z=zv.data();
+    double *vx=vxv.data(), *vy=vyv.data(), *vz=vzv.data();
+
+    Drivers drv;
+    drv.n_drivers  = n_drivers;
+    drv.idx        = drv_idx;
+    drv.amp        = drv_amp;
+    drv.freq       = drv_freq;
+    drv.phi        = drv_phi;
+    drv.eq         = drv_eq;
+    drv.ncycles    = drv_ncycles;
+    drv.has_period = drv_has_period;
+    if (n_drivers > 0)
+        drv.freeze.assign(n_drivers * 3, 0.0);
+
+#define DO_STEP() do { \
+    switch (method_id) { \
+    case 0: euler_step(n,x,y,z,vx,vy,vz,masses,fixed,Gx,Gy,Gz,Bx,By,Bz, \
+                       gravity_field,elastic_force,damping_force, \
+                       n_bonds,bond_pairs,bond_k,bond_r0,dt); break; \
+    case 1: implicit_euler_step(n,x,y,z,vx,vy,vz,masses,fixed,Gx,Gy,Gz,Bx,By,Bz, \
+                       gravity_field,elastic_force,damping_force, \
+                       n_bonds,bond_pairs,bond_k,bond_r0,dt); break; \
+    case 2: midpoint_step(n,x,y,z,vx,vy,vz,masses,fixed,Gx,Gy,Gz,Bx,By,Bz, \
+                       gravity_field,elastic_force,damping_force, \
+                       n_bonds,bond_pairs,bond_k,bond_r0,dt); break; \
+    default: leapfrog_step(n,x,y,z,vx,vy,vz,masses,fixed,Gx,Gy,Gz,Bx,By,Bz, \
+                       gravity_field,elastic_force,damping_force, \
+                       n_bonds,bond_pairs,bond_k,bond_r0,dt); break; \
+    } \
+    apply_boundary_and_constraints(n,x,y,z,vx,vy,vz,fixed,pos_init,box_a); \
+} while(0)
+
+    /* 蛙跳法：初始化 v(-dt/2) */
+    if (method_id == 3) {
+        std::vector<double> ibuf(n * 3);
+        double *ax0=ibuf.data(), *ay0=ax0+n, *az0=ay0+n;
+        accel_conservative(n, x, y, z, masses, Gx, Gy, Gz,
+                           gravity_field, elastic_force,
+                           n_bonds, bond_pairs, bond_k, bond_r0,
+                           ax0, ay0, az0);
+        for (int i = 0; i < n; i++) {
+            if (fixed[i*3] && fixed[i*3+1] && fixed[i*3+2]) continue;
+            vx[i] -= 0.5*ax0[i]*dt;
+            vy[i] -= 0.5*ay0[i]*dt;
+            vz[i] -= 0.5*az0[i]*dt;
+        }
+    }
+
+    /* 初始驱动 t=0 */
+    if (n_drivers > 0) apply_driving(n, x, y, z, vx, vy, vz, 0.0, 0, dt, drv);
+
+    /* 预热 */
+    for (int s = 0; s < warmup_steps; s++) {
+        double tw = (s + 1) * dt;
+        if (n_drivers > 0) apply_driving(n, x, y, z, vx, vy, vz, tw, s, dt, drv);
+        DO_STEP();
+    }
+
+    /* 记录循环 */
+    int record_steps = NT - warmup_steps;
+    int prog_interval = std::max(1, record_steps / 100);
+    int frame_idx = 0;
+
+    for (int s = 0; s < record_steps; s++) {
+        if (progress_cb && s % prog_interval == 0 && s > 0)
+            progress_cb(s, record_steps);
+
+        double t = (s + warmup_steps) * dt;
+        if (n_drivers > 0) apply_driving(n, x, y, z, vx, vy, vz, t, s, dt, drv);
+
+        if (s % NSTEP == 0 && frame_idx < n_frames) {
+            int base = frame_idx * n;
+            for (int i = 0; i < n; i++) {
+                out_x [base+i] = x[i];  out_y [base+i] = y[i];  out_z [base+i] = z[i];
+                out_vx[base+i] = vx[i]; out_vy[base+i] = vy[i]; out_vz[base+i] = vz[i];
+            }
+            frame_idx++;
+        }
+        DO_STEP();
+    }
+
+#undef DO_STEP
+    return 0;
+}

engines/src/fortran/Makefile

@@ -0,0 +1,49 @@
+# engines/src/fortran/Makefile
+# 编译 DLL 到 engines/release/（主程序通过 ctypes 直接调用）
+
+FC      = gfortran
+FFLAGS  = -O3 -march=native -Wall -Wextra
+LIB_SRC = dynamics_lib.f90
+
+UNAME_S := $(shell uname -s 2>/dev/null || echo Windows)
+
+# Windows 检测：Msys2/MINGW 也视为 Windows
+IS_WINDOWS := $(findstring MINGW,$(UNAME_S))
+ifneq ($(IS_WINDOWS),)
+  UNAME_S := Windows
+endif
+IS_WINDOWS := $(findstring MSYS,$(UNAME_S))
+ifneq ($(IS_WINDOWS),)
+  UNAME_S := Windows
+endif
+
+# DLL 输出到 engines/release/
+DLL_DIR = ../../release
+
+ifeq ($(UNAME_S),Linux)
+  DLL_TARGET = $(DLL_DIR)/dynamics_f90.so
+  DLL_FLAGS  = -shared -fPIC
+else ifeq ($(UNAME_S),Darwin)
+  DLL_TARGET = $(DLL_DIR)/dynamics_f90.dylib
+  DLL_FLAGS  = -dynamiclib
+else
+  # Windows: 完全静态链接，避免依赖 libgfortran-5.dll
+  DLL_TARGET = $(DLL_DIR)/dynamics_f90.dll
+  DLL_FLAGS  = -shared -fPIC -static
+endif
+
+.PHONY: all dll clean
+
+all: dll
+
+dll: $(DLL_TARGET)
+
+$(DLL_TARGET): $(LIB_SRC) | $(DLL_DIR)
+	$(FC) $(FFLAGS) $(DLL_FLAGS) -o $@ $(LIB_SRC)
+	@echo "  === Fortran DLL built: $@ ==="
+
+$(DLL_DIR):
+	mkdir -p $(DLL_DIR)
+
+clean:
+	rm -f $(DLL_TARGET)

engines/src/fortran/dynamics_lib.f90

@@ -0,0 +1,483 @@
+! engines/fortran/dynamics_lib.f90
+! ---------------------------------
+! 纯计算 DLL（Fortran 版）：无文件 I/O，由 Python ctypes 调用。
+! 算法与 main.f90 / compute.py 完全一致。
+! 使用 iso_c_binding 导出 C 兼容接口。
+!
+! 编译（Windows）:
+!   gfortran -O3 -march=native -shared -fPIC -o build/dynamics_f90.dll dynamics_lib.f90
+! 编译（Linux）:
+!   gfortran -O3 -march=native -shared -fPIC -o build/dynamics_f90.so dynamics_lib.f90
+! 编译（macOS）:
+!   gfortran -O3 -march=native -dynamiclib -o build/dynamics_f90.dylib dynamics_lib.f90
+
+module dynamics_dll
+    use iso_c_binding, only: c_int, c_double, c_funptr, c_f_procpointer, c_associated
+    implicit none
+    private
+
+    real(c_double), parameter :: TWO_PI = 2.0d0 * 3.14159265358979323846d0
+
+    public :: run_dynamics
+
+contains
+
+! ── 保守加速度 ───────────────────────────────────────────────
+subroutine accel_conservative(n, x, y, z, m, Gx, Gy, Gz, &
+                               gravity_field, elastic_force, &
+                               n_bonds, bond_pairs, bond_k, bond_r0, &
+                               ax, ay, az)
+    integer,        intent(in)  :: n, gravity_field, elastic_force, n_bonds
+    real(c_double), intent(in)  :: x(n), y(n), z(n), m(n)
+    real(c_double), intent(in)  :: Gx, Gy, Gz
+    integer,        intent(in)  :: bond_pairs(2, n_bonds)
+    real(c_double), intent(in)  :: bond_k(n_bonds), bond_r0(n_bonds)
+    real(c_double), intent(out) :: ax(n), ay(n), az(n)
+
+    integer        :: b, ii, jj
+    real(c_double) :: dx, dy, dz, dist, fac, fx, fy, fz_b
+
+    if (gravity_field /= 0) then
+        ax = Gx; ay = Gy; az = Gz
+    else
+        ax = 0.0d0; ay = 0.0d0; az = 0.0d0
+    end if
+
+    if (elastic_force == 0 .or. n_bonds == 0) return
+
+    do b = 1, n_bonds
+        ii = bond_pairs(1, b) + 1   ! 0-based → 1-based
+        jj = bond_pairs(2, b) + 1
+        dx = x(jj)-x(ii); dy = y(jj)-y(ii); dz = z(jj)-z(ii)
+        dist = sqrt(dx*dx + dy*dy + dz*dz)
+        if (dist < 1.0d-12) cycle
+        fac = bond_k(b) * (dist - bond_r0(b)) / dist
+        fx = fac*dx; fy = fac*dy; fz_b = fac*dz
+        ax(ii) = ax(ii) + fx/m(ii);  ay(ii) = ay(ii) + fy/m(ii);  az(ii) = az(ii) + fz_b/m(ii)
+        ax(jj) = ax(jj) - fx/m(jj);  ay(jj) = ay(jj) - fy/m(jj);  az(jj) = az(jj) - fz_b/m(jj)
+    end do
+end subroutine
+
+! ── 完整加速度（含阻尼）──────────────────────────────────────
+subroutine accel_full(n, x, y, z, vx, vy, vz, m, Gx, Gy, Gz, Bx, By, Bz, &
+                      gravity_field, elastic_force, damping_force, &
+                      n_bonds, bond_pairs, bond_k, bond_r0, ax, ay, az)
+    integer,        intent(in)  :: n, gravity_field, elastic_force, damping_force, n_bonds
+    real(c_double), intent(in)  :: x(n), y(n), z(n), vx(n), vy(n), vz(n), m(n)
+    real(c_double), intent(in)  :: Gx, Gy, Gz, Bx, By, Bz
+    integer,        intent(in)  :: bond_pairs(2, n_bonds)
+    real(c_double), intent(in)  :: bond_k(n_bonds), bond_r0(n_bonds)
+    real(c_double), intent(out) :: ax(n), ay(n), az(n)
+
+    integer :: i
+
+    call accel_conservative(n, x, y, z, m, Gx, Gy, Gz, &
+                            gravity_field, elastic_force, &
+                            n_bonds, bond_pairs, bond_k, bond_r0, ax, ay, az)
+    if (damping_force /= 0) then
+        do i = 1, n
+            ax(i) = ax(i) - Bx*vx(i)/m(i)
+            ay(i) = ay(i) - By*vy(i)/m(i)
+            az(i) = az(i) - Bz*vz(i)/m(i)
+        end do
+    end if
+end subroutine
+
+! ── 边界 + 固定约束 ──────────────────────────────────────────
+subroutine apply_bc(n, x, y, z, vx, vy, vz, fixed, pos_init, box_a)
+    integer,        intent(in)    :: n
+    real(c_double), intent(inout) :: x(n), y(n), z(n), vx(n), vy(n), vz(n)
+    integer,        intent(in)    :: fixed(3, n)
+    real(c_double), intent(in)    :: pos_init(3, n), box_a
+
+    integer        :: i
+    real(c_double) :: lo, hi
+
+    lo = -box_a; hi = box_a
+
+    ! 反弹
+    do i = 1, n
+        if (fixed(1,i)/=0 .and. fixed(2,i)/=0 .and. fixed(3,i)/=0) cycle
+        if (x(i)>hi) then; x(i)=hi; vx(i)=-abs(vx(i)); end if
+        if (x(i)<lo) then; x(i)=lo; vx(i)= abs(vx(i)); end if
+        if (y(i)>hi) then; y(i)=hi; vy(i)=-abs(vy(i)); end if
+        if (y(i)<lo) then; y(i)=lo; vy(i)= abs(vy(i)); end if
+        if (z(i)>hi) then; z(i)=hi; vz(i)=-abs(vz(i)); end if
+        if (z(i)<lo) then; z(i)=lo; vz(i)= abs(vz(i)); end if
+    end do
+    ! 回绕
+    do i = 1, n
+        if (x(i)>hi) x(i)=lo;  if (x(i)<lo) x(i)=hi
+        if (y(i)>hi) y(i)=lo;  if (y(i)<lo) y(i)=hi
+        if (z(i)>hi) z(i)=lo;  if (z(i)<lo) z(i)=hi
+    end do
+    ! 逐自由度固定约束
+    do i = 1, n
+        if (fixed(1,i)/=0) then; x(i)=pos_init(1,i); vx(i)=0.0d0; end if
+        if (fixed(2,i)/=0) then; y(i)=pos_init(2,i); vy(i)=0.0d0; end if
+        if (fixed(3,i)/=0) then; z(i)=pos_init(3,i); vz(i)=0.0d0; end if
+    end do
+end subroutine
+
+! ── 蛙跳法 ───────────────────────────────────────────────────
+subroutine leapfrog_step(n, x, y, z, vx, vy, vz, m, fixed, &
+                          Gx, Gy, Gz, Bx, By, Bz, &
+                          gravity_field, elastic_force, damping_force, &
+                          n_bonds, bond_pairs, bond_k, bond_r0, dt)
+    integer,        intent(in)    :: n, gravity_field, elastic_force, damping_force, n_bonds
+    real(c_double), intent(inout) :: x(n), y(n), z(n), vx(n), vy(n), vz(n)
+    real(c_double), intent(in)    :: m(n), bond_k(n_bonds), bond_r0(n_bonds)
+    integer,        intent(in)    :: fixed(3,n), bond_pairs(2,n_bonds)
+    real(c_double), intent(in)    :: Gx, Gy, Gz, Bx, By, Bz, dt
+
+    real(c_double) :: ax(n), ay(n), az(n), ax_, ay_, az_
+    logical        :: has_damp
+    integer        :: i
+
+    call accel_conservative(n, x, y, z, m, Gx, Gy, Gz, &
+                            gravity_field, elastic_force, &
+                            n_bonds, bond_pairs, bond_k, bond_r0, ax, ay, az)
+    has_damp = (damping_force/=0) .and. (abs(Bx)+abs(By)+abs(Bz) > 0.0d0)
+    do i = 1, n
+        if (fixed(1,i)/=0 .and. fixed(2,i)/=0 .and. fixed(3,i)/=0) cycle
+        if (has_damp) then
+            ax_ = Bx*dt/(2.0d0*m(i)); ay_ = By*dt/(2.0d0*m(i)); az_ = Bz*dt/(2.0d0*m(i))
+            vx(i) = (vx(i)*(1.0d0-ax_) + ax(i)*dt)/(1.0d0+ax_)
+            vy(i) = (vy(i)*(1.0d0-ay_) + ay(i)*dt)/(1.0d0+ay_)
+            vz(i) = (vz(i)*(1.0d0-az_) + az(i)*dt)/(1.0d0+az_)
+        else
+            vx(i) = vx(i)+ax(i)*dt;  vy(i) = vy(i)+ay(i)*dt;  vz(i) = vz(i)+az(i)*dt
+        end if
+        x(i) = x(i)+vx(i)*dt;  y(i) = y(i)+vy(i)*dt;  z(i) = z(i)+vz(i)*dt
+    end do
+end subroutine
+
+! ── 显式欧拉法 ───────────────────────────────────────────────
+subroutine euler_step(n, x, y, z, vx, vy, vz, m, fixed, &
+                       Gx, Gy, Gz, Bx, By, Bz, &
+                       gravity_field, elastic_force, damping_force, &
+                       n_bonds, bond_pairs, bond_k, bond_r0, dt)
+    integer,        intent(in)    :: n, gravity_field, elastic_force, damping_force, n_bonds
+    real(c_double), intent(inout) :: x(n), y(n), z(n), vx(n), vy(n), vz(n)
+    real(c_double), intent(in)    :: m(n), bond_k(n_bonds), bond_r0(n_bonds)
+    integer,        intent(in)    :: fixed(3,n), bond_pairs(2,n_bonds)
+    real(c_double), intent(in)    :: Gx, Gy, Gz, Bx, By, Bz, dt
+
+    real(c_double) :: ax(n), ay(n), az(n)
+    integer        :: i
+
+    call accel_full(n, x, y, z, vx, vy, vz, m, Gx, Gy, Gz, Bx, By, Bz, &
+                    gravity_field, elastic_force, damping_force, &
+                    n_bonds, bond_pairs, bond_k, bond_r0, ax, ay, az)
+    do i = 1, n
+        if (fixed(1,i)/=0 .and. fixed(2,i)/=0 .and. fixed(3,i)/=0) cycle
+        x(i) = x(i)+vx(i)*dt;  y(i) = y(i)+vy(i)*dt;  z(i) = z(i)+vz(i)*dt
+        vx(i)= vx(i)+ax(i)*dt; vy(i)= vy(i)+ay(i)*dt; vz(i)= vz(i)+az(i)*dt
+    end do
+end subroutine
+
+! ── 隐式欧拉法 ───────────────────────────────────────────────
+subroutine implicit_euler_step(n, x, y, z, vx, vy, vz, m, fixed, &
+                                Gx, Gy, Gz, Bx, By, Bz, &
+                                gravity_field, elastic_force, damping_force, &
+                                n_bonds, bond_pairs, bond_k, bond_r0, dt)
+    integer,        intent(in)    :: n, gravity_field, elastic_force, damping_force, n_bonds
+    real(c_double), intent(inout) :: x(n), y(n), z(n), vx(n), vy(n), vz(n)
+    real(c_double), intent(in)    :: m(n), bond_k(n_bonds), bond_r0(n_bonds)
+    integer,        intent(in)    :: fixed(3,n), bond_pairs(2,n_bonds)
+    real(c_double), intent(in)    :: Gx, Gy, Gz, Bx, By, Bz, dt
+
+    real(c_double) :: vxn(n), vyn(n), vzn(n), ax(n), ay(n), az(n)
+    real(c_double) :: gamma_x, gamma_y, gamma_z
+    integer        :: i
+
+    do i = 1, n
+        if (fixed(1,i)/=0 .and. fixed(2,i)/=0 .and. fixed(3,i)/=0) then
+            vxn(i)=0.0d0; vyn(i)=0.0d0; vzn(i)=0.0d0; cycle
+        end if
+        gamma_x = Bx/m(i); gamma_y = By/m(i); gamma_z = Bz/m(i)
+        vxn(i) = (vx(i)+Gx*dt)/(1.0d0+gamma_x*dt)
+        vyn(i) = (vy(i)+Gy*dt)/(1.0d0+gamma_y*dt)
+        vzn(i) = (vz(i)+Gz*dt)/(1.0d0+gamma_z*dt)
+    end do
+    call accel_full(n, x, y, z, vxn, vyn, vzn, m, Gx, Gy, Gz, Bx, By, Bz, &
+                    gravity_field, elastic_force, damping_force, &
+                    n_bonds, bond_pairs, bond_k, bond_r0, ax, ay, az)
+    do i = 1, n
+        if (fixed(1,i)/=0 .and. fixed(2,i)/=0 .and. fixed(3,i)/=0) cycle
+        vx(i)=vx(i)+ax(i)*dt; vy(i)=vy(i)+ay(i)*dt; vz(i)=vz(i)+az(i)*dt
+        x(i) =x(i) +vx(i)*dt; y(i) =y(i) +vy(i)*dt; z(i) =z(i) +vz(i)*dt
+    end do
+end subroutine
+
+! ── 中点法 ───────────────────────────────────────────────────
+subroutine midpoint_step(n, x, y, z, vx, vy, vz, m, fixed, &
+                          Gx, Gy, Gz, Bx, By, Bz, &
+                          gravity_field, elastic_force, damping_force, &
+                          n_bonds, bond_pairs, bond_k, bond_r0, dt)
+    integer,        intent(in)    :: n, gravity_field, elastic_force, damping_force, n_bonds
+    real(c_double), intent(inout) :: x(n), y(n), z(n), vx(n), vy(n), vz(n)
+    real(c_double), intent(in)    :: m(n), bond_k(n_bonds), bond_r0(n_bonds)
+    integer,        intent(in)    :: fixed(3,n), bond_pairs(2,n_bonds)
+    real(c_double), intent(in)    :: Gx, Gy, Gz, Bx, By, Bz, dt
+
+    real(c_double) :: ax(n), ay(n), az(n)
+    real(c_double) :: xm(n), ym(n), zm(n), vxm(n), vym(n), vzm(n)
+    real(c_double) :: axm(n), aym(n), azm(n)
+    integer        :: i
+
+    call accel_full(n, x, y, z, vx, vy, vz, m, Gx, Gy, Gz, Bx, By, Bz, &
+                    gravity_field, elastic_force, damping_force, &
+                    n_bonds, bond_pairs, bond_k, bond_r0, ax, ay, az)
+    do i = 1, n
+        if (fixed(1,i)/=0 .and. fixed(2,i)/=0 .and. fixed(3,i)/=0) then
+            xm(i)=x(i); ym(i)=y(i); zm(i)=z(i)
+            vxm(i)=0.0d0; vym(i)=0.0d0; vzm(i)=0.0d0; cycle
+        end if
+        xm(i)  = x(i) +0.5d0*vx(i)*dt;  ym(i)  = y(i) +0.5d0*vy(i)*dt;  zm(i)  = z(i) +0.5d0*vz(i)*dt
+        vxm(i) = vx(i)+0.5d0*ax(i)*dt;  vym(i) = vy(i)+0.5d0*ay(i)*dt;  vzm(i) = vz(i)+0.5d0*az(i)*dt
+        x(i)   = x(i) +vxm(i)*dt;        y(i)   = y(i) +vym(i)*dt;        z(i)   = z(i) +vzm(i)*dt
+    end do
+    call accel_full(n, xm, ym, zm, vxm, vym, vzm, m, Gx, Gy, Gz, Bx, By, Bz, &
+                    gravity_field, elastic_force, damping_force, &
+                    n_bonds, bond_pairs, bond_k, bond_r0, axm, aym, azm)
+    do i = 1, n
+        if (fixed(1,i)/=0 .and. fixed(2,i)/=0 .and. fixed(3,i)/=0) cycle
+        vx(i)=vx(i)+axm(i)*dt; vy(i)=vy(i)+aym(i)*dt; vz(i)=vz(i)+azm(i)*dt
+    end do
+end subroutine
+
+! ── 驱动力施加 ───────────────────────────────────────────────
+subroutine apply_drive(n, x, y, z, vx, vy, vz, t, step, dt, &
+                        nd, drv_idx, drv_amp, drv_freq, drv_phi, &
+                        drv_eq, drv_ncycles, drv_has_period, freeze)
+    integer,        intent(in)    :: n, nd, step
+    real(c_double), intent(inout) :: x(n), y(n), z(n), vx(n), vy(n), vz(n)
+    real(c_double), intent(in)    :: t, dt
+    integer,        intent(in)    :: drv_idx(nd), drv_has_period(nd)
+    real(c_double), intent(in)    :: drv_amp(3,nd), drv_freq(3,nd)
+    real(c_double), intent(in)    :: drv_phi(3,nd), drv_eq(3,nd)
+    real(c_double), intent(in)    :: drv_ncycles(nd)
+    real(c_double), intent(inout) :: freeze(3,nd)
+
+    integer        :: d, idx, ps
+    real(c_double) :: fx, fy, fz, mf, px, py, pz
+
+    do d = 1, nd
+        idx = drv_idx(d) + 1   ! 0-based → 1-based
+        fx = drv_freq(1,d); fy = drv_freq(2,d); fz = drv_freq(3,d)
+
+        if (drv_has_period(d) /= 0) then
+            mf = max(abs(fx), max(abs(fy), abs(fz)))
+            ps = 0
+            if (mf > 1.0d-12) ps = int(drv_ncycles(d)/mf/dt)
+            if (step > ps) then
+                x(idx)=freeze(1,d); y(idx)=freeze(2,d); z(idx)=freeze(3,d)
+                vx(idx)=0.0d0; vy(idx)=0.0d0; vz(idx)=0.0d0
+                cycle
+            end if
+            px = drv_eq(1,d)+drv_amp(1,d)*cos(TWO_PI*fx*t+drv_phi(1,d))
+            py = drv_eq(2,d)+drv_amp(2,d)*cos(TWO_PI*fy*t+drv_phi(2,d))
+            pz = drv_eq(3,d)+drv_amp(3,d)*cos(TWO_PI*fz*t+drv_phi(3,d))
+            if (step == ps) then
+                freeze(1,d)=px; freeze(2,d)=py; freeze(3,d)=pz
+            end if
+        end if
+        x(idx)  = drv_eq(1,d)+drv_amp(1,d)*cos(TWO_PI*fx*t+drv_phi(1,d))
+        y(idx)  = drv_eq(2,d)+drv_amp(2,d)*cos(TWO_PI*fy*t+drv_phi(2,d))
+        z(idx)  = drv_eq(3,d)+drv_amp(3,d)*cos(TWO_PI*fz*t+drv_phi(3,d))
+        vx(idx) = -drv_amp(1,d)*TWO_PI*fx*sin(TWO_PI*fx*t+drv_phi(1,d))
+        vy(idx) = -drv_amp(2,d)*TWO_PI*fy*sin(TWO_PI*fy*t+drv_phi(2,d))
+        vz(idx) = -drv_amp(3,d)*TWO_PI*fz*sin(TWO_PI*fz*t+drv_phi(3,d))
+    end do
+end subroutine
+
+! ══════════════════════════════════════════════════════════════
+! 导出函数：run_dynamics（C 兼容接口，bind(C)）
+! 接口与 C/C++ DLL 完全相同（扁平 C-contiguous 数组）。
+! ══════════════════════════════════════════════════════════════
+integer(c_int) function run_dynamics( &
+    n_atoms, pos_init, vel_init, masses, fixed, &
+    n_bonds, bond_pairs, bond_k, bond_r0, &
+    box_a, dt, NT, NSTEP, warmup_steps, method_id, &
+    Gx, Gy, Gz, Bx, By, Bz, &
+    gravity_field, elastic_force, damping_force, gravity_strength, &
+    n_drivers, drv_idx, drv_amp, drv_freq, drv_phi, drv_eq, &
+    drv_ncycles, drv_has_period, &
+    n_frames, out_x, out_y, out_z, out_vx, out_vy, out_vz, &
+    progress_cb) &
+    bind(C, name="run_dynamics")
+
+    integer(c_int),  value, intent(in) :: n_atoms, n_bonds, NT, NSTEP
+    integer(c_int),  value, intent(in) :: warmup_steps, method_id
+    integer(c_int),  value, intent(in) :: gravity_field, elastic_force, damping_force
+    integer(c_int),  value, intent(in) :: n_drivers, n_frames
+    real(c_double),  value, intent(in) :: box_a, dt
+    real(c_double),  value, intent(in) :: Gx, Gy, Gz, Bx, By, Bz
+    real(c_double),  value, intent(in) :: gravity_strength
+
+    ! 扁平数组：Python 传入 C-contiguous int32/float64
+    ! Fortran 以列优先解释，维度反转：(3,n) 对应 C 的 n×3
+    real(c_double),  intent(in)  :: pos_init(3, n_atoms)
+    real(c_double),  intent(in)  :: vel_init(3, n_atoms)
+    real(c_double),  intent(in)  :: masses(n_atoms)
+    integer(c_int),  intent(in)  :: fixed(3, n_atoms)
+    integer(c_int),  intent(in)  :: bond_pairs(2, n_bonds)
+    real(c_double),  intent(in)  :: bond_k(n_bonds), bond_r0(n_bonds)
+    integer(c_int),  intent(in)  :: drv_idx(n_drivers)
+    real(c_double),  intent(in)  :: drv_amp(3, n_drivers)
+    real(c_double),  intent(in)  :: drv_freq(3, n_drivers)
+    real(c_double),  intent(in)  :: drv_phi(3, n_drivers)
+    real(c_double),  intent(in)  :: drv_eq(3, n_drivers)
+    real(c_double),  intent(in)  :: drv_ncycles(n_drivers)
+    integer(c_int),  intent(in)  :: drv_has_period(n_drivers)
+
+    real(c_double),  intent(out) :: out_x(n_atoms, n_frames)
+    real(c_double),  intent(out) :: out_y(n_atoms, n_frames)
+    real(c_double),  intent(out) :: out_z(n_atoms, n_frames)
+    real(c_double),  intent(out) :: out_vx(n_atoms, n_frames)
+    real(c_double),  intent(out) :: out_vy(n_atoms, n_frames)
+    real(c_double),  intent(out) :: out_vz(n_atoms, n_frames)
+
+    type(c_funptr),  value, intent(in) :: progress_cb
+
+    ! 进度回调接口
+    abstract interface
+        subroutine cb_iface(step, total) bind(C)
+            use iso_c_binding
+            integer(c_int), value :: step, total
+        end subroutine
+    end interface
+    procedure(cb_iface), pointer :: cb_ptr
+
+    integer        :: n, s, frame_idx, record_steps, prog_interval, nd
+    real(c_double) :: t, tw
+    real(c_double), allocatable :: x(:), y(:), z(:), vx(:), vy(:), vz(:)
+    real(c_double), allocatable :: ax0(:), ay0(:), az0(:)
+    real(c_double), allocatable :: freeze(:,:)
+    logical        :: has_cb
+
+    n  = n_atoms
+    nd = n_drivers
+
+    allocate(x(n), y(n), z(n), vx(n), vy(n), vz(n))
+    do s = 1, n
+        x(s)  = pos_init(1,s); y(s)  = pos_init(2,s); z(s)  = pos_init(3,s)
+        vx(s) = vel_init(1,s); vy(s) = vel_init(2,s); vz(s) = vel_init(3,s)
+    end do
+
+    allocate(freeze(3, max(nd,1)))
+    freeze = 0.0d0
+
+    has_cb = c_associated(progress_cb)
+    if (has_cb) call c_f_procpointer(progress_cb, cb_ptr)
+
+    ! ── 蛙跳法：初始化 v(-dt/2) ─────────────────────────────
+    if (method_id == 3) then
+        allocate(ax0(n), ay0(n), az0(n))
+        call accel_conservative(n, x, y, z, masses, Gx, Gy, Gz, &
+                                gravity_field, elastic_force, &
+                                n_bonds, bond_pairs, bond_k, bond_r0, ax0, ay0, az0)
+        do s = 1, n
+            if (fixed(1,s)/=0 .and. fixed(2,s)/=0 .and. fixed(3,s)/=0) cycle
+            vx(s)=vx(s)-0.5d0*ax0(s)*dt
+            vy(s)=vy(s)-0.5d0*ay0(s)*dt
+            vz(s)=vz(s)-0.5d0*az0(s)*dt
+        end do
+        deallocate(ax0, ay0, az0)
+    end if
+
+    ! ── 初始驱动 t=0 ─────────────────────────────────────────
+    if (nd > 0) call apply_drive(n, x, y, z, vx, vy, vz, 0.0d0, 0, dt, &
+                                  nd, drv_idx, drv_amp, drv_freq, drv_phi, &
+                                  drv_eq, drv_ncycles, drv_has_period, freeze)
+
+    ! ── 预热 ─────────────────────────────────────────────────
+    do s = 0, warmup_steps-1
+        tw = (s+1)*dt
+        if (nd>0) call apply_drive(n, x, y, z, vx, vy, vz, tw, s, dt, &
+                                    nd, drv_idx, drv_amp, drv_freq, drv_phi, &
+                                    drv_eq, drv_ncycles, drv_has_period, freeze)
+        call do_step(n, x, y, z, vx, vy, vz, masses, fixed, &
+                     Gx, Gy, Gz, Bx, By, Bz, &
+                     gravity_field, elastic_force, damping_force, &
+                     n_bonds, bond_pairs, bond_k, bond_r0, dt, method_id, &
+                     pos_init, box_a)
+    end do
+
+    ! ── 记录循环 ─────────────────────────────────────────────
+    record_steps = NT - warmup_steps
+    prog_interval = max(1, record_steps/100)
+    frame_idx = 0
+
+    do s = 0, record_steps-1
+        if (has_cb .and. mod(s, prog_interval)==0 .and. s>0) call cb_ptr(s, record_steps)
+
+        t = (s+warmup_steps)*dt
+        if (nd>0) call apply_drive(n, x, y, z, vx, vy, vz, t, s, dt, &
+                                    nd, drv_idx, drv_amp, drv_freq, drv_phi, &
+                                    drv_eq, drv_ncycles, drv_has_period, freeze)
+
+        if (mod(s, NSTEP)==0 .and. frame_idx<n_frames) then
+            frame_idx = frame_idx+1
+            out_x(:, frame_idx)  = x
+            out_y(:, frame_idx)  = y
+            out_z(:, frame_idx)  = z
+            out_vx(:, frame_idx) = vx
+            out_vy(:, frame_idx) = vy
+            out_vz(:, frame_idx) = vz
+        end if
+
+        call do_step(n, x, y, z, vx, vy, vz, masses, fixed, &
+                     Gx, Gy, Gz, Bx, By, Bz, &
+                     gravity_field, elastic_force, damping_force, &
+                     n_bonds, bond_pairs, bond_k, bond_r0, dt, method_id, &
+                     pos_init, box_a)
+    end do
+
+    deallocate(x, y, z, vx, vy, vz, freeze)
+    run_dynamics = 0
+
+contains
+
+    subroutine do_step(n, x, y, z, vx, vy, vz, m, fixed, &
+                       Gx, Gy, Gz, Bx, By, Bz, &
+                       gravity_field, elastic_force, damping_force, &
+                       n_bonds, bond_pairs, bond_k, bond_r0, dt, method_id, &
+                       pos_init, box_a)
+        integer,        intent(in)    :: n, gravity_field, elastic_force, damping_force
+        integer,        intent(in)    :: n_bonds, method_id
+        real(c_double), intent(inout) :: x(n), y(n), z(n), vx(n), vy(n), vz(n)
+        real(c_double), intent(in)    :: m(n), bond_k(n_bonds), bond_r0(n_bonds)
+        integer,        intent(in)    :: fixed(3,n), bond_pairs(2,n_bonds)
+        real(c_double), intent(in)    :: Gx, Gy, Gz, Bx, By, Bz, dt, box_a
+        real(c_double), intent(in)    :: pos_init(3, n)
+
+        select case (method_id)
+        case (0)
+            call euler_step(n, x, y, z, vx, vy, vz, m, fixed, &
+                            Gx, Gy, Gz, Bx, By, Bz, &
+                            gravity_field, elastic_force, damping_force, &
+                            n_bonds, bond_pairs, bond_k, bond_r0, dt)
+        case (1)
+            call implicit_euler_step(n, x, y, z, vx, vy, vz, m, fixed, &
+                            Gx, Gy, Gz, Bx, By, Bz, &
+                            gravity_field, elastic_force, damping_force, &
+                            n_bonds, bond_pairs, bond_k, bond_r0, dt)
+        case (2)
+            call midpoint_step(n, x, y, z, vx, vy, vz, m, fixed, &
+                            Gx, Gy, Gz, Bx, By, Bz, &
+                            gravity_field, elastic_force, damping_force, &
+                            n_bonds, bond_pairs, bond_k, bond_r0, dt)
+        case default
+            call leapfrog_step(n, x, y, z, vx, vy, vz, m, fixed, &
+                            Gx, Gy, Gz, Bx, By, Bz, &
+                            gravity_field, elastic_force, damping_force, &
+                            n_bonds, bond_pairs, bond_k, bond_r0, dt)
+        end select
+        call apply_bc(n, x, y, z, vx, vy, vz, fixed, pos_init, box_a)
+    end subroutine do_step
+
+end function run_dynamics
+
+end module dynamics_dll

examples/Readme.html

@@ -0,0 +1,449 @@
+<!DOCTYPE html>
+<html lang="zh-CN">
+<head>
+<meta charset="UTF-8">
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<title>Dynamics 示例案例总览</title>
+<style>
+  :root {
+    --bg: #0d1117;
+    --surface: #161b22;
+    --border: #30363d;
+    --text: #c9d1d9;
+    --text-dim: #8b949e;
+    --accent: #58a6ff;
+    --green: #3fb950;
+    --orange: #d29922;
+    --red: #f85149;
+  }
+  * { margin: 0; padding: 0; box-sizing: border-box; }
+  body {
+    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", "Noto Sans SC", Helvetica, Arial, sans-serif;
+    background: var(--bg);
+    color: var(--text);
+    line-height: 1.6;
+    padding: 40px 24px;
+  }
+  .container { max-width: 960px; margin: 0 auto; }
+
+  h1 { font-size: 2rem; margin-bottom: 8px; color: #f0f6fc; }
+  h1 small { font-size: 1rem; color: var(--text-dim); font-weight: 400; }
+  .subtitle { color: var(--text-dim); margin-bottom: 32px; }
+
+  h2 {
+    font-size: 1.4rem;
+    margin-top: 40px;
+    margin-bottom: 16px;
+    padding-bottom: 8px;
+    border-bottom: 1px solid var(--border);
+    color: #f0f6fc;
+  }
+
+  /* 案例总览表格 */
+  .case-grid {
+    display: grid;
+    grid-template-columns: repeat(auto-fill, minmax(280px, 1fr));
+    gap: 16px;
+    margin-bottom: 32px;
+  }
+  .case-card {
+    background: var(--surface);
+    border: 1px solid var(--border);
+    border-radius: 8px;
+    padding: 20px;
+    transition: border-color 0.2s, transform 0.2s;
+  }
+  .case-card:hover {
+    border-color: var(--accent);
+    transform: translateY(-2px);
+  }
+  .case-card .num {
+    display: inline-block;
+    font-size: 0.75rem;
+    font-weight: 600;
+    padding: 2px 8px;
+    border-radius: 4px;
+    background: var(--accent);
+    color: #0d1117;
+    margin-bottom: 8px;
+  }
+  .case-card h3 {
+    font-size: 1.05rem;
+    margin-bottom: 6px;
+    color: #f0f6fc;
+  }
+  .case-card p {
+    font-size: 0.875rem;
+    color: var(--text-dim);
+    margin-bottom: 10px;
+  }
+  .case-card .meta {
+    display: flex;
+    flex-wrap: wrap;
+    gap: 6px;
+    font-size: 0.75rem;
+  }
+  .tag {
+    display: inline-block;
+    padding: 2px 8px;
+    border-radius: 4px;
+    font-weight: 500;
+  }
+  .tag-python { background: #3572A533; color: #3572A5; }
+  .tag-c       { background: #55555533; color: #aaa; }
+  .tag-fortran { background: #73422233; color: #e9954a; }
+  .tag-gravity { background: #d2992233; color: var(--orange); }
+  .tag-spring  { background: #3fb95033; color: var(--green); }
+  .tag-drive   { background: #58a6ff33; color: var(--accent); }
+  .tag-warning { background: #f8514933; color: var(--red); }
+
+  /* 详情区域 */
+  .detail-card {
+    background: var(--surface);
+    border: 1px solid var(--border);
+    border-radius: 8px;
+    padding: 20px 24px;
+    margin-bottom: 16px;
+  }
+  .detail-card h3 {
+    font-size: 1.1rem;
+    margin-bottom: 8px;
+    color: #f0f6fc;
+  }
+  .detail-card h3 a { color: var(--accent); text-decoration: none; }
+  .detail-card h3 a:hover { text-decoration: underline; }
+  .detail-card p { color: var(--text-dim); margin-bottom: 8px; }
+  .detail-card ul {
+    list-style: none;
+    display: flex;
+    flex-wrap: wrap;
+    gap: 6px;
+    margin-bottom: 6px;
+  }
+  .detail-card li { font-size: 0.8rem; }
+  .detail-card .highlight {
+    background: #1f242e;
+    border-left: 3px solid var(--accent);
+    padding: 8px 12px;
+    margin-top: 8px;
+    border-radius: 0 4px 4px 0;
+    font-size: 0.875rem;
+    color: var(--text);
+  }
+
+  /* 使用指南 */
+  .guide {
+    background: #1f242e;
+    border: 1px solid var(--border);
+    border-radius: 8px;
+    padding: 20px 24px;
+    margin-bottom: 32px;
+  }
+  .guide h3 { color: #f0f6fc; margin-bottom: 12px; }
+  .guide code {
+    display: block;
+    background: #0d1117;
+    padding: 12px 16px;
+    border-radius: 6px;
+    font-family: "SF Mono", "Fira Code", monospace;
+    font-size: 0.875rem;
+    line-height: 1.5;
+    margin-bottom: 12px;
+    color: var(--green);
+  }
+  .guide table { width: 100%; border-collapse: collapse; font-size: 0.875rem; }
+  .guide th, .guide td {
+    text-align: left;
+    padding: 8px 12px;
+    border-bottom: 1px solid var(--border);
+  }
+  .guide th { color: var(--text-dim); font-weight: 600; }
+  .guide td:first-child { color: var(--accent); font-weight: 500; }
+
+  @media (max-width: 640px) {
+    body { padding: 16px; }
+    .case-grid { grid-template-columns: 1fr; }
+  }
+</style>
+</head>
+<body>
+<div class="container">
+
+<h1>Dynamics 示例案例 <small>v2.1</small></h1>
+<p class="subtitle">10 个从简单到复杂的物理模拟案例，展示分子动力学模拟框架的多种应用场景</p>
+
+<h2>📋 案例总览</h2>
+<div class="case-grid">
+
+<div class="case-card">
+  <span class="num">01</span>
+  <h3>双粒子弹簧系统</h3>
+  <p>两个原子由弹簧连接，在重力场中运动</p>
+  <div class="meta">
+    <span class="tag tag-python">Python</span>
+    <span class="tag tag-spring">弹簧</span>
+    <span class="tag tag-gravity">重力</span>
+  </div>
+</div>
+
+<div class="case-card">
+  <span class="num">02</span>
+  <h3>行星运动</h3>
+  <p>地球绕太阳椭圆公转（万有引力）</p>
+  <div class="meta">
+    <span class="tag tag-python">Python</span>
+    <span class="tag tag-gravity">万有引力</span>
+  </div>
+</div>
+
+<div class="case-card">
+  <span class="num">03</span>
+  <h3>日地月系统（失稳）</h3>
+  <p>三体系统参数不当导致轨道发散</p>
+  <div class="meta">
+    <span class="tag tag-python">Python</span>
+    <span class="tag tag-gravity">万有引力</span>
+    <span class="tag tag-warning">失败案例</span>
+  </div>
+</div>
+
+<div class="case-card">
+  <span class="num">04</span>
+  <h3>日地月系统（稳定）</h3>
+  <p>三体系统稳定轨道，经希尔半径检验</p>
+  <div class="meta">
+    <span class="tag tag-python">Python</span>
+    <span class="tag tag-gravity">万有引力</span>
+  </div>
+</div>
+
+<div class="case-card">
+  <span class="num">05</span>
+  <h3>一维原子链纵波</h3>
+  <p>驱动原子 1 沿 x 振动，产生纵波传播</p>
+  <div class="meta">
+    <span class="tag tag-python">Python</span>
+    <span class="tag tag-spring">弹簧</span>
+    <span class="tag tag-drive">驱动力</span>
+  </div>
+</div>
+
+<div class="case-card">
+  <span class="num">06</span>
+  <h3>一维原子链横波</h3>
+  <p>带阻尼的横波传播（FPU 非线性）</p>
+  <div class="meta">
+    <span class="tag tag-c">C 引擎</span>
+    <span class="tag tag-spring">弹簧</span>
+    <span class="tag tag-drive">驱动力</span>
+  </div>
+</div>
+
+<div class="case-card">
+  <span class="num">07</span>
+  <h3>一维链横波·双端驱动</h3>
+  <p>原子 1 + 原子 120 同时驱动，波相遇干涉</p>
+  <div class="meta">
+    <span class="tag tag-c">C 引擎</span>
+    <span class="tag tag-spring">弹簧</span>
+    <span class="tag tag-drive">驱动力</span>
+  </div>
+</div>
+
+<div class="case-card">
+  <span class="num">08</span>
+  <h3>双原子弹簧·C 引擎测试</h3>
+  <p>2 原子快速验证 C 引擎正确性</p>
+  <div class="meta">
+    <span class="tag tag-c">C 引擎</span>
+    <span class="tag tag-spring">弹簧</span>
+  </div>
+</div>
+
+<div class="case-card">
+  <span class="num">09</span>
+  <h3>一维链纵波·Fortran 引擎</h3>
+  <p>Fortran 引擎驱动的纵波，GPU 实例化渲染</p>
+  <div class="meta">
+    <span class="tag tag-fortran">Fortran</span>
+    <span class="tag tag-spring">弹簧</span>
+    <span class="tag tag-drive">驱动力</span>
+  </div>
+</div>
+
+<div class="case-card">
+  <span class="num">10</span>
+  <h3>一维链纵波·能量分析</h3>
+  <p>纵波传播 + 轨迹/能量图绘制</p>
+  <div class="meta">
+    <span class="tag tag-c">C 引擎</span>
+    <span class="tag tag-spring">弹簧</span>
+    <span class="tag tag-drive">驱动力</span>
+  </div>
+</div>
+
+</div>
+
+<h2>📖 各案例详情</h2>
+
+<div class="detail-card">
+  <h3><a href="./case01/">case01 — 双粒子弹簧系统</a></h3>
+  <ul>
+    <li class="tag tag-python">Python 引擎</li>
+    <li class="tag tag-spring">弹簧键力</li>
+    <li class="tag tag-gravity">重力场</li>
+  </ul>
+  <p>两个原子通过弹簧连接，在均匀重力场（G=[0,0,-9.8]）中自由运动。展示重力作用下的耦合振动与落体运动的复合。</p>
+  <div class="highlight">🔬 教学案例：算法 leapfrog，渲染 Sphere 模式，建议作为入门第一个案例</div>
+</div>
+
+<div class="detail-card">
+  <h3><a href="./case02/">case02 — 行星运动</a></h3>
+  <ul>
+    <li class="tag tag-python">Python 引擎</li>
+    <li class="tag tag-gravity">万有引力</li>
+  </ul>
+  <p>模拟地球绕太阳的椭圆轨道运动。大质量中心体固定，小质量体绕行。</p>
+  <div class="highlight">🌍 万有引力强度 gravity_strength=100.0，leapfrog 算法确保能量守恒</div>
+</div>
+
+<div class="detail-card">
+  <h3><a href="./case03/">case03 — 日地月系统（失败案例）</a></h3>
+  <ul>
+    <li class="tag tag-python">Python 引擎</li>
+    <li class="tag tag-gravity">万有引力</li>
+    <li class="tag tag-warning">失稳</li>
+  </ul>
+  <p>三体系统（太阳-地球-月球）。初始条件或参数设置不当，轨道不稳定。展示数值模拟中参数选择的重要性。</p>
+</div>
+
+<div class="detail-card">
+  <h3><a href="./case04/">case04 — 日地月系统（成功案例）</a></h3>
+  <ul>
+    <li class="tag tag-python">Python 引擎</li>
+    <li class="tag tag-gravity">万有引力</li>
+  </ul>
+  <p>与 case03 相同的三体系统，但采用恰当的初始条件：地球置于近日点（$r=10$），$v_z=520$ 接近圆轨道；月球缩至希尔半径（$r_H\approx1.0$）以内的 $r=0.5$，相对速度 $v_{\text{rel}}\approx127$，确保月球被地球稳定束缚。</p>
+  <div class="highlight">✅ 与 case03 对比学习：初始条件对数值稳定性的影响。地月距 0.5 在地球希尔半径以内，满足稳定性条件</div>
+</div>
+
+<div class="detail-card">
+  <h3><a href="./case05/">case05 — 一维原子链纵波</a></h3>
+  <ul>
+    <li class="tag tag-python">Python 引擎</li>
+    <li class="tag tag-spring">弹簧键力</li>
+    <li class="tag tag-drive">驱动力</li>
+  </ul>
+  <p>60 原子沿 x 轴排列。原子 1 受 x 方向驱动力，产生沿链传播的纵波（压缩波）。原子 x 自由，y/z 锁定。</p>
+  <div class="highlight">📈 纵波波速快（x 方向弹簧力线性），T_total=10, NSTEP=50</div>
+</div>
+
+<div class="detail-card">
+  <h3><a href="./case06/">case06 — 一维原子链横波（带阻尼）</a></h3>
+  <ul>
+    <li class="tag tag-c">C 引擎</li>
+    <li class="tag tag-spring">弹簧键力</li>
+    <li class="tag tag-drive">驱动力</li>
+  </ul>
+  <p>120 原子沿 x 轴排列，带横向阻尼。驱动沿 z 方向，原子 z 自由，x/y 锁定。横波传播具有 FPU 型非线性。</p>
+  <div class="highlight">⚡ C 引擎高性能计算，T_total=1000, NSTEP=500，支持运动相机</div>
+</div>
+
+<div class="detail-card">
+  <h3><a href="./case07/">case07 — 一维链横波·双端驱动</a></h3>
+  <ul>
+    <li class="tag tag-c">C 引擎</li>
+    <li class="tag tag-spring">弹簧键力</li>
+    <li class="tag tag-drive">驱动力</li>
+  </ul>
+  <p>120 原子，原子 1 和原子 120 同时受 z 方向驱动（同频率、相位差 90°），两端向中间传播的横波相遇。</p>
+  <div class="highlight">🌊 波干涉演示，视觉放大 display_amp=[1,1,10] 便于观察小幅度振动</div>
+</div>
+
+<div class="detail-card">
+  <h3><a href="./case08/">case08 — 双原子弹簧（C 引擎快速测试）</a></h3>
+  <ul>
+    <li class="tag tag-c">C 引擎</li>
+    <li class="tag tag-spring">弹簧键力</li>
+  </ul>
+  <p>2 原子弹簧系统，T_total=100 的短时模拟。用于快速验证 C 引擎的正确性和性能。</p>
+  <div class="highlight">🧪 引擎快速验证用例，无动画输出</div>
+</div>
+
+<div class="detail-card">
+  <h3><a href="./case09/">case09 — 一维链纵波·Fortran 引擎</a></h3>
+  <ul>
+    <li class="tag tag-fortran">Fortran 引擎</li>
+    <li class="tag tag-spring">弹簧键力</li>
+    <li class="tag tag-drive">驱动力</li>
+  </ul>
+  <p>40 原子沿 x 轴排列，Fortran 引擎驱动的纵波传播测试。使用 <code>use_marker: 1</code>（GPU 实例化 Marker 模式）加速渲染，验证 Fortran 引擎与其他引擎的输出兼容性。</p>
+  <div class="highlight">🔧 Fortran 引擎兼容性验证，T_total=200, NSTEP=100。Marker 模式下 40 原子以 GPU 点精灵渲染，帧率高</div>
+</div>
+
+<div class="detail-card">
+  <h3><a href="./case10/">case10 — 一维链纵波·能量分析</a></h3>
+  <ul>
+    <li class="tag tag-c">C 引擎</li>
+    <li class="tag tag-spring">弹簧键力</li>
+    <li class="tag tag-drive">驱动力</li>
+  </ul>
+  <p>40 原子纵波传播，支持轨迹/能量图绘制（step_plot=1）。原子 x/y/z 全部自由。</p>
+  <div class="highlight">📊 能量分析演示，T_total=10, NSTEP=20</div>
+</div>
+
+<h2>🚀 使用方法</h2>
+<div class="guide">
+  <h3>命令行</h3>
+  <code># 进入案例目录并运行<br>cd examples/case05<br>python run_dynamics.py<br><br># 仅运行模拟，跳过动画<br>python run_dynamics.py --no-plot<br><br># 手动启动 3D 动画<br>python ../../draw.py output/</code>
+
+  <h3>案例选择指南</h3>
+  <table>
+    <tr><th>目标</th><th>推荐案例</th></tr>
+    <tr><td>快速上手框架</td><td>case01</td></tr>
+    <tr><td>天体力学/万有引力</td><td>case02 / case04</td></tr>
+    <tr><td>波动物理（纵波）</td><td>case05</td></tr>
+    <tr><td>波动物理（横波/非线性/阻尼）</td><td>case06</td></tr>
+    <tr><td>双端驱动/波干涉</td><td>case07</td></tr>
+    <tr><td>引擎性能对比</td><td>case08 (C) / case09 (Fortran)</td></tr>
+    <tr><td>能量分析</td><td>case10</td></tr>
+  </table>
+
+  <h3>配置</h3>
+  <p style="color:var(--text-dim); font-size:0.875rem;">
+    每个案例的 <code>input/input.txt</code> 可配置物理参数、力开关、算法、引擎、渲染方式等。
+  </p>
+
+  <h3>引擎架构</h3>
+  <p style="color:var(--text-dim); font-size:0.875rem;">
+    外部引擎（C / C++ / Fortran）以 <strong>DLL 方式</strong> 运行，主程序通过 ctypes 在进程内直接调用，不启动子进程。DLL 预编译在 <code>engines/release/</code> 中，源码位于 <code>engines/src/{c,cpp,fortran}/</code>。重新编译：
+    <code>cd engines/src/c && make dll</code>
+  </p>
+</div>
+
+<h2>📁 框架结构</h2>
+<div class="detail-card">
+<pre style="font-size:0.825rem; color:var(--text-dim); line-height:1.5;">
+dynamics/
+├── dynamics.py          # 统一运行入口
+├── compute.py           # 物理引擎 + 显示数据生成
+├── draw.py              # VisPy 3D 动画
+├── plot_wave.py         # 波形能量图
+├── .gitattributes       # DLL/二进制文件保护
+├── engines/
+│   ├── engine_dll.py    # DLL 加载器（ctypes）
+│   ├── python/          # Python 引擎（dynamics_lib.py）
+│   ├── release/         # 预编译 DLL（C / C++ / Fortran）
+│   └── src/             # 引擎源码
+│       ├── c/           # C 源码 + Makefile → dynamics_c.dll
+│       ├── cpp/         # C++ 源码 + Makefile → dynamics_cpp.dll
+│       └── fortran/     # Fortran 源码 + Makefile → dynamics_f90.dll
+├── examples/            # 案例目录
+│   ├── case01/  ~  case10/
+└── output/              # 默认输出目录
+</pre>
+</div>
+
+</div>
+</body>
+</html>

examples/Readme.md

@@ -1,19 +1,23 @@
 # Dynamics 示例案例
 
-本目录包含 6 个从简单到复杂的物理模拟案例，均基于 `../dynamics.py` 框架运行。
+本目录包含 10 个从简单到复杂的物理模拟案例，均基于 `../dynamics.py` 框架运行。
 
 ---
 
 ## 案例一览
 
-| 案例 | 标题 | 简介 | 原子数 | 力类型 |
-|---|---|---|---|---|
-| [case01](./case01/) | **双粒子弹簧系统** | 两个原子由弹簧连接，在重力场中运动 | 2 | 重力 + 弹簧 |
-| [case02](./case02/) | **行星运动** | 地球绕太阳椭圆公转（万有引力） | 2 | 万有引力 |
-| [case03](./case03/) | **日地月系统（失败）** | 地球绕太阳、月球绕地球，参数不当导致失稳 | 3 | 万有引力 |
-| [case04](./case04/) | **日地月系统（成功）** | 地球绕太阳、月球绕地球，稳定轨道 | 3 | 万有引力 |
-| [case05](./case05/) | **一维原子链纵波** | 驱动原子 1 沿 x 轴振动，产生纵波传播 | 60 | 弹簧 + 驱动力 |
-| [case06](./case06/) | **一维原子链横波** | 驱动原子 1 沿 z 轴振动，产生横波传播 | 60 | 弹簧 + 驱动力 |
+| 案例 | 标题 | 简介 | 原子数 | 引擎 | 力类型 |
+|------|------|------|--------|------|--------|
+| [case01](./case01/) | **双粒子弹簧系统** | 两个原子由弹簧连接，在重力场中运动 | 2 | Python | 重力 + 弹簧 |
+| [case02](./case02/) | **行星运动** | 地球绕太阳椭圆公转（万有引力） | 2 | Python | 万有引力 |
+| [case03](./case03/) | **日地月系统（失稳）** | 地球绕太阳、月球绕地球，参数不当导致失稳 | 3 | Python | 万有引力 |
+| [case04](./case04/) | **日地月系统（稳定）** | 地球绕太阳、月球绕地球，稳定轨道 | 3 | Python | 万有引力 |
+| [case05](./case05/) | **一维原子链纵波** | 驱动原子 1 沿 x 轴振动，产生纵波传播 | 60 | Python | 弹簧 + 驱动力 |
+| [case06](./case06/) | **一维原子链横波（阻尼）** | 驱动原子 1 沿 z 轴振动，带阻尼的横波传播 | 120 | C | 弹簧 + 阻尼 + 驱动力 |
+| [case07](./case07/) | **一维原子链横波（双端驱动）** | 原子 1 和原子 120 同时受 z 方向驱动 | 120 | C | 弹簧 + 阻尼 + 驱动力 |
+| [case08](./case08/) | **双原子弹簧（C 引擎测试）** | 两个原子弹簧系统，C 引擎快速验证 | 2 | C | 弹簧 + 阻尼 + 驱动力 |
+| [case09](./case09/) | **一维链纵波（Fortran 引擎）** | Fortran 引擎驱动的纵波传播测试 | 40 | Fortran | 弹簧 + 驱动力 |
+| [case10](./case10/) | **一维链纵波（能量分析）** | 纵波传播 + 轨迹/能量图绘制 | 40 | C | 弹簧 + 驱动力 |
 
 ---
 
@@ -26,14 +30,16 @@
 - **力开关**：重力场开，弹簧键力开
 - **算法**：leapfrog（蛙跳法）
 - **物理**：重力 m·g + 弹簧胡克力
+- **渲染**：Sphere 模式（精细网格球体）
 
 ### case02 — 行星运动
 
 模拟地球绕太阳的椭圆轨道运动（一个固定大质量中心体 + 一个绕行小质量体）。采用万有引力相互作用。
 
-- **力开关**：万有引力开（含强度参数）
+- **力开关**：万有引力开（含强度参数 `gravity_strength: 100.0`）
 - **算法**：leapfrog（蛙跳法）
 - **物理**：牛顿万有引力 F = G·m₁·m₂/r²
+- **渲染**：Sphere 模式
 
 ### case03 — 日地月系统（失败案例）
 
@@ -60,14 +66,53 @@
 - **波速**：快（x 方向弹簧力为线性）
 - **渲染**：Marker 模式（GPU 实例化，60 原子）
 
-### case06 — 一维原子链横波
+### case06 — 一维原子链横波（带阻尼）
 
-与 case05 相同的原子链，但驱动力沿 z 方向 `z(t)=0.5·cos(2π·0.1·t+90°)`，原子 z 方向自由（fix_z=0），x/y 锁定。振动在横向传播，形成**横波**。
+120 个原子沿 x 轴等间距排列（间距 1），相邻原子用弹簧（k=1.0, L₀=1.0）连接，带横向阻尼（B=[0.01, 0, 0.01]）。驱动在 z 方向 `z(t)=0.5·cos(2π·0.1·t+90°)`，原子 z 方向自由（fix_z=0），x/y 锁定。
 
-- **力开关**：弹簧键力开，驱动力开
+- **力开关**：弹簧键力开，驱动力开，阻尼开
 - **算法**：leapfrog（蛙跳法）
+- **引擎**：C（高性能）
+- **参数**：T_total=1000, NSTEP=500
 - **波速**：慢（z 方向弹簧力呈几何非线性，类似 FPU 系统）
-- **渲染**：Marker 模式（GPU 实例化，60 原子）
+
+### case07 — 一维原子链横波（双端驱动）
+
+120 个原子沿 x 轴排列，原子 1 **和**原子 120 同时受 z 方向驱动力驱动（频率相同，初相位错开 90°），产生两端向中间传播的横波相遇。
+
+- **力开关**：弹簧键力开，驱动力开，阻尼开
+- **引擎**：C
+- **参数**：T_total=1000, NSTEP=500
+- **视觉放大**：z 方向位移放大 10 倍（`display_amp: [1, 1, 10]`），便于观察小幅度横波
+
+### case08 — 双原子弹簧（C 引擎快速测试）
+
+2 个原子的简单弹簧系统，用于快速验证 C 引擎的正确性和性能。T_total 仅为 100s。
+
+- **力开关**：弹簧键力开，驱动力开，阻尼开
+- **引擎**：C
+- **用途**：引擎验证 / 调试
+- **视觉放大**：z 方向位移放大 10 倍
+- **动画**：关闭（step_animation=0），仅输出波形图
+
+### case09 — 一维链纵波（Fortran 引擎）
+
+40 个原子沿 x 轴排列，使用 **Fortran 引擎**驱动的纵波传播模拟。验证 Fortran 引擎的输出兼容性和性能。
+
+- **力开关**：弹簧键力开，驱动力开，阻尼关
+- **引擎**：Fortran
+- **参数**：T_total=200, NSTEP=100
+- **视觉放大**：z 方向位移放大 10 倍
+
+### case10 — 一维链纵波（能量分析）
+
+40 个原子沿 x 轴排列，纵波传播。与 case05 相比，x/y/z 全部自由（fix_x/y/z 均为 0），物理行为更复杂。支持轨迹/能量图绘制（step_plot=1）。
+
+- **力开关**：弹簧键力开，驱动力开，阻尼关
+- **引擎**：C
+- **参数**：T_total=10, NSTEP=20
+- **视觉放大**：z 方向位移放大 10 倍
+- **动画**：关闭（step_animation=0），仅输出轨迹/能量图
 
 ---
 
@@ -77,7 +122,7 @@
 # 进入任意案例目录
 cd examples/case05
 
-# 完整运行（模拟 + 采样 + 3D 动画）
+# 完整运行（模拟 + 3D 动画）
 python run_dynamics.py
 
 # 仅运行模拟，跳过 3D 动画
@@ -89,6 +134,18 @@ python ../../draw.py output/
 
 每个案例的 `input/input.txt` 中可配置所有物理参数、力开关、算法、渲染方式等。
 
+## 案例选择指南
+
+| 你想做什么 | 推荐案例 |
+|-----------|---------|
+| 快速上手、理解基本框架 | case01 |
+| 天体力学 / 万有引力 | case02 / case04 |
+| 波动物理（纵波） | case05 |
+| 波动物理（横波、非线性、阻尼） | case06 |
+| 双端驱动/波干涉 | case07 |
+| 对比不同引擎性能 | case08 (C) / case09 (Fortran) |
+| 能量分析 | case10 |
+
 ## 框架结构
 
 ```
@@ -101,6 +158,6 @@ dynamics/
 ├── examples/            # 案例（本目录）
 │   ├── case01/
 │   ├── ...
-│   └── case06/
+│   └── case10/
 └── output/              # 默认输出目录
 ```

examples/add_k2.py

@@ -0,0 +1,92 @@
+"""
+为指定案例添加次紧邻键 (k2, k=100, r0=1.41421356)。
+
+用法:  python add_k2.py case16
+       python add_k2.py case16 case17 case18
+       python add_k2.py --all
+"""
+
+import os
+import sys
+
+def add_k2(case_dir):
+    coord_path = os.path.join(case_dir, "input", "coord.txt")
+    conn_path = os.path.join(case_dir, "input", "connection.txt")
+    bond_path = os.path.join(case_dir, "input", "bond.txt")
+
+    if not os.path.exists(coord_path):
+        print(f"  [跳过] {case_dir}: 找不到 coord.txt")
+        return False
+
+    # 读取 coord.txt 获取网格尺寸
+    with open(coord_path, "r", encoding="utf-8") as f:
+        lines = f.readlines()
+    n_atoms = len(lines) - 1  # 去掉表头
+    N = int(n_atoms ** 0.5)
+    if N * N != n_atoms:
+        print(f"  [跳过] {case_dir}: 非正方形网格 (n_atoms={n_atoms})")
+        return False
+
+    print(f"  {case_dir}: {N}x{N} 网格")
+
+    # 读取现有 connection.txt，检查是否已有 k2
+    has_k2 = False
+    if os.path.exists(conn_path):
+        with open(conn_path, "r") as f:
+            for line in f:
+                if "k2" in line:
+                    has_k2 = True
+                    break
+
+    if has_k2:
+        print(f"    k2 已存在，跳过 connection.txt")
+    else:
+        # 追加 k2 键到 connection.txt
+        with open(conn_path, "a", encoding="utf-8") as f:
+            cnt = 0
+            for row in range(N):
+                for col in range(N):
+                    id1 = row * N + col + 1
+                    if col + 1 < N and row + 1 < N:
+                        f.write(f"{id1} {(row + 1) * N + (col + 1) + 1} k2\n")
+                        cnt += 1
+                    if col - 1 >= 0 and row + 1 < N:
+                        f.write(f"{id1} {(row + 1) * N + (col - 1) + 1} k2\n")
+                        cnt += 1
+        print(f"    connection.txt: 追加 {cnt} 条 k2 键")
+
+    # 检查 bond.txt 是否有 k2
+    has_bond = False
+    if os.path.exists(bond_path):
+        with open(bond_path, "r") as f:
+            for line in f:
+                if line.startswith("k2"):
+                    has_bond = True
+                    break
+
+    if has_bond:
+        print(f"    bond.txt: k2 已存在")
+    else:
+        with open(bond_path, "a", encoding="utf-8") as f:
+            f.write("k2 100.0 1.41421356\n")
+        print(f"    bond.txt: 追加 k2 定义")
+
+    return True
+
+
+if __name__ == "__main__":
+    targets = []
+    if "--all" in sys.argv:
+        base = os.path.dirname(os.path.abspath(__file__))
+        for d in sorted(os.listdir(base)):
+            if d.startswith("case") and os.path.isdir(os.path.join(base, d)):
+                targets.append(os.path.join(base, d))
+    else:
+        for arg in sys.argv[1:]:
+            if arg.startswith("--"):
+                continue
+            p = arg if os.path.isabs(arg) else os.path.join(os.path.dirname(os.path.abspath(__file__)), arg)
+            targets.append(p)
+
+    for t in targets:
+        add_k2(t)

examples/case01/input/input.txt

@@ -6,7 +6,7 @@
 # 每步用 0/1 单独开关，1=执行，0=跳过
 # 依赖关系：抽帧依赖模拟结果，绘图依赖模拟+抽帧
 step_simulate:  1   # 运行物理模拟 → output/trajectory.txt
-step_sample:    1   # 抽帧 → output/display.txt
+step_sample:    0   # 抽帧 → output/display.txt
 step_plot:      1   # 绘制轨迹/能量图 → output/trajectory_plots.png
 step_plot_wave: 0   # 绘制波形能量动画
 plot_wave_save_gif: 0  # 输出波形 GIF（需 step_plot_wave=1）

examples/case04/Readme.html

@@ -0,0 +1,829 @@
+<!DOCTYPE html>
+<html lang="zh-CN">
+<head>
+<meta charset="UTF-8">
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<title>case04 — 日地月三体系统</title>
+<script>
+MathJax = {
+  tex: { inlineMath: [['$','$'], ['\\(','\\)']], displayMath: [['$$','$$'], ['\\[','\\]']] },
+  svg: { fontCache: 'global' }
+};
+</script>
+<script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js" async></script>
+<style>
+  :root {
+    --bg: #0d1117;
+    --surface: #161b22;
+    --border: #30363d;
+    --text: #c9d1d9;
+    --text-dim: #8b949e;
+    --accent: #58a6ff;
+    --green: #3fb950;
+    --orange: #d29922;
+    --red: #f85149;
+    --teal: #56d4dd;
+  }
+  * { margin: 0; padding: 0; box-sizing: border-box; }
+  body {
+    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", "Noto Sans SC", Helvetica, Arial, sans-serif;
+    background: var(--bg);
+    color: var(--text);
+    line-height: 1.8;
+    padding: 40px 24px;
+  }
+  .container { max-width: 860px; margin: 0 auto; }
+
+  h1 { font-size: 1.8rem; margin-bottom: 6px; color: #f0f6fc; }
+  h1 small { font-size: 1rem; color: var(--text-dim); font-weight: 400; }
+  .subtitle { color: var(--text-dim); margin-bottom: 32px; }
+
+  h2 {
+    font-size: 1.35rem;
+    margin-top: 36px;
+    margin-bottom: 14px;
+    padding-bottom: 6px;
+    border-bottom: 1px solid var(--border);
+    color: #f0f6fc;
+  }
+  h3 { font-size: 1.1rem; margin-top: 24px; margin-bottom: 10px; color: #f0f6fc; }
+
+  p { margin-bottom: 12px; color: var(--text); }
+
+  .card {
+    background: var(--surface);
+    border: 1px solid var(--border);
+    border-radius: 8px;
+    padding: 20px 24px;
+    margin-bottom: 20px;
+  }
+
+  table {
+    width: 100%;
+    border-collapse: collapse;
+    margin: 12px 0;
+    font-size: 0.9rem;
+  }
+  th, td {
+    text-align: left;
+    padding: 8px 14px;
+    border-bottom: 1px solid var(--border);
+  }
+  th { color: var(--text-dim); font-weight: 600; background: #1c2128; }
+
+  .highlight {
+    background: #1f242e;
+    border-left: 3px solid var(--accent);
+    padding: 10px 16px;
+    margin: 12px 0;
+    border-radius: 0 6px 6px 0;
+    font-size: 0.9rem;
+  }
+  .highlight-eq {
+    background: #1f242e;
+    border-left: 3px solid var(--teal);
+    padding: 14px 18px;
+    margin: 14px 0;
+    border-radius: 0 6px 6px 0;
+  }
+  .highlight-eq p { margin: 6px 0; }
+
+  code {
+    background: #1c2128;
+    padding: 2px 6px;
+    border-radius: 4px;
+    font-family: "SF Mono", "Fira Code", monospace;
+    font-size: 0.85em;
+    color: var(--green);
+  }
+
+  .tag {
+    display: inline-block;
+    padding: 2px 10px;
+    border-radius: 4px;
+    font-size: 0.78rem;
+    font-weight: 500;
+    margin: 2px;
+  }
+  .tag-python { background: #3572A533; color: #3572A5; }
+  .tag-gravity { background: #d2992233; color: var(--orange); }
+
+  ul, ol { margin: 8px 0 12px 24px; }
+  li { margin-bottom: 4px; }
+
+  .formula-block {
+    overflow-x: auto;
+    padding: 8px 0;
+  }
+
+  .diagram-wrap {
+    background: #0d1117;
+    border: 1px solid var(--border);
+    border-radius: 8px;
+    padding: 16px;
+    margin: 16px 0;
+    text-align: center;
+  }
+  .diagram-wrap canvas {
+    display: block;
+    margin: 0 auto;
+    max-width: 100%;
+    height: auto;
+  }
+  .diagram-controls {
+    display: flex;
+    flex-wrap: wrap;
+    align-items: center;
+    justify-content: center;
+    gap: 16px;
+    margin-top: 12px;
+  }
+  .diagram-controls label {
+    font-size: 0.85rem;
+    color: var(--text-dim);
+  }
+  .diagram-controls input[type="range"] {
+    width: 200px;
+    accent-color: var(--accent);
+  }
+  .diagram-controls .val {
+    font-size: 0.9rem;
+    font-weight: 500;
+    color: var(--teal);
+    min-width: 48px;
+    display: inline-block;
+    text-align: center;
+  }
+  .diagram-info {
+    display: flex;
+    flex-wrap: wrap;
+    justify-content: center;
+    gap: 20px;
+    margin-top: 10px;
+    font-size: 0.82rem;
+    color: var(--text-dim);
+  }
+  .diagram-info span {
+    display: inline-flex;
+    align-items: center;
+    gap: 4px;
+  }
+  .diagram-info .dot {
+    display: inline-block;
+    width: 10px;
+    height: 10px;
+    border-radius: 50%;
+    margin-right: 2px;
+  }
+
+  @media (max-width: 640px) {
+    body { padding: 16px; }
+    .diagram-controls { flex-direction: column; gap: 8px; }
+  }
+</style>
+</head>
+<body>
+<div class="container">
+
+<h1>case04 — 日地月三体系统 <small>稳定轨道版本</small></h1>
+<p class="subtitle">太阳、地球、月球三体系统，采用真实比例的质量和万有引力模拟，地球和月球维持稳定椭圆轨道。</p>
+
+<div class="card" style="display:flex; flex-wrap:wrap; gap:8px; align-items:center; margin-bottom:20px;">
+  <span class="tag tag-python">Python 引擎</span>
+  <span class="tag tag-gravity">万有引力</span>
+  <span style="color:var(--text-dim); font-size:0.85rem; margin-left:8px;">3 粒子 | leapfrog 算法 | 稳定轨道</span>
+</div>
+
+<h2>一、物理系统概览</h2>
+
+<div class="card">
+  <p>本案例模拟真实的日-地-月三体系统：</p>
+  <ul>
+    <li><strong>太阳</strong>：位于原点，质量为 $M_\odot$，固定不动（fix_x=fix_y=fix_z=1）</li>
+    <li><strong>地球</strong>：绕太阳公转，质量为 $M_\oplus$，近日点出发</li>
+    <li><strong>月球</strong>：绕地球公转（同时跟随地球绕太阳），质量为 $M_\text{moon}$</li>
+  </ul>
+  <p>原子间万有引力由 <code>gravity_strength</code> 缩放控制，$F = G \dfrac{m_1 m_2}{r^2}$。</p>
+</div>
+
+<h2>二、天体真实参数</h2>
+
+<h3>2.1 质量</h3>
+
+<table>
+  <tr><th>天体</th><th>质量 / kg</th><th>模拟质量（月球=1）</th></tr>
+  <tr><td>太阳</td><td>$1.989 \times 10^{30}$</td><td>$27\,000$</td></tr>
+  <tr><td>地球</td><td>$5.972 \times 10^{24}$</td><td>$81$</td></tr>
+  <tr><td>月球</td><td>$7.35 \times 10^{22}$</td><td>$1$</td></tr>
+</table>
+
+<div class="highlight">
+  <strong>质量比</strong>：$M_\odot : M_\oplus : M_\text{moon} \approx 27\,100\,000 : 81.3 : 1$<br>
+  模拟中采用缩放比例 $27\,000 : 81 : 1$（太阳质量缩至 $1/1000$ 以保持数值稳定）。
+</div>
+
+<h3>2.2 轨道参数</h3>
+
+<table>
+  <tr><th>轨道</th><th>半长轴 $a$</th><th>偏心率 $e$</th><th>半短轴 $b$</th><th>周期</th></tr>
+  <tr><td>地球绕太阳</td><td>$1.4960 \times 10^8$ km (1 AU)</td><td>$0.0167$</td><td>$1.4958 \times 10^8$ km</td><td>365.25 天</td></tr>
+  <tr><td>月球绕地球</td><td>$3.844 \times 10^5$ km</td><td>$0.0549$</td><td>$3.838 \times 10^5$ km</td><td>27.32 天</td></tr>
+</table>
+
+<div class="highlight">
+  <strong>比例</strong>：$R_{\text{日地}} : R_{\text{地月}} \approx 389 : 1$<br>
+  地月距离约为日地距离的 $1/389$。
+</div>
+
+<h2>三、轨道力学</h2>
+
+<h3>3.1 交互式轨道示意图</h3>
+
+<p>拖动下方滑块改变偏心率 $e$，观察轨道形状的变化和参数标注：</p>
+
+<div class="diagram-wrap">
+  <canvas id="orbitCanvas" width="760" height="400"></canvas>
+  <div class="diagram-controls">
+    <label>偏心率 e = <span class="val" id="eDisplay">0.0170</span>（地球真实值 0.0167）</label>
+    <input type="range" id="eSlider" min="0" max="850" value="17">
+  </div>
+  <div class="diagram-info" id="diagramInfo"></div>
+</div>
+
+<h3>3.2 月球绕地球轨道</h3>
+
+<p>拖动下方滑块改变月球轨道偏心率 $e_\text{moon}$（真实值 0.0549）：</p>
+
+<div class="diagram-wrap">
+  <canvas id="moonCanvas" width="760" height="400"></canvas>
+  <div class="diagram-controls">
+    <label>偏心率 e = <span class="val" id="moonEDisplay">0.0549</span>（月球真实值 0.0549）</label>
+    <input type="range" id="moonESlider" min="0" max="850" value="55">
+  </div>
+  <div class="diagram-info" id="moonInfo"></div>
+</div>
+
+<h3>3.3 偏心率定义</h3>
+
+<div class="highlight-eq">
+  <p>偏心率 $e$ 描述椭圆轨道偏离正圆的程度：</p>
+  <div class="formula-block">
+    $$e = \frac{c}{a}$$
+  </div>
+  <p>其中 $c = ea$ 为偏心距（焦点到椭圆中心的距离），$a$ 为半长轴。</p>
+</div>
+
+<table>
+  <tr><th>$e$ 值</th><th>轨道形状</th><th>说明</th></tr>
+  <tr><td>$e = 0$</td><td>正圆形</td><td>速度恒定，距离恒定</td></tr>
+  <tr><td>$0 &lt; e &lt; 1$</td><td>椭圆</td><td>近日点/近地点速度最大，远日点/远地点速度最小</td></tr>
+  <tr><td>$e = 1$</td><td>抛物线</td><td>逃逸轨道，速度恰好达到逃逸速度</td></tr>
+  <tr><td>$e &gt; 1$</td><td>双曲线</td><td>飞越轨道，速度超过逃逸速度</td></tr>
+</table>
+
+<h3>3.4 半长轴与半短轴的关系</h3>
+
+<div class="highlight-eq">
+  <div class="formula-block">
+    $$b = a\sqrt{1 - e^2}$$
+  </div>
+  <p>当 $e \ll 1$ 时，$b \approx a\left(1 - \dfrac{e^2}{2}\right)$，椭圆度非常微小。</p>
+</div>
+
+<h3>3.5 近日点与远日点</h3>
+
+<div class="highlight-eq">
+  <p>近日点（距太阳最近）和远日点（距太阳最远）的距离分别为：</p>
+  <div class="formula-block">
+    $$r_{\text{peri}} = a(1 - e), \qquad r_{\text{ap}} = a(1 + e)$$
+  </div>
+  <p>在近日点轨道速度最大，在远日点轨道速度最小：</p>
+  <div class="formula-block">
+    $$v_{\text{peri}} = \sqrt{\frac{GM(1+e)}{a(1-e)}}, \qquad
+    v_{\text{ap}} = \sqrt{\frac{GM(1-e)}{a(1+e)}}$$
+  </div>
+</div>
+
+<h3>3.6 开普勒三大定律</h3>
+
+<ol>
+  <li><strong>椭圆定律</strong>：行星轨道是椭圆，太阳位于椭圆的一个焦点上。</li>
+  <li><strong>面积定律</strong>：行星与太阳的连线在相等时间内扫过相等的面积。</li>
+  <li><strong>周期定律</strong>：公转周期的平方与半长轴的立方成正比：$T^2 \propto a^3$。</li>
+</ol>
+
+<div class="highlight">
+  <strong>验证</strong>：在本模拟中，你可以通过轨迹图观察面积定律是否成立——地球在近日点移动更快，远日点移动更慢。
+</div>
+
+<h2>四、模拟参数</h2>
+
+<h3>4.1 缩放说明</h3>
+
+<p>真实尺度无法直接用于模拟（日地距离 1.5 亿 km），因此采用缩放参数。当前 case04 的配置为教学演示而简化：</p>
+
+<table>
+  <tr><th>参数</th><th>值</th><th>说明</th></tr>
+  <tr><td><code>gravity_strength</code></td><td>100.0</td><td>万有引力强度</td></tr>
+  <tr><td><code>box_a</code></td><td>30.0</td><td>盒子半边长</td></tr>
+  <tr><td><code>method</code></td><td>leapfrog</td><td>蛙跳法（辛积分器，能量守恒）</td></tr>
+  <tr><td><code>T_total</code></td><td>10.0 s</td><td>总模拟时间</td></tr>
+  <tr><td><code>NSTEP</code></td><td>2</td><td>抽帧间隔（密采帧）</td></tr>
+</table>
+
+<h3>4.2 初始构型</h3>
+
+<table>
+  <tr><th>天体</th><th>质量</th><th>位置 $(x,y,z)$</th><th>速度 $(v_x,v_y,v_z)$</th><th>固定约束</th></tr>
+  <tr><td>太阳</td><td>$27\,000$</td><td>$(0,0,0)$</td><td>$(0,0,0)$</td><td>全部固定</td></tr>
+  <tr><td>地球</td><td>$81$</td><td>$(10,0,0)$</td><td>$(0,0,520)$</td><td>无</td></tr>
+  <tr><td>月球</td><td>$1$</td><td>$(10.5,0,0)$</td><td>$(0,0,647)$</td><td>无</td></tr>
+</table>
+
+<p>地球在 $z$ 方向获得初速度 $v=520$，产生绕太阳的轨道运动（接近圆轨道）；月球在地球基础上附加 $v\approx127$ 的绕地速度，形成绕地球的轨道。速度由圆形轨道公式 $v = \sqrt{G_{\text{eff}} M / r}$ 计算，其中 $G_{\text{eff}} = \text{gravity\_strength} = 100$。</p>
+
+<div class="highlight">
+  <strong>验证</strong>：地球速度 $v_\oplus = \sqrt{100 \times 27\,000 / 10} \approx 519.6$，设 520 正确。月球相对速度 $v_{\text{rel}} = \sqrt{100 \times 81 / 0.5} \approx 127.3$，设 127 正确。地月距离 0.5 在地球希尔半径 $r_H \approx 10 \times (81 / 81\,000)^{1/3} \approx 1.0$ 之内，可确保轨道稳定。
+</div>
+
+<h2>五、使用方法</h2>
+
+<div class="card">
+  <code style="display:block; padding:14px 18px; margin-bottom:10px;">
+    # 进入 case04 目录并运行<br>
+    cd examples/case04<br>
+    python run_dynamics.py<br><br>
+    # 仅输出轨迹图，跳过动画<br>
+    python run_dynamics.py --no-plot
+  </code>
+  <p>配置文件：<code>input/input.txt</code>（物理参数）、<code>input/coord.txt</code>（初始位置/速度）。</p>
+</div>
+
+<h2>六、与 case03 的对比</h2>
+
+<table>
+  <tr><th></th><th>case03（失败案例）</th><th>case04（成功案例）</th></tr>
+  <tr><td>轨道状态</td><td>轨道发散或碰撞</td><td>稳定椭圆轨道</td></tr>
+  <tr><td>关键差异</td><td>初始速度或质量比不恰当</td><td>合理的初值和参数</td></tr>
+  <tr><td>教学意义</td><td>展示参数选择的重要性</td><td>展示正确的三体运动</td></tr>
+</table>
+
+<div class="highlight">
+  <strong>教学建议</strong>：先运行 case03 观察失稳，再运行 case04 对比稳定轨道，理解初始条件对数值模拟的关键影响。
+</div>
+
+<h2>七、已知局限</h2>
+
+<ul>
+  <li>太阳真实质量为月球 $27\,100\,000$ 倍，模拟中缩至 $27\,000$ 倍以保持数值稳定（$1/1000$）</li>
+  <li>轨道半径未按真实比例缩放（真实日地距是地月距的 389 倍，模拟中约为 20 倍，受希尔半径约束，月球已尽可能放远）</li>
+  <li>未考虑月球轨道倾角（真实地月轨道有约 5° 的倾角）</li>
+  <li>leapfrog 算法为能量守恒的辛积分器，长期稳定，但步长过大时仍可能偏离真实轨道</li>
+  <li>太阳固定不动可作为教学简化，但严格三体模拟中应让所有天体在质心系中自由运动</li>
+</ul>
+
+</div>
+
+<script>
+(function() {
+  var canvas = document.getElementById('orbitCanvas');
+  var ctx = canvas.getContext('2d');
+  var slider = document.getElementById('eSlider');
+  var eDisplay = document.getElementById('eDisplay');
+  var infoDiv = document.getElementById('diagramInfo');
+
+  var W = 760, H = 400;
+  var cx = 380, cy = 200;
+
+  // 实际绘图区域半径
+  var A = 140;
+
+  function draw(e) {
+    ctx.clearRect(0, 0, W, H);
+
+    var b = A * Math.sqrt(1 - e * e);
+    var f = e * A;
+
+    // 长轴辅助线
+    ctx.beginPath();
+    ctx.moveTo(cx - A - 20, cy);
+    ctx.lineTo(cx + A + 20, cy);
+    ctx.strokeStyle = '#30363d';
+    ctx.lineWidth = 0.5;
+    ctx.setLineDash([4, 3]);
+    ctx.stroke();
+    ctx.setLineDash([]);
+
+    // 椭圆轨道（中心在 cx+f，左焦点=cx 为太阳）
+    ctx.beginPath();
+    ctx.ellipse(cx + f, cy, A, b, 0, 0, Math.PI * 2);
+    ctx.strokeStyle = '#58a6ff';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+
+    // 半长轴 a（标注线，从椭圆中心到右顶点）
+    var aY = cy + 28;
+    ctx.beginPath();
+    ctx.moveTo(cx + f, aY);
+    ctx.lineTo(cx + f + A, aY);
+    ctx.strokeStyle = '#c9d1d9';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    // 箭头（左端：椭圆中心 cx+f）
+    ctx.beginPath();
+    ctx.moveTo(cx + f + 6, aY - 4);
+    ctx.lineTo(cx + f, aY);
+    ctx.lineTo(cx + f + 6, aY + 4);
+    ctx.strokeStyle = '#c9d1d9';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    // 箭头（右端：右顶点 cx+f+A）
+    ctx.beginPath();
+    ctx.moveTo(cx + f + A - 6, aY - 4);
+    ctx.lineTo(cx + f + A, aY);
+    ctx.lineTo(cx + f + A - 6, aY + 4);
+    ctx.strokeStyle = '#c9d1d9';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    ctx.fillStyle = '#c9d1d9';
+    ctx.font = '13px "Segoe UI", Arial, sans-serif';
+    ctx.textAlign = 'center';
+    ctx.textBaseline = 'top';
+    ctx.fillText('a = ' + A.toFixed(0), cx + f + A/2, aY + 6);
+
+    // 偏心距 c = ea（从左焦点到椭圆中心）
+    var cY = cy - b - 20;
+    ctx.beginPath();
+    ctx.moveTo(cx, cY);
+    ctx.lineTo(cx + f, cY);
+    ctx.strokeStyle = '#d29922';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    // 箭头（左端：左焦点=cx 太阳）
+    ctx.beginPath();
+    ctx.moveTo(cx + 5, cY - 4);
+    ctx.lineTo(cx, cY);
+    ctx.lineTo(cx + 5, cY + 4);
+    ctx.strokeStyle = '#d29922';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    // 箭头（右端：椭圆中心 cx+f）
+    ctx.beginPath();
+    ctx.moveTo(cx + f - 5, cY - 4);
+    ctx.lineTo(cx + f, cY);
+    ctx.lineTo(cx + f - 5, cY + 4);
+    ctx.strokeStyle = '#d29922';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    ctx.fillStyle = '#d29922';
+    ctx.font = '13px "Segoe UI", Arial, sans-serif';
+    ctx.textAlign = 'center';
+    ctx.textBaseline = 'bottom';
+    ctx.fillText('c = ea = ' + f.toFixed(1), cx + f/2, cY - 4);
+
+    // 半短轴 b 标注（从椭圆中心到上顶点）
+    var bX = cx + f + A + 18;
+    ctx.beginPath();
+    ctx.moveTo(bX, cy);
+    ctx.lineTo(bX, cy - b);
+    ctx.strokeStyle = '#3fb950';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    ctx.beginPath();
+    ctx.moveTo(bX - 4, cy - 6);
+    ctx.lineTo(bX, cy);
+    ctx.lineTo(bX + 4, cy - 6);
+    ctx.strokeStyle = '#3fb950';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    ctx.beginPath();
+    ctx.moveTo(bX - 4, cy - b + 6);
+    ctx.lineTo(bX, cy - b);
+    ctx.lineTo(bX + 4, cy - b + 6);
+    ctx.strokeStyle = '#3fb950';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    ctx.fillStyle = '#3fb950';
+    ctx.font = '13px "Segoe UI", Arial, sans-serif';
+    ctx.textAlign = 'left';
+    ctx.textBaseline = 'middle';
+    ctx.fillText('b = ' + b.toFixed(1), bX + 8, cy - b/2);
+
+    // 太阳（焦点）
+    ctx.beginPath();
+    ctx.arc(cx, cy, 7, 0, Math.PI * 2);
+    ctx.fillStyle = '#d29922';
+    ctx.fill();
+    ctx.strokeStyle = '#f0883e';
+    ctx.lineWidth = 1;
+    ctx.stroke();
+    ctx.fillStyle = '#f0f6fc';
+    ctx.font = '13px "Segoe UI", Arial, sans-serif';
+    ctx.textAlign = 'center';
+    ctx.textBaseline = 'bottom';
+    ctx.fillText('太阳（左焦点）', cx, cy - 12);
+
+    // 近日点（左顶点：距左焦点最近）
+    var periX = cx + f - A;
+    ctx.fillStyle = '#58a6ff';
+    ctx.beginPath();
+    ctx.arc(periX, cy, 4, 0, Math.PI * 2);
+    ctx.fill();
+    ctx.fillStyle = '#8b949e';
+    ctx.font = '12px "Segoe UI", Arial, sans-serif';
+    ctx.textAlign = 'center';
+    ctx.textBaseline = 'top';
+    ctx.fillText('近日点 r = a(1-e) = ' + (A * (1 - e)).toFixed(1), periX, cy + 12);
+
+    // 远日点标注（右顶点：距左焦点最远）
+    var apX = cx + f + A;
+    ctx.fillStyle = '#58a6ff';
+    ctx.beginPath();
+    ctx.arc(apX, cy, 4, 0, Math.PI * 2);
+    ctx.fill();
+    ctx.fillStyle = '#8b949e';
+    ctx.font = '12px "Segoe UI", Arial, sans-serif';
+    ctx.textAlign = 'center';
+    ctx.textBaseline = 'top';
+    ctx.fillText('远日点 r = a(1+e) = ' + (A * (1 + e)).toFixed(1), apX, cy + 12);
+
+    // 地球（轨道上的点）
+    var angle = 0.4;
+    var ex = cx + f + A * Math.cos(angle);
+    var ey = cy - b * Math.sin(angle);
+    ctx.beginPath();
+    ctx.arc(ex, ey, 5, 0, Math.PI * 2);
+    ctx.fillStyle = '#58a6ff';
+    ctx.fill();
+    ctx.strokeStyle = '#1f6feb';
+    ctx.lineWidth = 1;
+    ctx.stroke();
+    ctx.fillStyle = '#58a6ff';
+    ctx.font = '12px "Segoe UI", Arial, sans-serif';
+    ctx.textAlign = 'left';
+    ctx.textBaseline = 'bottom';
+    ctx.fillText('地球', ex + 8, ey);
+
+    // 速度矢量
+    var vlen = 32;
+    var vx = -A * Math.sin(angle) * 0.7;
+    var vy = b * Math.cos(angle) * 0.7;
+    var vl = Math.sqrt(vx*vx + vy*vy);
+    if (vl > 0) {
+      vx = vx / vl * vlen;
+      vy = vy / vl * vlen;
+    }
+    ctx.beginPath();
+    ctx.moveTo(ex, ey);
+    ctx.lineTo(ex + vx, ey + vy);
+    ctx.strokeStyle = '#3fb950';
+    ctx.lineWidth = 2;
+    ctx.stroke();
+    ctx.beginPath();
+    var tipX = ex + vx, tipY = ey + vy;
+    var a1 = 0.3;
+    ctx.moveTo(tipX, tipY);
+    ctx.lineTo(tipX - vx * a1 + vy * a1 * 0.5, tipY - vy * a1 - vx * a1 * 0.5);
+    ctx.lineTo(tipX - vx * a1 - vy * a1 * 0.5, tipY - vy * a1 + vx * a1 * 0.5);
+    ctx.closePath();
+    ctx.fillStyle = '#3fb950';
+    ctx.fill();
+
+    // 信息面板
+    var roundE = Math.round(e * 10000) / 10000;
+    infoDiv.innerHTML =
+      '<span><span class="dot" style="background:#58a6ff"></span>椭圆轨道 e = ' + roundE.toFixed(4) + '</span>' +
+      '<span><span class="dot" style="background:#d29922"></span>偏心距 c = ' + f.toFixed(1) + '</span>' +
+      '<span><span class="dot" style="background:#3fb950"></span>b/a = ' + (b / A).toFixed(4) + '</span>' +
+      '<span>近日点 ' + (A * (1 - e)).toFixed(1) + ' / 远日点 ' + (A * (1 + e)).toFixed(1) + '</span>';
+  }
+
+  function update() {
+    var val = parseInt(slider.value);
+    var e = val / 1000;
+    eDisplay.textContent = e.toFixed(4);
+    draw(e);
+  }
+
+  slider.addEventListener('input', update);
+  update();
+})();
+
+// ── 月球绕地球轨道图 ──
+(function() {
+  var canvas = document.getElementById('moonCanvas');
+  var ctx = canvas.getContext('2d');
+  var slider = document.getElementById('moonESlider');
+  var eDisplay = document.getElementById('moonEDisplay');
+  var infoDiv = document.getElementById('moonInfo');
+
+  var W = 760, H = 400;
+  var cx = 380, cy = 200;
+  var A = 140;
+
+  function draw(e) {
+    ctx.clearRect(0, 0, W, H);
+
+    var b = A * Math.sqrt(1 - e * e);
+    var f = e * A;
+
+    // 长轴辅助线
+    ctx.beginPath();
+    ctx.moveTo(cx - A - 20, cy);
+    ctx.lineTo(cx + A + 20, cy);
+    ctx.strokeStyle = '#30363d';
+    ctx.lineWidth = 0.5;
+    ctx.setLineDash([4, 3]);
+    ctx.stroke();
+    ctx.setLineDash([]);
+
+    // 椭圆轨道（中心在 cx+f，左焦点=cx 为地球）
+    ctx.beginPath();
+    ctx.ellipse(cx + f, cy, A, b, 0, 0, Math.PI * 2);
+    ctx.strokeStyle = '#7ee787';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+
+    // 半长轴 a（标注线，从椭圆中心到右顶点）
+    var aY = cy + 28;
+    ctx.beginPath();
+    ctx.moveTo(cx + f, aY);
+    ctx.lineTo(cx + f + A, aY);
+    ctx.strokeStyle = '#c9d1d9';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    ctx.beginPath();
+    ctx.moveTo(cx + f + 6, aY - 4);
+    ctx.lineTo(cx + f, aY);
+    ctx.lineTo(cx + f + 6, aY + 4);
+    ctx.strokeStyle = '#c9d1d9';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    ctx.beginPath();
+    ctx.moveTo(cx + f + A - 6, aY - 4);
+    ctx.lineTo(cx + f + A, aY);
+    ctx.lineTo(cx + f + A - 6, aY + 4);
+    ctx.strokeStyle = '#c9d1d9';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    ctx.fillStyle = '#c9d1d9';
+    ctx.font = '13px "Segoe UI", Arial, sans-serif';
+    ctx.textAlign = 'center';
+    ctx.textBaseline = 'top';
+    ctx.fillText('a = ' + A.toFixed(0), cx + f + A/2, aY + 6);
+
+    // 偏心距 c = ea（从左焦点=地球 到椭圆中心）
+    var cY = cy - b - 20;
+    ctx.beginPath();
+    ctx.moveTo(cx, cY);
+    ctx.lineTo(cx + f, cY);
+    ctx.strokeStyle = '#d29922';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    ctx.beginPath();
+    ctx.moveTo(cx + 5, cY - 4);
+    ctx.lineTo(cx, cY);
+    ctx.lineTo(cx + 5, cY + 4);
+    ctx.strokeStyle = '#d29922';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    ctx.beginPath();
+    ctx.moveTo(cx + f - 5, cY - 4);
+    ctx.lineTo(cx + f, cY);
+    ctx.lineTo(cx + f - 5, cY + 4);
+    ctx.strokeStyle = '#d29922';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    ctx.fillStyle = '#d29922';
+    ctx.font = '13px "Segoe UI", Arial, sans-serif';
+    ctx.textAlign = 'center';
+    ctx.textBaseline = 'bottom';
+    ctx.fillText('c = ea = ' + f.toFixed(1), cx + f/2, cY - 4);
+
+    // 半短轴 b 标注（从椭圆中心到上顶点）
+    var bX = cx + f + A + 18;
+    ctx.beginPath();
+    ctx.moveTo(bX, cy);
+    ctx.lineTo(bX, cy - b);
+    ctx.strokeStyle = '#3fb950';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    ctx.beginPath();
+    ctx.moveTo(bX - 4, cy - 6);
+    ctx.lineTo(bX, cy);
+    ctx.lineTo(bX + 4, cy - 6);
+    ctx.strokeStyle = '#3fb950';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    ctx.beginPath();
+    ctx.moveTo(bX - 4, cy - b + 6);
+    ctx.lineTo(bX, cy - b);
+    ctx.lineTo(bX + 4, cy - b + 6);
+    ctx.strokeStyle = '#3fb950';
+    ctx.lineWidth = 1.5;
+    ctx.stroke();
+    ctx.fillStyle = '#3fb950';
+    ctx.font = '13px "Segoe UI", Arial, sans-serif';
+    ctx.textAlign = 'left';
+    ctx.textBaseline = 'middle';
+    ctx.fillText('b = ' + b.toFixed(1), bX + 8, cy - b/2);
+
+    // 地球（左焦点）
+    ctx.beginPath();
+    ctx.arc(cx, cy, 8, 0, Math.PI * 2);
+    ctx.fillStyle = '#58a6ff';
+    ctx.fill();
+    ctx.strokeStyle = '#1f6feb';
+    ctx.lineWidth = 1;
+    ctx.stroke();
+    ctx.fillStyle = '#f0f6fc';
+    ctx.font = '13px "Segoe UI", Arial, sans-serif';
+    ctx.textAlign = 'center';
+    ctx.textBaseline = 'bottom';
+    ctx.fillText('地球（左焦点）', cx, cy - 14);
+
+    // 近地点（左顶点：距地球最近）
+    var periX = cx + f - A;
+    ctx.fillStyle = '#7ee787';
+    ctx.beginPath();
+    ctx.arc(periX, cy, 4, 0, Math.PI * 2);
+    ctx.fill();
+    ctx.fillStyle = '#8b949e';
+    ctx.font = '12px "Segoe UI", Arial, sans-serif';
+    ctx.textAlign = 'center';
+    ctx.textBaseline = 'top';
+    ctx.fillText('近地点 r = a(1-e) = ' + (A * (1 - e)).toFixed(1), periX, cy + 12);
+
+    // 远地点（右顶点：距地球最远）
+    var apX = cx + f + A;
+    ctx.fillStyle = '#7ee787';
+    ctx.beginPath();
+    ctx.arc(apX, cy, 4, 0, Math.PI * 2);
+    ctx.fill();
+    ctx.fillStyle = '#8b949e';
+    ctx.font = '12px "Segoe UI", Arial, sans-serif';
+    ctx.textAlign = 'center';
+    ctx.textBaseline = 'top';
+    ctx.fillText('远地点 r = a(1+e) = ' + (A * (1 + e)).toFixed(1), apX, cy + 12);
+
+    // 月球（轨道上的点）
+    var angle = 0.6;
+    var mx = cx + f + A * Math.cos(angle);
+    var my = cy - b * Math.sin(angle);
+    ctx.beginPath();
+    ctx.arc(mx, my, 4, 0, Math.PI * 2);
+    ctx.fillStyle = '#e2e8f0';
+    ctx.fill();
+    ctx.strokeStyle = '#8b949e';
+    ctx.lineWidth = 0.5;
+    ctx.stroke();
+    ctx.fillStyle = '#e2e8f0';
+    ctx.font = '12px "Segoe UI", Arial, sans-serif';
+    ctx.textAlign = 'left';
+    ctx.textBaseline = 'bottom';
+    ctx.fillText('月球', mx + 8, my);
+
+    // 速度矢量
+    var vlen = 32;
+    var vx = -A * Math.sin(angle) * 0.7;
+    var vy = b * Math.cos(angle) * 0.7;
+    var vl = Math.sqrt(vx*vx + vy*vy);
+    if (vl > 0) { vx = vx/vl*vlen; vy = vy/vl*vlen; }
+    ctx.beginPath();
+    ctx.moveTo(mx, my);
+    ctx.lineTo(mx + vx, my + vy);
+    ctx.strokeStyle = '#3fb950';
+    ctx.lineWidth = 2;
+    ctx.stroke();
+    var tipX = mx + vx, tipY = my + vy;
+    ctx.beginPath();
+    ctx.moveTo(tipX, tipY);
+    ctx.lineTo(tipX - vx*0.3 + vy*0.15, tipY - vy*0.3 - vx*0.15);
+    ctx.lineTo(tipX - vx*0.3 - vy*0.15, tipY - vy*0.3 + vx*0.15);
+    ctx.closePath();
+    ctx.fillStyle = '#3fb950';
+    ctx.fill();
+
+    // 信息面板
+    var roundE = Math.round(e * 10000) / 10000;
+    infoDiv.innerHTML =
+      '<span><span class="dot" style="background:#7ee787"></span>椭圆轨道 e = ' + roundE.toFixed(4) + '</span>' +
+      '<span><span class="dot" style="background:#d29922"></span>偏心距 c = ' + f.toFixed(1) + '</span>' +
+      '<span><span class="dot" style="background:#3fb950"></span>b/a = ' + (b / A).toFixed(4) + '</span>' +
+      '<span>近地点 ' + (A * (1 - e)).toFixed(1) + ' / 远地点 ' + (A * (1 + e)).toFixed(1) + '</span>';
+  }
+
+  function update() {
+    var val = parseInt(slider.value);
+    var e = val / 1000;
+    eDisplay.textContent = e.toFixed(4);
+    draw(e);
+  }
+
+  slider.addEventListener('input', update);
+  update();
+})();
+</script>
+
+</body>
+</html>

examples/case04/input/coord.txt

@@ -1,4 +1,4 @@
-n mass radius x y z vx vy vz fix_x fix_y fix_z
-1 1    0.28   0 0 0  0  0  0     1     1     1
-2 1    0.28   4 0 0  0  0  4     0     0     0
-3 0.1  0.18   5 0 0  0  0  6     0     0     0
+n mass  radius    x   y   z   vx   vy   vz fix_x fix_y fix_z
+1 27000    1.0    0   0   0    0    0    0     1     1     1
+2    81    0.2   10   0   0    0    0  520     0     0     0
+3     1    0.1   10.5 0   0    0    0  647     0     0     0

examples/case04/input/input.txt

@@ -23,7 +23,7 @@ force_calc: 0       # 强制重新计算：1=跳过缓存强算，0=自动使用
 engine: python        # 默认使用 Python 引擎
 
 # ── 盒子 ──────────────────────────────────────
-box_a: 20.0         # 立方体半边长，粒子被限制在 [-box_a, box_a]³ 内
+box_a: 30.0         # 立方体半边长，粒子被限制在 [-box_a, box_a]³ 内
 
 # ── 初始构型 ──────────────────────────────────
 # 坐标文件格式：
@@ -74,7 +74,7 @@ T_total: 10.0
 NSTEP: 2
 
 # ── 时间步长 ──────────────────────────────────
-DT:    0.001         # 时间步长 (s)
+DT:    0.0001         # 时间步长 (s)
 
 # 抽帧范围：只保存 [sample_start, sample_end) 区间内的帧
 sample_start: null        # null 表示从头开始（帧索引从 0 起）

examples/case05/input/coord.txt

@@ -1,5 +1,5 @@
 n mass radius x y z vx vy vz fix_x fix_y fix_z
-1 1 0.1 0 0 1 0 0 0   0 1 1
+1 1 0.1 0 0 0 0 0 0   0 1 1
 2 1 0.1 1 0 0 0 0 0   0 1 1
 3 1 0.1 2 0 0 0 0 0   0 1 1
 4 1 0.1 3 0 0 0 0 0   0 1 1

examples/case05/input/input.txt

@@ -8,7 +8,7 @@
 step_simulate:  0   # 运行物理模拟 → output/trajectory.txt
 step_sample:    0   # 抽帧 → output/display.txt
 step_plot:      0   # 绘制轨迹/能量图 → output/trajectory_plots.png
-step_animation: 0   # 自动播放 VisPy 3D 动画窗口（需安装 vispy）
+step_animation: 1   # 自动播放 VisPy 3D 动画窗口（需安装 vispy）
 step_plot_wave: 1   # 绘制波形能量动画
 plot_wave_save_gif: 0  # 输出波形 GIF（需 step_plot_wave=1）
 plot_wave_save_mp4: 0  # 输出波形 MP4（需 step_plot_wave=1）

examples/case06/Readme.md

@@ -6,7 +6,7 @@
 
 | 参数 | 值 |
 |---|---|
-| 原子数 | 60 |
+| 原子数 | 120 |
 | 排列 | 沿 x 轴等间距排列，间距为 1 |
 | 约束 | 原子**沿 z 方向自由振动**（fix_x=1, fix_y=1, fix_z=0），x, y 锁定 |
 | 弹簧 | 劲度系数 k=1.0，原长 L₀=1.0 |

examples/case06/doc/index.html

@@ -155,7 +155,7 @@
 <!-- ============================================================ -->
 <header class="hero">
   <h1>一维原子链驱动力学模拟</h1>
-  <p class="subtitle">60 个原子沿 x 轴排列 · 弹簧连接 · z 方向受迫振动</p>
+  <p class="subtitle">120 个原子沿 x 轴排列 · 弹簧连接 · z 方向受迫振动</p>
   <span class="badge">case06  ·  examples/case06</span>
 </header>
 
@@ -185,7 +185,7 @@
 
   <div class="card">
     <h3>1.1 一维原子链</h3>
-    <p>60 个原子沿 <strong>x 轴</strong> 等间距排列，原子间距为 1。相邻原子之间用 <strong>理想弹簧</strong> 连接，弹簧的劲度系数 <em>k</em> = 1.0，原长 <em>L</em>₀ = 1.0（与原子间距一致，初始状态弹簧无拉伸）。</p>
+    <p>120 个原子沿 <strong>x 轴</strong> 等间距排列，原子间距为 1。相邻原子之间用 <strong>理想弹簧</strong> 连接，弹簧的劲度系数 <em>k</em> = 1.0，原长 <em>L</em>₀ = 1.0（与原子间距一致，初始状态弹簧无拉伸）。</p>
     <p>每个原子被限制在 <strong>z 方向</strong> 自由振动，x 和 y 方向锁定（<code>fix_x=1, fix_y=1, fix_z=0</code>）。</p>
   </div>
 
@@ -415,13 +415,13 @@ step_animation: 1   # 播放动画</pre>
   <pre>case06/
 ├── input/
 │   ├── input.txt          # 主配置文件（YAML 格式）
-│   ├── coord.txt          # 原子坐标（60 个原子）
+│   ├── coord.txt          # 原子坐标（120 个原子）
 │   ├── connection.txt     # 弹簧连接关系（59 条键）
 │   ├── bond.txt           # 弹簧参数（k=1.0, L₀=1.0）
 │   └── <strong>driver.txt</strong>       # <span class="cm">驱动力定义（本案例新增）</span>
 ├── output/
-│   ├── trajectory.txt     # 全量轨迹数据（10000 步 × 60 原子）
-│   ├── display.txt        # 抽帧后的动画数据（200 帧 × 60 原子）
+│   ├── trajectory.txt     # 全量轨迹数据（50000 步 × 120 原子）
+│   ├── display.txt        # 抽帧后的动画数据（500 帧 × 120 原子）
 │   ├── dynamics.log       # 计算日志
 │   ├── animation.log      # 动画启动日志（闪退时排查用）
 │   └── wave_animation.gif # 波形能量动画（step_plot_wave=1 时生成）

examples/case06/input/bond.txt

@@ -1,2 +1,2 @@
-bond_name k rest_length
-k1 1.0 1.0
+bond_name k      rest_length
+k1        10.0   1.0

examples/case06/input/connection.txt

@@ -58,3 +58,63 @@ n1 n2 bond_name
 57 58 k1
 58 59 k1
 59 60 k1
+60 61 k1
+61 62 k1
+62 63 k1
+63 64 k1
+64 65 k1
+65 66 k1
+66 67 k1
+67 68 k1
+68 69 k1
+69 70 k1
+70 71 k1
+71 72 k1
+72 73 k1
+73 74 k1
+74 75 k1
+75 76 k1
+76 77 k1
+77 78 k1
+78 79 k1
+79 80 k1
+80 81 k1
+81 82 k1
+82 83 k1
+83 84 k1
+84 85 k1
+85 86 k1
+86 87 k1
+87 88 k1
+88 89 k1
+89 90 k1
+90 91 k1
+91 92 k1
+92 93 k1
+93 94 k1
+94 95 k1
+95 96 k1
+96 97 k1
+97 98 k1
+98 99 k1
+99 100 k1
+100 101 k1
+101 102 k1
+102 103 k1
+103 104 k1
+104 105 k1
+105 106 k1
+106 107 k1
+107 108 k1
+108 109 k1
+109 110 k1
+110 111 k1
+111 112 k1
+112 113 k1
+113 114 k1
+114 115 k1
+115 116 k1
+116 117 k1
+117 118 k1
+118 119 k1
+119 120 k1

examples/case06/input/coord.txt

@@ -1,61 +1,121 @@
 n mass radius x y z vx vy vz fix_x fix_y fix_z
-1 1 0.1 0 0 0 0 0 0 1 1 0
-2 1 0.1 1 0 0 0 0 0 1 1 0
-3 1 0.1 2 0 0 0 0 0 1 1 0
-4 1 0.1 3 0 0 0 0 0 1 1 0
-5 1 0.1 4 0 0 0 0 0 1 1 0
-6 1 0.1 5 0 0 0 0 0 1 1 0
-7 1 0.1 6 0 0 0 0 0 1 1 0
-8 1 0.1 7 0 0 0 0 0 1 1 0
-9 1 0.1 8 0 0 0 0 0 1 1 0
-10 1 0.1 9 0 0 0 0 0 1 1 0
-11 1 0.1 10 0 0 0 0 0 1 1 0
-12 1 0.1 11 0 0 0 0 0 1 1 0
-13 1 0.1 12 0 0 0 0 0 1 1 0
-14 1 0.1 13 0 0 0 0 0 1 1 0
-15 1 0.1 14 0 0 0 0 0 1 1 0
-16 1 0.1 15 0 0 0 0 0 1 1 0
-17 1 0.1 16 0 0 0 0 0 1 1 0
-18 1 0.1 17 0 0 0 0 0 1 1 0
-19 1 0.1 18 0 0 0 0 0 1 1 0
-20 1 0.1 19 0 0 0 0 0 1 1 0
-21 1 0.1 20 0 0 0 0 0 1 1 0
-22 1 0.1 21 0 0 0 0 0 1 1 0
-23 1 0.1 22 0 0 0 0 0 1 1 0
-24 1 0.1 23 0 0 0 0 0 1 1 0
-25 1 0.1 24 0 0 0 0 0 1 1 0
-26 1 0.1 25 0 0 0 0 0 1 1 0
-27 1 0.1 26 0 0 0 0 0 1 1 0
-28 1 0.1 27 0 0 0 0 0 1 1 0
-29 1 0.1 28 0 0 0 0 0 1 1 0
-30 1 0.1 29 0 0 0 0 0 1 1 0
-31 1 0.1 30 0 0 0 0 0 1 1 0
-32 1 0.1 31 0 0 0 0 0 1 1 0
-33 1 0.1 32 0 0 0 0 0 1 1 0
-34 1 0.1 33 0 0 0 0 0 1 1 0
-35 1 0.1 34 0 0 0 0 0 1 1 0
-36 1 0.1 35 0 0 0 0 0 1 1 0
-37 1 0.1 36 0 0 0 0 0 1 1 0
-38 1 0.1 37 0 0 0 0 0 1 1 0
-39 1 0.1 38 0 0 0 0 0 1 1 0
-40 1 0.1 39 0 0 0 0 0 1 1 0
-41 1 0.1 40 0 0 0 0 0 1 1 0
-42 1 0.1 41 0 0 0 0 0 1 1 0
-43 1 0.1 42 0 0 0 0 0 1 1 0
-44 1 0.1 43 0 0 0 0 0 1 1 0
-45 1 0.1 44 0 0 0 0 0 1 1 0
-46 1 0.1 45 0 0 0 0 0 1 1 0
-47 1 0.1 46 0 0 0 0 0 1 1 0
-48 1 0.1 47 0 0 0 0 0 1 1 0
-49 1 0.1 48 0 0 0 0 0 1 1 0
-50 1 0.1 49 0 0 0 0 0 1 1 0
-51 1 0.1 50 0 0 0 0 0 1 1 0
-52 1 0.1 51 0 0 0 0 0 1 1 0
-53 1 0.1 52 0 0 0 0 0 1 1 0
-54 1 0.1 53 0 0 0 0 0 1 1 0
-55 1 0.1 54 0 0 0 0 0 1 1 0
-56 1 0.1 55 0 0 0 0 0 1 1 0
-57 1 0.1 56 0 0 0 0 0 1 1 0
-58 1 0.1 57 0 0 0 0 0 1 1 0
-59 1 0.1 58 0 0 0 0 0 1 1 0
-60 1 0.1 59 0 0 0 0 0 1 1 0
+1 1 0.1 0 0 0 0 0 0       0 1 0
+2 1 0.1 1 0 0 0 0 0       0 1 0
+3 1 0.1 2 0 0 0 0 0       0 1 0
+4 1 0.1 3 0 0 0 0 0       0 1 0
+5 1 0.1 4 0 0 0 0 0       0 1 0
+6 1 0.1 5 0 0 0 0 0       0 1 0
+7 1 0.1 6 0 0 0 0 0       0 1 0
+8 1 0.1 7 0 0 0 0 0       0 1 0
+9 1 0.1 8 0 0 0 0 0       0 1 0
+10 1 0.1 9 0 0 0 0 0       0 1 0
+11 1 0.1 10 0 0 0 0 0       0 1 0
+12 1 0.1 11 0 0 0 0 0       0 1 0
+13 1 0.1 12 0 0 0 0 0       0 1 0
+14 1 0.1 13 0 0 0 0 0       0 1 0
+15 1 0.1 14 0 0 0 0 0       0 1 0
+16 1 0.1 15 0 0 0 0 0       0 1 0
+17 1 0.1 16 0 0 0 0 0       0 1 0
+18 1 0.1 17 0 0 0 0 0       0 1 0
+19 1 0.1 18 0 0 0 0 0       0 1 0
+20 1 0.1 19 0 0 0 0 0       0 1 0
+21 1 0.1 20 0 0 0 0 0       0 1 0
+22 1 0.1 21 0 0 0 0 0       0 1 0
+23 1 0.1 22 0 0 0 0 0       0 1 0
+24 1 0.1 23 0 0 0 0 0       0 1 0
+25 1 0.1 24 0 0 0 0 0       0 1 0
+26 1 0.1 25 0 0 0 0 0       0 1 0
+27 1 0.1 26 0 0 0 0 0       0 1 0
+28 1 0.1 27 0 0 0 0 0       0 1 0
+29 1 0.1 28 0 0 0 0 0       0 1 0
+30 1 0.1 29 0 0 0 0 0       0 1 0
+31 1 0.1 30 0 0 0 0 0       0 1 0
+32 1 0.1 31 0 0 0 0 0       0 1 0
+33 1 0.1 32 0 0 0 0 0       0 1 0
+34 1 0.1 33 0 0 0 0 0       0 1 0
+35 1 0.1 34 0 0 0 0 0       0 1 0
+36 1 0.1 35 0 0 0 0 0       0 1 0
+37 1 0.1 36 0 0 0 0 0       0 1 0
+38 1 0.1 37 0 0 0 0 0       0 1 0
+39 1 0.1 38 0 0 0 0 0       0 1 0
+40 1 0.1 39 0 0 0 0 0       0 1 0
+41 1 0.1 40 0 0 0 0 0       0 1 0
+42 1 0.1 41 0 0 0 0 0       0 1 0
+43 1 0.1 42 0 0 0 0 0       0 1 0
+44 1 0.1 43 0 0 0 0 0       0 1 0
+45 1 0.1 44 0 0 0 0 0       0 1 0
+46 1 0.1 45 0 0 0 0 0       0 1 0
+47 1 0.1 46 0 0 0 0 0       0 1 0
+48 1 0.1 47 0 0 0 0 0       0 1 0
+49 1 0.1 48 0 0 0 0 0       0 1 0
+50 1 0.1 49 0 0 0 0 0       0 1 0
+51 1 0.1 50 0 0 0 0 0       0 1 0
+52 1 0.1 51 0 0 0 0 0       0 1 0
+53 1 0.1 52 0 0 0 0 0       0 1 0
+54 1 0.1 53 0 0 0 0 0       0 1 0
+55 1 0.1 54 0 0 0 0 0       0 1 0
+56 1 0.1 55 0 0 0 0 0       0 1 0
+57 1 0.1 56 0 0 0 0 0       0 1 0
+58 1 0.1 57 0 0 0 0 0       0 1 0
+59 1 0.1 58 0 0 0 0 0       0 1 0
+60 1 0.1 59 0 0 0 0 0       0 1 0
+61 1 0.1 60 0 0 0 0 0       0 1 0
+62 1 0.1 61 0 0 0 0 0       0 1 0
+63 1 0.1 62 0 0 0 0 0       0 1 0
+64 1 0.1 63 0 0 0 0 0       0 1 0
+65 1 0.1 64 0 0 0 0 0       0 1 0
+66 1 0.1 65 0 0 0 0 0       0 1 0
+67 1 0.1 66 0 0 0 0 0       0 1 0
+68 1 0.1 67 0 0 0 0 0       0 1 0
+69 1 0.1 68 0 0 0 0 0       0 1 0
+70 1 0.1 69 0 0 0 0 0       0 1 0
+71 1 0.1 70 0 0 0 0 0       0 1 0
+72 1 0.1 71 0 0 0 0 0       0 1 0
+73 1 0.1 72 0 0 0 0 0       0 1 0
+74 1 0.1 73 0 0 0 0 0       0 1 0
+75 1 0.1 74 0 0 0 0 0       0 1 0
+76 1 0.1 75 0 0 0 0 0       0 1 0
+77 1 0.1 76 0 0 0 0 0       0 1 0
+78 1 0.1 77 0 0 0 0 0       0 1 0
+79 1 0.1 78 0 0 0 0 0       0 1 0
+80 1 0.1 79 0 0 0 0 0       0 1 0
+81 1 0.1 80 0 0 0 0 0       0 1 0
+82 1 0.1 81 0 0 0 0 0       0 1 0
+83 1 0.1 82 0 0 0 0 0       0 1 0
+84 1 0.1 83 0 0 0 0 0       0 1 0
+85 1 0.1 84 0 0 0 0 0       0 1 0
+86 1 0.1 85 0 0 0 0 0       0 1 0
+87 1 0.1 86 0 0 0 0 0       0 1 0
+88 1 0.1 87 0 0 0 0 0       0 1 0
+89 1 0.1 88 0 0 0 0 0       0 1 0
+90 1 0.1 89 0 0 0 0 0       0 1 0
+91 1 0.1 90 0 0 0 0 0       0 1 0
+92 1 0.1 91 0 0 0 0 0       0 1 0
+93 1 0.1 92 0 0 0 0 0       0 1 0
+94 1 0.1 93 0 0 0 0 0       0 1 0
+95 1 0.1 94 0 0 0 0 0       0 1 0
+96 1 0.1 95 0 0 0 0 0       0 1 0
+97 1 0.1 96 0 0 0 0 0       0 1 0
+98 1 0.1 97 0 0 0 0 0       0 1 0
+99 1 0.1 98 0 0 0 0 0       0 1 0
+100 1 0.1 99 0 0 0 0 0       0 1 0
+101 1 0.1 100 0 0 0 0 0       0 1 0
+102 1 0.1 101 0 0 0 0 0       0 1 0
+103 1 0.1 102 0 0 0 0 0       0 1 0
+104 1 0.1 103 0 0 0 0 0       0 1 0
+105 1 0.1 104 0 0 0 0 0       0 1 0
+106 1 0.1 105 0 0 0 0 0       0 1 0
+107 1 0.1 106 0 0 0 0 0       0 1 0
+108 1 0.1 107 0 0 0 0 0       0 1 0
+109 1 0.1 108 0 0 0 0 0       0 1 0
+110 1 0.1 109 0 0 0 0 0       0 1 0
+111 1 0.1 110 0 0 0 0 0       0 1 0
+112 1 0.1 111 0 0 0 0 0       0 1 0
+113 1 0.1 112 0 0 0 0 0       0 1 0
+114 1 0.1 113 0 0 0 0 0       0 1 0
+115 1 0.1 114 0 0 0 0 0       0 1 0
+116 1 0.1 115 0 0 0 0 0       0 1 0
+117 1 0.1 116 0 0 0 0 0       0 1 0
+118 1 0.1 117 0 0 0 0 0       0 1 0
+119 1 0.1 118 0 0 0 0 0       0 1 0
+120 1 0.1 119 0 0 0 0 0       1 1 1

examples/case06/input/driver.txt

@@ -1,2 +1,2 @@
 n amp_x amp_y amp_z freq_x freq_y freq_z phi_x phi_y phi_z period
-1     0     0   0.5      0      0    0.1     0     0   90    all
+1     0     0   2.0      0      0   0.05     0     0    90    all

examples/case06/input/input.txt

@@ -5,21 +5,24 @@
 # ── 流程控制 ──────────────────────────────────
 # 每步用 0/1 单独开关，1=执行，0=跳过
 # 依赖关系：抽帧依赖模拟结果，绘图依赖模拟+抽帧
-step_simulate:  1   # 运行物理模拟 → output/trajectory.txt
-step_sample:    1   # 抽帧 → output/display.txt
+step_simulate:  1   # 运行物理模拟 → output/display.txt（引擎直接抽帧）
+step_sample:    0   # （旧版）从 trajectory.txt 重新抽帧，默认0=不执行
 step_plot:      0   # 绘制轨迹/能量图 → output/trajectory_plots.png
-step_plot_wave: 0   # 绘制波形能量动画
-plot_wave_save_gif: 0  # 输出波形 GIF（需 step_plot_wave=1）
-plot_wave_save_mp4: 0  # 输出波形 MP4（需 step_plot_wave=1）
 step_animation: 1   # 自动播放 VisPy 3D 动画窗口（需安装 vispy）
-force_calc: 0       # 强制重新计算：1=跳过缓存强算，0=自动使用已有输出
+step_plot_wave: 0   # 绘制波形能量动画
+force_calc: 1       # 强制重新计算：1=跳过缓存强算，0=自动使用已有输出
+plot_wave_save_gif: 1  # 输出波形 GIF（需 step_plot_wave=1）
+plot_wave_save_mp4: 1  # 输出波形 MP4（需 step_plot_wave=1）
+
+# ── 文件保存 ──────────────────────────────────
+save_trajectory: 0  # 0=不保留完整轨迹文件, 1=保留 trajectory.txt（用于后续单独抽帧）
 
 # ── 计算引擎 ──────────────────────────────────
 # 可选: python, c, cpp, fortran, java
-engine: python      # 默认使用 python 引擎
+engine: c # 默认使用 python 引擎
 
 # ── 盒子 ──────────────────────────────────────
-box_a: 80.0         # 立方体半边长，粒子被限制在 [-box_a, box_a]³ 内
+box_a: 300.0         # 立方体半边长，粒子被限制在 [-box_a, box_a]³ 内
 
 # ── 初始构型 ──────────────────────────────────
 # 坐标文件格式：
@@ -35,14 +38,14 @@ plot_atom: 1
 
 # ── 物理参数 ──────────────────────────────────
 # 三个方向分量分别对应 x, y, z
-G: [0.0, 0.0, 0.0]   # 重力场分量 (m/s²)
-B: [0.0, 0.0, 0.0]   # 阻尼分量
+G: [0.00, 0.00, 0.00]   # 重力场分量 (m/s²)
+B: [0.01, 0.00, 0.01]   # 阻尼分量
 
 # ── 力开关（0=关闭, 1=开启）──────────────────
 gravity_field: 0         # 均匀重力场 (G)
 gravity_interaction: 0   # 原子间万有引力
 elastic_force: 1         # 弹簧键力
-damping_force: 0         # 阻尼 (B)
+damping_force: 1         # 阻尼 (B)
 driving_force: 1         # 驱动力（需 driver_file 定义）
 #
 gravity_strength: 1.0    # 万有引力强度（仅 gravity_interaction=1 时有效）
@@ -63,10 +66,10 @@ warmup_steps: 0           # 默认 0（立即开始记录）
 
 # 总模拟时间（秒），程序自动计算 NT = T_total / DT
 # 如果同时指定了 NT，以 NT 为准
-T_total: 50.0
+T_total:  1000.0
 
 # 抽帧间隔（每 NSTEP 步取一帧用于动画）
-NSTEP: 100
+NSTEP: 500
 
 # ── 时间步长 ──────────────────────────────────
 DT:    0.001         # 时间步长 (s)
@@ -85,7 +88,7 @@ use_marker: 1
 
 # ── 显示参数 ──────────────────────────────────
 # 盒子透明度：单个数值（统一）或 6 个数的数组，按 [-x,+x,-y,+y,-z,+z] 顺序
-alpha: [0.0, 0.0, 0.0, 0.0, 0.0, 0.5]
+alpha: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 
 # 小球颜色
 # 小球半径从 coord_file 的 radius 列读取
@@ -97,3 +100,12 @@ ball_color_b: 0.90  # B 分量
 box_color_r:  0.80
 box_color_g:  0.80
 box_color_b:  0.85
+
+# ── 摄像机初始位置 ────────────────────────────
+camera_distance:   120.0    # 摄像机到场景中心的距离
+camera_elevation:    0.0    # 俯仰角（度），负值=俯视
+camera_azimuth:      0.0    # 方位角（度）
+camera_center_x:    60.0    # 摄像机注视点 x
+camera_center_y:     0.0    # 摄像机注视点 y
+camera_center_z:     0.0    # 摄像机注视点 z
+move_camera:         0      # 0=固定视角, 1=按 move_camera.txt 运动

examples/case06/input/move_camera.txt

@@ -0,0 +1,9 @@
+# move_camera.txt — 摄像机速度段驱动
+# 格式: start-end  vx=f vy=f vz=f  rx=d ry=d rz=d
+#   vx/vy/vz: 平移速度（每帧移动单位）
+#   rx/ry/rz: 旋转速度（每帧度数）
+#     rx → elevation（俯仰）, ry → azimuth（方位）, rz → (预留)
+#
+# 示例：前60帧向右平移+绕x旋转，30-90帧向上平移+绕y绕z旋转
+all   vx=0.02
+# 30-90  vy=0.02  ry=1  rz=1

examples/case06/run_dynamics.py

@@ -31,7 +31,7 @@ def load_dynamics_module(module_path: Path):
 
 
 def main():
-    parser = argparse.ArgumentParser(description="运行 Dynamics 示例案例 case01")
+    parser = argparse.ArgumentParser(description="运行 Dynamics 示例案例 case06")
     parser.add_argument("--no-plot", action="store_true", help="跳过 matplotlib 绘图")
     args = parser.parse_args()
 

examples/case07/Readme.md

@@ -0,0 +1,40 @@
+# case06: 一维原子链横波模拟
+
+60 个原子沿 x 轴排列，相邻原子用弹簧连接。原子 1 受 z 方向驱动力作用，产生沿链传播的横波。
+
+## 物理设定
+
+| 参数 | 值 |
+|---|---|
+| 原子数 | 120 |
+| 排列 | 沿 x 轴等间距排列，间距为 1 |
+| 约束 | 原子**沿 z 方向自由振动**（fix_x=1, fix_y=1, fix_z=0），x, y 锁定 |
+| 弹簧 | 劲度系数 k=1.0，原长 L₀=1.0 |
+| 重力 | 无 |
+| 万有引力 | 无 |
+| 阻尼 | 无 |
+| 驱动力 | 原子 1（z 方向驱动） |
+| 算法 | leapfrog（蛙跳法，能量守恒） |
+
+## 驱动力
+
+原子 1 的位置由 `input/driver.txt` 中的驱动力公式决定：
+
+```math
+z(t) = A_z \cdot \cos(2\pi f_z t + \phi_z)
+```
+
+当前参数：A_z = 0.5, f_z = 0.1 Hz, φ_z = 90°, period = all（全程驱动）。
+
+## 动力学行为
+
+原子 1 沿 z 方向的受迫振动通过弹簧逐次传递给相邻原子，形成沿链传播的**横波**。由于 z 方向的振动是横向的，弹簧大部分张力在 x 方向，z 方向的有效刚度是非线性的——等效于一个三次方恢复力（FPU 型非线性），因此波速较慢。
+
+## 使用方法
+
+```bash
+cd examples/case06
+python run_dynamics.py
+```
+
+配置参数详见 `input/input.txt`，驱动力定义见 `input/driver.txt`，完整文档见 `doc/index.html`。

examples/case07/doc/index.html

@@ -0,0 +1,477 @@
+<!DOCTYPE html>
+<html lang="zh-CN">
+<head>
+<meta charset="UTF-8">
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<title>case06 — 一维原子链驱动力学模拟 | 物理原理 &amp; 使用文档</title>
+<style>
+  :root {
+    --bg: #f8f9fa;
+    --card: #fff;
+    --text: #1a1a2e;
+    --accent: #2563eb;
+    --accent-light: #dbeafe;
+    --code-bg: #1e293b;
+    --code-text: #e2e8f0;
+    --border: #e2e8f0;
+    --muted: #64748b;
+  }
+  * { margin: 0; padding: 0; box-sizing: border-box; }
+  body {
+    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Noto Sans SC", sans-serif;
+    background: var(--bg);
+    color: var(--text);
+    line-height: 1.7;
+  }
+
+  /* ── Header ── */
+  .hero {
+    background: linear-gradient(135deg, #1e293b 0%, #334155 100%);
+    color: #fff;
+    padding: 56px 24px 48px;
+    text-align: center;
+  }
+  .hero h1 { font-size: 2rem; font-weight: 700; letter-spacing: -0.02em; }
+  .hero .subtitle {
+    margin-top: 10px;
+    font-size: 1.05rem;
+    opacity: 0.8;
+  }
+  .hero .badge {
+    display: inline-block;
+    margin-top: 14px;
+    padding: 4px 14px;
+    border-radius: 999px;
+    background: rgba(255,255,255,0.12);
+    font-size: 0.82rem;
+  }
+
+  /* ── Layout ── */
+  .container { max-width: 820px; margin: 0 auto; padding: 32px 20px; }
+
+  section { margin-bottom: 44px; }
+  h2 {
+    font-size: 1.35rem;
+    font-weight: 600;
+    margin-bottom: 16px;
+    padding-bottom: 8px;
+    border-bottom: 2px solid var(--accent);
+    display: inline-block;
+  }
+  h3 {
+    font-size: 1.05rem;
+    font-weight: 600;
+    margin: 20px 0 10px;
+  }
+
+  p, li { margin-bottom: 10px; }
+  ul, ol { padding-left: 22px; }
+  strong { color: var(--accent); }
+
+  /* ── Cards ── */
+  .card {
+    background: var(--card);
+    border-radius: 12px;
+    padding: 20px 24px;
+    margin-bottom: 16px;
+    border: 1px solid var(--border);
+    box-shadow: 0 1px 3px rgba(0,0,0,0.04);
+  }
+
+  /* ── Formula / Code blocks ── */
+  .formula {
+    background: var(--card);
+    border-left: 4px solid var(--accent);
+    padding: 14px 20px;
+    margin: 14px 0;
+    font-family: "Times New Roman", "STIX", serif;
+    font-size: 1.05rem;
+    overflow-x: auto;
+    border-radius: 0 8px 8px 0;
+  }
+  code {
+    background: var(--accent-light);
+    padding: 2px 7px;
+    border-radius: 4px;
+    font-family: "JetBrains Mono", "Fira Code", monospace;
+    font-size: 0.88em;
+  }
+  pre {
+    background: var(--code-bg);
+    color: var(--code-text);
+    padding: 16px 20px;
+    border-radius: 10px;
+    overflow-x: auto;
+    font-size: 0.85rem;
+    line-height: 1.5;
+    margin: 14px 0;
+  }
+  pre .cm { color: #94a3b8; font-style: italic; }   /* comment */
+
+  /* ── Table ── */
+  table {
+    width: 100%;
+    border-collapse: collapse;
+    margin: 14px 0;
+    font-size: 0.92rem;
+  }
+  th, td {
+    padding: 8px 12px;
+    text-align: left;
+    border-bottom: 1px solid var(--border);
+  }
+  th { background: var(--accent-light); font-weight: 600; }
+
+  /* ── TOC ── */
+  .toc { counter-reset: toc; }
+  .toc li { counter-increment: toc; list-style: none; margin-bottom: 6px; }
+  .toc li::before { content: counter(toc) ". "; font-weight: 600; color: var(--accent); }
+  .toc a { color: var(--accent); text-decoration: none; }
+  .toc a:hover { text-decoration: underline; }
+
+  /* ── Flow diagram ── */
+  .flow { display: flex; flex-wrap: wrap; gap: 8px; align-items: center; justify-content: center; margin: 16px 0; }
+  .flow-step {
+    background: var(--accent-light);
+    border: 1px solid var(--accent);
+    border-radius: 8px;
+    padding: 8px 16px;
+    font-size: 0.88rem;
+    font-weight: 500;
+  }
+  .flow-arrow { color: var(--muted); font-size: 1.2rem; }
+
+  @media (max-width: 600px) {
+    .hero h1 { font-size: 1.5rem; }
+    .flow { flex-direction: column; }
+    .flow-arrow { transform: rotate(90deg); }
+  }
+</style>
+</head>
+<body>
+
+<!-- ============================================================ -->
+<!--  Header                                                       -->
+<!-- ============================================================ -->
+<header class="hero">
+  <h1>一维原子链驱动力学模拟</h1>
+  <p class="subtitle">120 个原子沿 x 轴排列 · 弹簧连接 · z 方向受迫振动</p>
+  <span class="badge">case06  ·  examples/case06</span>
+</header>
+
+<div class="container">
+
+<!-- ============================================================ -->
+<!--  TOC                                                          -->
+<!-- ============================================================ -->
+<section>
+  <h2>目录</h2>
+  <ol class="toc">
+    <li><a href="#physics">物理原理</a></li>
+    <li><a href="#algorithm">数值算法</a></li>
+    <li><a href="#driver">驱动力模型</a></li>
+    <li><a href="#usage">使用方法</a></li>
+    <li><a href="#params">参数参考</a></li>
+    <li><a href="#files">文件结构</a></li>
+    <li><a href="#troubleshoot">常见问题</a></li>
+  </ol>
+</section>
+
+<!-- ============================================================ -->
+<!--  1. Physics                                                   -->
+<!-- ============================================================ -->
+<section id="physics">
+  <h2>一、物理原理</h2>
+
+  <div class="card">
+    <h3>1.1 一维原子链</h3>
+    <p>120 个原子沿 <strong>x 轴</strong> 等间距排列，原子间距为 1。相邻原子之间用 <strong>理想弹簧</strong> 连接，弹簧的劲度系数 <em>k</em> = 1.0，原长 <em>L</em>₀ = 1.0（与原子间距一致，初始状态弹簧无拉伸）。</p>
+    <p>每个原子被限制在 <strong>z 方向</strong> 自由振动，x 和 y 方向锁定（<code>fix_x=1, fix_y=1, fix_z=0</code>）。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.2 弹簧力（胡克定律）</h3>
+    <p>当原子 <em>i</em> 和 <em>j</em> 之间有弹簧连接时，原子 <em>i</em> 受到的弹簧力为：</p>
+    <div class="formula">
+      <strong>F</strong> = −<em>k</em> · (<em>d</em> − <em>L</em>₀) · <strong>u</strong><sub><em>ij</em></sub>
+    </div>
+    <p>其中 <em>d</em> = |<strong>r</strong><sub><em>j</em></sub> − <strong>r</strong><sub><em>i</em></sub>| 为两原子间距离，<strong>u</strong><sub><em>ij</em></sub> 为从 <em>i</em> 指向 <em>j</em> 的单位向量。由于原子只在 z 方向振动，弹簧在 z 方向的分量是 <strong>几何非线性</strong> 的——对于小振幅近似，z 方向等效于一个三次方恢复力（FPU 型非线性）。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.3 运动方程</h3>
+    <p>对于第 <em>i</em> 个自由原子（非受驱），牛顿第二定律给出：</p>
+    <div class="formula">
+      <em>m</em> · <strong>a</strong><sub><em>i</em></sub> = <strong>F</strong><sub><em>i</em></sub><sup>spring</sup> + <strong>F</strong><sub><em>i</em></sub><sup>driving</sup>
+    </div>
+    <p>本案例中 <strong>唯一的外力</strong> 来自驱动力（仅施加于原子 1）。无重力、无万有引力、无阻尼，系统总能量守恒。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.4 波传播</h3>
+    <p>原子 1 的受迫振动通过弹簧逐次传递给相邻原子，形成沿链传播的 <strong>横波</strong>。由于横向振动的几何非线性（弹簧大部分张力在 x 方向，z 方向的有效刚度远小于 1），波的传播速度较慢，且高阶频率成分会在链中产生复杂的非线性动力学行为（类似 FPU 回波现象）。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  2. Algorithm                                                 -->
+<!-- ============================================================ -->
+<section id="algorithm">
+  <h2>二、数值算法</h2>
+
+  <div class="card">
+    <h3>2.1 蛙跳法（Leapfrog / Velocity-Verlet）</h3>
+    <p>采用能量守恒特性优异的 <strong>蛙跳法</strong>（二阶辛积分器），更新公式为：</p>
+    <div class="formula">
+      <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) = <strong>v</strong>(<em>t</em>) + ½ <strong>a</strong>(<em>t</em>) · Δ<em>t</em><br>
+      <strong>r</strong>(<em>t</em> + Δ<em>t</em>) = <strong>r</strong>(<em>t</em>) + <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) · Δ<em>t</em><br>
+      <strong>a</strong>(<em>t</em> + Δ<em>t</em>) = <strong>F</strong>(<strong>r</strong>(<em>t</em> + Δ<em>t</em>), <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>)) / <em>m</em><br>
+      <strong>v</strong>(<em>t</em> + Δ<em>t</em>) = <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) + ½ <strong>a</strong>(<em>t</em> + Δ<em>t</em>) · Δ<em>t</em>
+    </div>
+    <p>蛙跳法在长时间模拟中能量漂移极小（本案例验证 <strong>&lt; 0.004%</strong>），适合无阻尼的保守系统。</p>
+  </div>
+
+  <div class="card">
+    <h3>2.2 时间步长与采样</h3>
+    <table>
+      <tr><th>参数</th><th>值</th><th>说明</th></tr>
+      <tr><td>DT</td><td>0.01 s</td><td>积分步长（远小于 1/ω ≈ 0.16 s，满足稳定性条件）</td></tr>
+      <tr><td>T_total</td><td>100 s</td><td>总模拟时间 → NT = 10000 步</td></tr>
+      <tr><td>NSTEP</td><td>50</td><td>每 NSTEP 步取一帧用于动画 → 200 帧</td></tr>
+      <tr><td>method</td><td>leapfrog</td><td>蛙跳法（Velocity-Verlet）</td></tr>
+    </table>
+  </div>
+
+  <div class="card">
+    <h3>2.3 计算流程</h3>
+    <div class="flow">
+      <span class="flow-step">读入 coord.txt<br>connection.txt<br>bond.txt</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">施加驱动力<br>（驱动原子 1）</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">记录轨迹</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">蛙跳法<br>更新位置/速度</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">固定约束<br>（x, y 锁定）</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step" style="background:#fef3c7;border-color:#f59e0b;">循环<br>NT 次</span>
+    </div>
+    <p style="margin-top:12px;">注意：驱动力在 <strong>每次积分前</strong> 施加，确保受驱原子的位置正确传递给弹簧力计算。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  3. Driving Force                                             -->
+<!-- ============================================================ -->
+<section id="driver">
+  <h2>三、驱动力模型</h2>
+
+  <div class="card">
+    <h3>3.1 定义文件</h3>
+    <p>驱动力由 <code>input/driver.txt</code> 定义，格式如下：</p>
+    <pre>n amp_x amp_y amp_z freq_x freq_y freq_z phi_x phi_y phi_z period
+1     0     0     5      0      0      1     0     0    90    all</pre>
+  </div>
+
+  <div class="card">
+    <h3>3.2 数学公式</h3>
+    <p>受驱原子的位置由下式决定（<strong>完全替换</strong> coord.txt 中的初始坐标和固定约束）：</p>
+    <div class="formula">
+      <strong>r</strong>(<em>t</em>) = <strong>A</strong> · cos(2π<em>f</em> · <em>t</em> + <strong>φ</strong>)
+    </div>
+    <p>速度由解析导数给出：</p>
+    <div class="formula">
+      <strong>v</strong>(<em>t</em>) = −<strong>A</strong> · 2π<em>f</em> · sin(2π<em>f</em> · <em>t</em> + <strong>φ</strong>)
+    </div>
+    <p>其中 <strong>A</strong> = (amp_x, amp_y, amp_z)，<strong>f</strong> = (freq_x, freq_y, freq_z) 为不同方向的驱动频率，<strong>φ</strong> = (phi_x, phi_y, phi_z) 为相位（<strong>角度制</strong>，代码自动转换为弧度）。</p>
+  </div>
+
+  <div class="card">
+    <h3>3.3 本案例驱动参数</h3>
+    <table>
+      <tr><th>参数</th><th>值</th><th>含义</th></tr>
+      <tr><td>amp_z</td><td>5.0</td><td>z 方向驱动振幅</td></tr>
+      <tr><td>freq_z</td><td>1.0 Hz</td><td>驱动频率（周期 1 s）</td></tr>
+      <tr><td>phi_z</td><td>90°</td><td>驱动相位 → z(0) = 5·cos(90°) = 0</td></tr>
+      <tr><td>period</td><td>all</td><td>全程驱动，永不停止</td></tr>
+    </table>
+    <div class="formula">
+      <em>z</em>(<em>t</em>) = 5.0 · cos(2π · 1.0 · <em>t</em> + 90°)
+    </div>
+  </div>
+
+  <div class="card">
+    <h3>3.4 有限周期驱动</h3>
+    <p><code>period</code> 参数支持三种模式：</p>
+    <ul>
+      <li><strong>all</strong> — 全程驱动</li>
+      <li><strong>数值</strong> — 驱动指定周期数后 <strong>静止</strong>（冻结在最终位置，速度归零）。例如 <code>period: 1</code> 表示驱动 1 个完整周期后停止。</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>3.5 驱动与固定约束的关系</h3>
+    <p>对于受驱原子（<code>driver.txt</code> 中 <code>n</code> 指定的原子），其在 <code>coord.txt</code> 中的初始坐标和 <code>fix_x/fix_y/fix_z</code> 约束被 <strong>完全忽略</strong>。原子的位置和速度完全由驱动力公式决定。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  4. Usage                                                     -->
+<!-- ============================================================ -->
+<section id="usage">
+  <h2>四、使用方法</h2>
+
+  <div class="card">
+    <h3>4.1 完整运行（模拟 + 动画）</h3>
+    <pre>cd examples/case06
+python run_dynamics.py</pre>
+    <p>这步会依次执行：物理模拟 → 抽帧 → 打开 VisPy 3D 动画窗口。</p>
+  </div>
+
+  <div class="card">
+    <h3>4.2 仅查看已有结果</h3>
+    <p>如果已经跑完模拟且生成了 <code>output/display.txt</code>，可以通过修改 <code>input.txt</code> 跳过计算，只开动画：</p>
+    <pre>step_simulate:  0   # 跳过模拟
+step_sample:    0   # 跳过抽帧
+step_animation: 1   # 播放动画</pre>
+    <p>然后运行：<code>python run_dynamics.py</code></p>
+  </div>
+
+  <div class="card">
+    <h3>4.3 手动 3D 动画</h3>
+    <p>也可以单独启动 VisPy 窗口：</p>
+    <pre>python ../../draw.py output/</pre>
+  </div>
+
+  <div class="card">
+    <h3>4.4 强制重新计算</h3>
+    <p>修改参数后需要重新运行模拟时，设置：</p>
+    <pre>force_calc: 1        # 忽略缓存，强制重新计算</pre>
+  </div>
+
+  <div class="card">
+    <h3>4.5 动画交互</h3>
+    <table>
+      <tr><th>操作</th><th>效果</th></tr>
+      <tr><td>鼠标拖动</td><td>旋转视角</td></tr>
+      <tr><td>滚轮</td><td>缩放</td></tr>
+      <tr><td>W / S 键</td><td>相机沿 Z 轴向前 / 向后移动（靠近/远离场景）</td></tr>
+      <tr><td>A / D 键</td><td>视角向右 / 向左平移</td></tr>
+      <tr><td>E / Q 键</td><td>视角上升 / 下降（屏幕方向）</td></tr>
+      <tr><td>C / X 键</td><td>增大 / 减小步长</td></tr>
+      <tr><td>V 键</td><td>切换透视 / 正交投影</td></tr>
+      <tr><td>左上角 <strong>reset</strong> 按钮</td><td>复位视角到初始位置</td></tr>
+      <tr><td>左上角 <strong>info</strong> 按钮</td><td>切换信息面板显示/隐藏</td></tr>
+      <tr><td>左上角 <strong>axes</strong> 按钮</td><td>切换坐标轴显示/隐藏</td></tr>
+    </table>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  5. Parameters                                                -->
+<!-- ============================================================ -->
+<section id="params">
+  <h2>五、参数参考</h2>
+
+  <div class="card">
+    <h3>5.1 input.txt 关键参数</h3>
+    <table>
+      <tr><th>参数</th><th>默认值</th><th>说明</th></tr>
+      <tr><td>gravity_field</td><td>0</td><td>均匀重力场（已关闭）</td></tr>
+      <tr><td>gravity_interaction</td><td>0</td><td>原子间万有引力（已关闭）</td></tr>
+      <tr><td>elastic_force</td><td>1</td><td>弹簧键力（已开启）</td></tr>
+      <tr><td>damping_force</td><td>0</td><td>阻尼（已关闭）</td></tr>
+      <tr><td><strong>driving_force</strong></td><td><strong>1</strong></td><td>驱动力开关（1=开启，需 driver.txt）</td></tr>
+      <tr><td>method</td><td>leapfrog</td><td>数值积分方法</td></tr>
+      <tr><td>DT</td><td>0.01</td><td>积分步长 (s)</td></tr>
+      <tr><td>T_total</td><td>100.0</td><td>总模拟时间 (s)</td></tr>
+      <tr><td>NSTEP</td><td>50</td><td>抽帧步数间隔</td></tr>
+      <tr><td>engine</td><td>python</td><td>计算引擎（python / c / cpp / fortran）</td></tr>
+      <tr><td>use_marker</td><td>1</td><td>渲染模式（0=Sphere 网格, 1=Marker GPU 实例化）</td></tr>
+    </table>
+  </div>
+
+  <div class="card">
+    <h3>5.2 流程控制参数</h3>
+    <table>
+      <tr><th>参数</th><th>0</th><th>1</th></tr>
+      <tr><td>step_simulate</td><td>跳过模拟（加载已有轨迹）</td><td>运行物理模拟</td></tr>
+      <tr><td>step_sample</td><td>跳过抽帧</td><td>从轨迹抽取显示帧</td></tr>
+      <tr><td>step_plot</td><td>不生成图表</td><td>生成轨迹/能量图</td></tr>
+      <tr><td><strong>step_plot_wave</strong></td><td>不生成波形图</td><td>生成波形能量动画 GIF</td></tr>
+      <tr><td>step_animation</td><td>不启动动画</td><td>自动打开 VisPy 3D 窗口</td></tr>
+      <tr><td>force_calc</td><td>自动检测缓存</td><td>强制重新计算</td></tr>
+    </table>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  6. File Structure                                            -->
+<!-- ============================================================ -->
+<section id="files">
+  <h2>六、文件结构</h2>
+
+  <pre>case06/
+├── input/
+│   ├── input.txt          # 主配置文件（YAML 格式）
+│   ├── coord.txt          # 原子坐标（120 个原子）
+│   ├── connection.txt     # 弹簧连接关系（59 条键）
+│   ├── bond.txt           # 弹簧参数（k=1.0, L₀=1.0）
+│   └── <strong>driver.txt</strong>       # <span class="cm">驱动力定义（本案例新增）</span>
+├── output/
+│   ├── trajectory.txt     # 全量轨迹数据（50000 步 × 120 原子）
+│   ├── display.txt        # 抽帧后的动画数据（500 帧 × 120 原子）
+│   ├── dynamics.log       # 计算日志
+│   ├── animation.log      # 动画启动日志（闪退时排查用）
+│   └── wave_animation.gif # 波形能量动画（step_plot_wave=1 时生成）
+├── doc/
+│   └── index.html         # <span class="cm">本文档</span>
+├── Readme.md              # 案例简介
+└── run_dynamics.py        # 案例运行入口</pre>
+</section>
+
+<!-- ============================================================ -->
+<!--  7. Troubleshooting                                           -->
+<!-- ============================================================ -->
+<section id="troubleshoot">
+  <h2>七、常见问题</h2>
+
+  <div class="card">
+    <h3>7.1 动画窗口闪退</h3>
+    <p>如果 VisPy 窗口一闪就消失，请检查：</p>
+    <ul>
+      <li><code>output/animation.log</code> 中是否有错误信息</li>
+      <li><code>output/display.txt</code> 是否存在（需先跑 <code>step_sample: 1</code>）</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>7.2 原子不振动</h3>
+    <p>可能原因：</p>
+    <ul>
+      <li><strong>NSTEP 过大</strong>：抽帧间隔大于驱动周期的一半时，动画会丢失振动细节。建议 NSTEP ≤ 1/(freq · DT · 10)</li>
+      <li><strong>相位 φ 使采样点落在零值</strong>：试试 <code>phi_z: 0</code> 让原子在 t=0 处于振幅峰值</li>
+      <li>确认 <code>driving_force: 1</code> 且 <code>driver.txt</code> 中 amp_z 不为 0</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>7.3 渲染性能慢</h3>
+    <p>原子数多时动画卡顿：</p>
+    <ul>
+      <li>设置 <code>use_marker: 1</code>（使用 GPU 实例化渲染替代独立网格球体）</li>
+      <li>增大 <code>NSTEP</code> 减少动画帧数</li>
+    </ul>
+  </div>
+</section>
+
+<hr style="border:none;border-top:1px solid var(--border);margin:40px 0;">
+
+<footer style="text-align:center;color:var(--muted);font-size:0.85rem;margin-bottom:40px;">
+  Dynamics Simulation Framework &nbsp;·&nbsp; 生成于 2026-06-10
+</footer>
+
+</div>
+</body>
+</html>

examples/case07/input/bond.txt

@@ -0,0 +1,2 @@
+bond_name k       rest_length
+k1        500.0   1.0

examples/case07/input/connection.txt

@@ -0,0 +1,120 @@
+n1 n2 bond_name
+1 2 k1
+2 3 k1
+3 4 k1
+4 5 k1
+5 6 k1
+6 7 k1
+7 8 k1
+8 9 k1
+9 10 k1
+10 11 k1
+11 12 k1
+12 13 k1
+13 14 k1
+14 15 k1
+15 16 k1
+16 17 k1
+17 18 k1
+18 19 k1
+19 20 k1
+20 21 k1
+21 22 k1
+22 23 k1
+23 24 k1
+24 25 k1
+25 26 k1
+26 27 k1
+27 28 k1
+28 29 k1
+29 30 k1
+30 31 k1
+31 32 k1
+32 33 k1
+33 34 k1
+34 35 k1
+35 36 k1
+36 37 k1
+37 38 k1
+38 39 k1
+39 40 k1
+40 41 k1
+41 42 k1
+42 43 k1
+43 44 k1
+44 45 k1
+45 46 k1
+46 47 k1
+47 48 k1
+48 49 k1
+49 50 k1
+50 51 k1
+51 52 k1
+52 53 k1
+53 54 k1
+54 55 k1
+55 56 k1
+56 57 k1
+57 58 k1
+58 59 k1
+59 60 k1
+60 61 k1
+61 62 k1
+62 63 k1
+63 64 k1
+64 65 k1
+65 66 k1
+66 67 k1
+67 68 k1
+68 69 k1
+69 70 k1
+70 71 k1
+71 72 k1
+72 73 k1
+73 74 k1
+74 75 k1
+75 76 k1
+76 77 k1
+77 78 k1
+78 79 k1
+79 80 k1
+80 81 k1
+81 82 k1
+82 83 k1
+83 84 k1
+84 85 k1
+85 86 k1
+86 87 k1
+87 88 k1
+88 89 k1
+89 90 k1
+90 91 k1
+91 92 k1
+92 93 k1
+93 94 k1
+94 95 k1
+95 96 k1
+96 97 k1
+97 98 k1
+98 99 k1
+99 100 k1
+100 101 k1
+101 102 k1
+102 103 k1
+103 104 k1
+104 105 k1
+105 106 k1
+106 107 k1
+107 108 k1
+108 109 k1
+109 110 k1
+110 111 k1
+111 112 k1
+112 113 k1
+113 114 k1
+114 115 k1
+115 116 k1
+116 117 k1
+117 118 k1
+118 119 k1
+119 120 k1

examples/case07/input/coord.txt

@@ -0,0 +1,121 @@
+n mass radius x y z vx vy vz fix_x fix_y fix_z
+1 1 0.1 0 0 0 0 0 0       0 1 0
+2 1 0.1 1 0 0 0 0 0       0 1 0
+3 1 0.1 2 0 0 0 0 0       0 1 0
+4 1 0.1 3 0 0 0 0 0       0 1 0
+5 1 0.1 4 0 0 0 0 0       0 1 0
+6 1 0.1 5 0 0 0 0 0       0 1 0
+7 1 0.1 6 0 0 0 0 0       0 1 0
+8 1 0.1 7 0 0 0 0 0       0 1 0
+9 1 0.1 8 0 0 0 0 0       0 1 0
+10 1 0.1 9 0 0 0 0 0       0 1 0
+11 1 0.1 10 0 0 0 0 0       0 1 0
+12 1 0.1 11 0 0 0 0 0       0 1 0
+13 1 0.1 12 0 0 0 0 0       0 1 0
+14 1 0.1 13 0 0 0 0 0       0 1 0
+15 1 0.1 14 0 0 0 0 0       0 1 0
+16 1 0.1 15 0 0 0 0 0       0 1 0
+17 1 0.1 16 0 0 0 0 0       0 1 0
+18 1 0.1 17 0 0 0 0 0       0 1 0
+19 1 0.1 18 0 0 0 0 0       0 1 0
+20 1 0.1 19 0 0 0 0 0       0 1 0
+21 1 0.1 20 0 0 0 0 0       0 1 0
+22 1 0.1 21 0 0 0 0 0       0 1 0
+23 1 0.1 22 0 0 0 0 0       0 1 0
+24 1 0.1 23 0 0 0 0 0       0 1 0
+25 1 0.1 24 0 0 0 0 0       0 1 0
+26 1 0.1 25 0 0 0 0 0       0 1 0
+27 1 0.1 26 0 0 0 0 0       0 1 0
+28 1 0.1 27 0 0 0 0 0       0 1 0
+29 1 0.1 28 0 0 0 0 0       0 1 0
+30 1 0.1 29 0 0 0 0 0       0 1 0
+31 1 0.1 30 0 0 0 0 0       0 1 0
+32 1 0.1 31 0 0 0 0 0       0 1 0
+33 1 0.1 32 0 0 0 0 0       0 1 0
+34 1 0.1 33 0 0 0 0 0       0 1 0
+35 1 0.1 34 0 0 0 0 0       0 1 0
+36 1 0.1 35 0 0 0 0 0       0 1 0
+37 1 0.1 36 0 0 0 0 0       0 1 0
+38 1 0.1 37 0 0 0 0 0       0 1 0
+39 1 0.1 38 0 0 0 0 0       0 1 0
+40 1 0.1 39 0 0 0 0 0       0 1 0
+41 1 0.1 40 0 0 0 0 0       0 1 0
+42 1 0.1 41 0 0 0 0 0       0 1 0
+43 1 0.1 42 0 0 0 0 0       0 1 0
+44 1 0.1 43 0 0 0 0 0       0 1 0
+45 1 0.1 44 0 0 0 0 0       0 1 0
+46 1 0.1 45 0 0 0 0 0       0 1 0
+47 1 0.1 46 0 0 0 0 0       0 1 0
+48 1 0.1 47 0 0 0 0 0       0 1 0
+49 1 0.1 48 0 0 0 0 0       0 1 0
+50 1 0.1 49 0 0 0 0 0       0 1 0
+51 1 0.1 50 0 0 0 0 0       0 1 0
+52 1 0.1 51 0 0 0 0 0       0 1 0
+53 1 0.1 52 0 0 0 0 0       0 1 0
+54 1 0.1 53 0 0 0 0 0       0 1 0
+55 1 0.1 54 0 0 0 0 0       0 1 0
+56 1 0.1 55 0 0 0 0 0       0 1 0
+57 1 0.1 56 0 0 0 0 0       0 1 0
+58 1 0.1 57 0 0 0 0 0       0 1 0
+59 1 0.1 58 0 0 0 0 0       0 1 0
+60 1 0.1 59 0 0 0 0 0       0 1 0
+61 1 0.1 60 0 0 0 0 0       0 1 0
+62 1 0.1 61 0 0 0 0 0       0 1 0
+63 1 0.1 62 0 0 0 0 0       0 1 0
+64 1 0.1 63 0 0 0 0 0       0 1 0
+65 1 0.1 64 0 0 0 0 0       0 1 0
+66 1 0.1 65 0 0 0 0 0       0 1 0
+67 1 0.1 66 0 0 0 0 0       0 1 0
+68 1 0.1 67 0 0 0 0 0       0 1 0
+69 1 0.1 68 0 0 0 0 0       0 1 0
+70 1 0.1 69 0 0 0 0 0       0 1 0
+71 1 0.1 70 0 0 0 0 0       0 1 0
+72 1 0.1 71 0 0 0 0 0       0 1 0
+73 1 0.1 72 0 0 0 0 0       0 1 0
+74 1 0.1 73 0 0 0 0 0       0 1 0
+75 1 0.1 74 0 0 0 0 0       0 1 0
+76 1 0.1 75 0 0 0 0 0       0 1 0
+77 1 0.1 76 0 0 0 0 0       0 1 0
+78 1 0.1 77 0 0 0 0 0       0 1 0
+79 1 0.1 78 0 0 0 0 0       0 1 0
+80 1 0.1 79 0 0 0 0 0       0 1 0
+81 1 0.1 80 0 0 0 0 0       0 1 0
+82 1 0.1 81 0 0 0 0 0       0 1 0
+83 1 0.1 82 0 0 0 0 0       0 1 0
+84 1 0.1 83 0 0 0 0 0       0 1 0
+85 1 0.1 84 0 0 0 0 0       0 1 0
+86 1 0.1 85 0 0 0 0 0       0 1 0
+87 1 0.1 86 0 0 0 0 0       0 1 0
+88 1 0.1 87 0 0 0 0 0       0 1 0
+89 1 0.1 88 0 0 0 0 0       0 1 0
+90 1 0.1 89 0 0 0 0 0       0 1 0
+91 1 0.1 90 0 0 0 0 0       0 1 0
+92 1 0.1 91 0 0 0 0 0       0 1 0
+93 1 0.1 92 0 0 0 0 0       0 1 0
+94 1 0.1 93 0 0 0 0 0       0 1 0
+95 1 0.1 94 0 0 0 0 0       0 1 0
+96 1 0.1 95 0 0 0 0 0       0 1 0
+97 1 0.1 96 0 0 0 0 0       0 1 0
+98 1 0.1 97 0 0 0 0 0       0 1 0
+99 1 0.1 98 0 0 0 0 0       0 1 0
+100 1 0.1 99 0 0 0 0 0       0 1 0
+101 1 0.1 100 0 0 0 0 0       0 1 0
+102 1 0.1 101 0 0 0 0 0       0 1 0
+103 1 0.1 102 0 0 0 0 0       0 1 0
+104 1 0.1 103 0 0 0 0 0       0 1 0
+105 1 0.1 104 0 0 0 0 0       0 1 0
+106 1 0.1 105 0 0 0 0 0       0 1 0
+107 1 0.1 106 0 0 0 0 0       0 1 0
+108 1 0.1 107 0 0 0 0 0       0 1 0
+109 1 0.1 108 0 0 0 0 0       0 1 0
+110 1 0.1 109 0 0 0 0 0       0 1 0
+111 1 0.1 110 0 0 0 0 0       0 1 0
+112 1 0.1 111 0 0 0 0 0       0 1 0
+113 1 0.1 112 0 0 0 0 0       0 1 0
+114 1 0.1 113 0 0 0 0 0       0 1 0
+115 1 0.1 114 0 0 0 0 0       0 1 0
+116 1 0.1 115 0 0 0 0 0       0 1 0
+117 1 0.1 116 0 0 0 0 0       0 1 0
+118 1 0.1 117 0 0 0 0 0       0 1 0
+119 1 0.1 118 0 0 0 0 0       0 1 0
+120 1 0.1 119 0 0 0 0 0       1 1 1

examples/case07/input/driver.txt

@@ -0,0 +1,3 @@
+  n amp_x amp_y amp_z freq_x freq_y  freq_z phi_x phi_y phi_z period
+  1     0     0   0.1      0      0 0.01333     0     0    90    all
+120     0     0   0.1      0      0 0.01333     0     0    90    all

examples/case07/input/input.txt

@@ -0,0 +1,114 @@
+# 物理模拟参数配置
+# 格式：YAML
+# 用法：python run_dynamics.py
+
+# ── 流程控制 ──────────────────────────────────
+# 每步用 0/1 单独开关，1=执行，0=跳过
+# 依赖关系：抽帧依赖模拟结果，绘图依赖模拟+抽帧
+step_simulate:  1   # 运行物理模拟 → output/display.txt（引擎直接抽帧）
+step_sample:    0   # （旧版）从 trajectory.txt 重新抽帧，默认0=不执行
+step_plot:      0   # 绘制轨迹/能量图 → output/trajectory_plots.png
+step_animation: 0   # 自动播放 VisPy 3D 动画窗口（需安装 vispy）
+step_plot_wave: 1   # 绘制波形能量动画
+force_calc: 1       # 强制重新计算：1=跳过缓存强算，0=自动使用已有输出
+plot_wave_save_gif: 0  # 输出波形 GIF（需 step_plot_wave=1）
+plot_wave_save_mp4: 0  # 输出波形 MP4（需 step_plot_wave=1）
+
+# ── 文件保存 ──────────────────────────────────
+save_trajectory: 0  # 0=不保留完整轨迹文件, 1=保留 trajectory.txt（用于后续单独抽帧）
+
+# ── 计算引擎 ──────────────────────────────────
+# 可选: python, c, cpp, fortran, java
+engine: c # 默认使用 python 引擎
+
+# ── 盒子 ──────────────────────────────────────
+box_a: 300.0         # 立方体半边长，粒子被限制在 [-box_a, box_a]³ 内
+
+# ── 初始构型 ──────────────────────────────────
+# 坐标文件格式：
+#   第一行：n mass radius x y z vx vy vz fix_x fix_y fix_z
+#   后续行：原子序号 质量 半径 x y z vx vy vz fix_x fix_y fix_z
+coord_file: input/coord.txt
+connection_file: input/connection.txt
+bond_file: input/bond.txt
+driver_file: input/driver.txt     # 驱动力定义文件（driving_force=1 时生效）
+
+# 绘图/动画展示的原子序号（对应 coord_file 第一列 n）
+plot_atom: 1
+
+# ── 物理参数 ──────────────────────────────────
+# 三个方向分量分别对应 x, y, z
+G: [0.000, 0.000, 0.000]   # 重力场分量 (m/s²)
+B: [0.005, 0.000, 0.005]   # 阻尼分量
+
+# ── 力开关（0=关闭, 1=开启）──────────────────
+gravity_field: 0         # 均匀重力场 (G)
+gravity_interaction: 0   # 原子间万有引力
+elastic_force: 1         # 弹簧键力
+damping_force: 1         # 阻尼 (B)
+driving_force: 1         # 驱动力（需 driver_file 定义）
+#
+gravity_strength: 1.0    # 万有引力强度（仅 gravity_interaction=1 时有效）
+
+# ── 数值算法 ──────────────────────────────────
+# 可选：
+#   explicit_euler  显式欧拉法
+#   implicit_euler  隐式欧拉法
+#   midpoint        中点法
+#   leapfrog        蛙跳法
+method: leapfrog
+
+# ── 步骤控制 ──────────────────────────────────
+# 以下参数控制哪些步骤被执行和保存
+
+# 预热步数：模拟开始时跳过不保存的步数（用于稳定初始状态）
+warmup_steps: 0           # 默认 0（立即开始记录）
+
+# 总模拟时间（秒），程序自动计算 NT = T_total / DT
+# 如果同时指定了 NT，以 NT 为准
+T_total:  1000.0
+
+# 抽帧间隔（每 NSTEP 步取一帧用于动画）
+NSTEP: 500
+
+# ── 时间步长 ──────────────────────────────────
+DT:    0.001         # 时间步长 (s)
+
+# 抽帧范围：只保存 [sample_start, sample_end) 区间内的帧
+sample_start: null        # null 表示从头开始（帧索引从 0 起）
+sample_end: null          # null 表示到末尾
+
+
+
+# ── 渲染方式 ──────────────────────────────────
+# 3D 动画中原子渲染方式：
+#   0 = Sphere （网格球体，效果精细，原子数少时推荐）
+#   1 = Marker （GPU 实例化点，原子数多时性能更佳）
+use_marker: 1
+
+# ── 显示参数 ──────────────────────────────────
+# 盒子透明度：单个数值（统一）或 6 个数的数组，按 [-x,+x,-y,+y,-z,+z] 顺序
+alpha: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+
+# 小球颜色
+# 小球半径从 coord_file 的 radius 列读取
+ball_color_r: 0.20  # R 分量 (0~1)
+ball_color_g: 0.60  # G 分量
+ball_color_b: 0.90  # B 分量
+
+# 盒子面颜色
+box_color_r:  0.80
+box_color_g:  0.80
+box_color_b:  0.85
+
+# ── 摄像机初始位置 ────────────────────────────
+camera_distance:   120.0    # 摄像机到场景中心的距离
+camera_elevation:    0.0    # 俯仰角（度），负值=俯视
+camera_azimuth:      0.0    # 方位角（度）
+camera_center_x:    60.0    # 摄像机注视点 x
+camera_center_y:     0.0    # 摄像机注视点 y
+camera_center_z:     0.0    # 摄像机注视点 z
+move_camera:         0      # 0=固定视角, 1=按 move_camera.txt 运动
+
+# ── 视觉放大 ──────────────────────────────────
+display_amp: [1.0, 1.0, 10.0]   # x/y/z 方向视觉位移放大倍数（不影响物理）

examples/case07/input/move_camera.txt

@@ -0,0 +1,9 @@
+# move_camera.txt — 摄像机速度段驱动
+# 格式: start-end  vx=f vy=f vz=f  rx=d ry=d rz=d
+#   vx/vy/vz: 平移速度（每帧移动单位）
+#   rx/ry/rz: 旋转速度（每帧度数）
+#     rx → elevation（俯仰）, ry → azimuth（方位）, rz → (预留)
+#
+# 示例：前60帧向右平移+绕x旋转，30-90帧向上平移+绕y绕z旋转
+all   vx=0.02
+# 30-90  vy=0.02  ry=1  rz=1

examples/case07/run_dynamics.py

@@ -0,0 +1,54 @@
+"""
+Case runner for Dynamics case06 — 1D atomic chain (transverse wave).
+
+This script keeps program and data separated:
+  - program: ../../dynamics.py
+  - input:   ./input
+  - output:  ./output
+"""
+
+from __future__ import annotations
+
+import argparse
+import importlib.util
+from pathlib import Path
+
+
+CASE_DIR = Path(__file__).resolve().parent
+DYNAMICS_PATH = Path("..") / ".." / "dynamics.py"
+INPUT_DIR = Path("input")
+OUTPUT_DIR = Path("output")
+CONFIG_FILE = INPUT_DIR / "input.txt"
+
+
+def load_dynamics_module(module_path: Path):
+    spec = importlib.util.spec_from_file_location("dynamics_module", module_path)
+    if spec is None or spec.loader is None:
+        raise ImportError(f"无法加载 dynamics.py: {module_path}")
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def main():
+    parser = argparse.ArgumentParser(description="运行 Dynamics 示例案例 case06")
+    parser.add_argument("--no-plot", action="store_true", help="跳过 matplotlib 绘图")
+    args = parser.parse_args()
+
+    dynamics_path = (CASE_DIR / DYNAMICS_PATH).resolve()
+    input_dir = (CASE_DIR / INPUT_DIR).resolve()
+    output_dir = (CASE_DIR / OUTPUT_DIR).resolve()
+    config_path = (CASE_DIR / CONFIG_FILE).resolve()
+
+    module = load_dynamics_module(dynamics_path)
+    module.run_case(
+        config_path=config_path,
+        runtime_base=CASE_DIR,
+        input_dir=input_dir,
+        output_dir=output_dir,
+        no_plot=args.no_plot,
+    )
+
+
+if __name__ == "__main__":
+    main()

examples/case08/Readme.md

@@ -0,0 +1,40 @@
+# case06: 一维原子链横波模拟
+
+60 个原子沿 x 轴排列，相邻原子用弹簧连接。原子 1 受 z 方向驱动力作用，产生沿链传播的横波。
+
+## 物理设定
+
+| 参数 | 值 |
+|---|---|
+| 原子数 | 120 |
+| 排列 | 沿 x 轴等间距排列，间距为 1 |
+| 约束 | 原子**沿 z 方向自由振动**（fix_x=1, fix_y=1, fix_z=0），x, y 锁定 |
+| 弹簧 | 劲度系数 k=1.0，原长 L₀=1.0 |
+| 重力 | 无 |
+| 万有引力 | 无 |
+| 阻尼 | 无 |
+| 驱动力 | 原子 1（z 方向驱动） |
+| 算法 | leapfrog（蛙跳法，能量守恒） |
+
+## 驱动力
+
+原子 1 的位置由 `input/driver.txt` 中的驱动力公式决定：
+
+```math
+z(t) = A_z \cdot \cos(2\pi f_z t + \phi_z)
+```
+
+当前参数：A_z = 0.5, f_z = 0.1 Hz, φ_z = 90°, period = all（全程驱动）。
+
+## 动力学行为
+
+原子 1 沿 z 方向的受迫振动通过弹簧逐次传递给相邻原子，形成沿链传播的**横波**。由于 z 方向的振动是横向的，弹簧大部分张力在 x 方向，z 方向的有效刚度是非线性的——等效于一个三次方恢复力（FPU 型非线性），因此波速较慢。
+
+## 使用方法
+
+```bash
+cd examples/case06
+python run_dynamics.py
+```
+
+配置参数详见 `input/input.txt`，驱动力定义见 `input/driver.txt`，完整文档见 `doc/index.html`。

examples/case08/doc/index.html

@@ -0,0 +1,477 @@
+<!DOCTYPE html>
+<html lang="zh-CN">
+<head>
+<meta charset="UTF-8">
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<title>case06 — 一维原子链驱动力学模拟 | 物理原理 &amp; 使用文档</title>
+<style>
+  :root {
+    --bg: #f8f9fa;
+    --card: #fff;
+    --text: #1a1a2e;
+    --accent: #2563eb;
+    --accent-light: #dbeafe;
+    --code-bg: #1e293b;
+    --code-text: #e2e8f0;
+    --border: #e2e8f0;
+    --muted: #64748b;
+  }
+  * { margin: 0; padding: 0; box-sizing: border-box; }
+  body {
+    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Noto Sans SC", sans-serif;
+    background: var(--bg);
+    color: var(--text);
+    line-height: 1.7;
+  }
+
+  /* ── Header ── */
+  .hero {
+    background: linear-gradient(135deg, #1e293b 0%, #334155 100%);
+    color: #fff;
+    padding: 56px 24px 48px;
+    text-align: center;
+  }
+  .hero h1 { font-size: 2rem; font-weight: 700; letter-spacing: -0.02em; }
+  .hero .subtitle {
+    margin-top: 10px;
+    font-size: 1.05rem;
+    opacity: 0.8;
+  }
+  .hero .badge {
+    display: inline-block;
+    margin-top: 14px;
+    padding: 4px 14px;
+    border-radius: 999px;
+    background: rgba(255,255,255,0.12);
+    font-size: 0.82rem;
+  }
+
+  /* ── Layout ── */
+  .container { max-width: 820px; margin: 0 auto; padding: 32px 20px; }
+
+  section { margin-bottom: 44px; }
+  h2 {
+    font-size: 1.35rem;
+    font-weight: 600;
+    margin-bottom: 16px;
+    padding-bottom: 8px;
+    border-bottom: 2px solid var(--accent);
+    display: inline-block;
+  }
+  h3 {
+    font-size: 1.05rem;
+    font-weight: 600;
+    margin: 20px 0 10px;
+  }
+
+  p, li { margin-bottom: 10px; }
+  ul, ol { padding-left: 22px; }
+  strong { color: var(--accent); }
+
+  /* ── Cards ── */
+  .card {
+    background: var(--card);
+    border-radius: 12px;
+    padding: 20px 24px;
+    margin-bottom: 16px;
+    border: 1px solid var(--border);
+    box-shadow: 0 1px 3px rgba(0,0,0,0.04);
+  }
+
+  /* ── Formula / Code blocks ── */
+  .formula {
+    background: var(--card);
+    border-left: 4px solid var(--accent);
+    padding: 14px 20px;
+    margin: 14px 0;
+    font-family: "Times New Roman", "STIX", serif;
+    font-size: 1.05rem;
+    overflow-x: auto;
+    border-radius: 0 8px 8px 0;
+  }
+  code {
+    background: var(--accent-light);
+    padding: 2px 7px;
+    border-radius: 4px;
+    font-family: "JetBrains Mono", "Fira Code", monospace;
+    font-size: 0.88em;
+  }
+  pre {
+    background: var(--code-bg);
+    color: var(--code-text);
+    padding: 16px 20px;
+    border-radius: 10px;
+    overflow-x: auto;
+    font-size: 0.85rem;
+    line-height: 1.5;
+    margin: 14px 0;
+  }
+  pre .cm { color: #94a3b8; font-style: italic; }   /* comment */
+
+  /* ── Table ── */
+  table {
+    width: 100%;
+    border-collapse: collapse;
+    margin: 14px 0;
+    font-size: 0.92rem;
+  }
+  th, td {
+    padding: 8px 12px;
+    text-align: left;
+    border-bottom: 1px solid var(--border);
+  }
+  th { background: var(--accent-light); font-weight: 600; }
+
+  /* ── TOC ── */
+  .toc { counter-reset: toc; }
+  .toc li { counter-increment: toc; list-style: none; margin-bottom: 6px; }
+  .toc li::before { content: counter(toc) ". "; font-weight: 600; color: var(--accent); }
+  .toc a { color: var(--accent); text-decoration: none; }
+  .toc a:hover { text-decoration: underline; }
+
+  /* ── Flow diagram ── */
+  .flow { display: flex; flex-wrap: wrap; gap: 8px; align-items: center; justify-content: center; margin: 16px 0; }
+  .flow-step {
+    background: var(--accent-light);
+    border: 1px solid var(--accent);
+    border-radius: 8px;
+    padding: 8px 16px;
+    font-size: 0.88rem;
+    font-weight: 500;
+  }
+  .flow-arrow { color: var(--muted); font-size: 1.2rem; }
+
+  @media (max-width: 600px) {
+    .hero h1 { font-size: 1.5rem; }
+    .flow { flex-direction: column; }
+    .flow-arrow { transform: rotate(90deg); }
+  }
+</style>
+</head>
+<body>
+
+<!-- ============================================================ -->
+<!--  Header                                                       -->
+<!-- ============================================================ -->
+<header class="hero">
+  <h1>一维原子链驱动力学模拟</h1>
+  <p class="subtitle">120 个原子沿 x 轴排列 · 弹簧连接 · z 方向受迫振动</p>
+  <span class="badge">case06  ·  examples/case06</span>
+</header>
+
+<div class="container">
+
+<!-- ============================================================ -->
+<!--  TOC                                                          -->
+<!-- ============================================================ -->
+<section>
+  <h2>目录</h2>
+  <ol class="toc">
+    <li><a href="#physics">物理原理</a></li>
+    <li><a href="#algorithm">数值算法</a></li>
+    <li><a href="#driver">驱动力模型</a></li>
+    <li><a href="#usage">使用方法</a></li>
+    <li><a href="#params">参数参考</a></li>
+    <li><a href="#files">文件结构</a></li>
+    <li><a href="#troubleshoot">常见问题</a></li>
+  </ol>
+</section>
+
+<!-- ============================================================ -->
+<!--  1. Physics                                                   -->
+<!-- ============================================================ -->
+<section id="physics">
+  <h2>一、物理原理</h2>
+
+  <div class="card">
+    <h3>1.1 一维原子链</h3>
+    <p>120 个原子沿 <strong>x 轴</strong> 等间距排列，原子间距为 1。相邻原子之间用 <strong>理想弹簧</strong> 连接，弹簧的劲度系数 <em>k</em> = 1.0，原长 <em>L</em>₀ = 1.0（与原子间距一致，初始状态弹簧无拉伸）。</p>
+    <p>每个原子被限制在 <strong>z 方向</strong> 自由振动，x 和 y 方向锁定（<code>fix_x=1, fix_y=1, fix_z=0</code>）。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.2 弹簧力（胡克定律）</h3>
+    <p>当原子 <em>i</em> 和 <em>j</em> 之间有弹簧连接时，原子 <em>i</em> 受到的弹簧力为：</p>
+    <div class="formula">
+      <strong>F</strong> = −<em>k</em> · (<em>d</em> − <em>L</em>₀) · <strong>u</strong><sub><em>ij</em></sub>
+    </div>
+    <p>其中 <em>d</em> = |<strong>r</strong><sub><em>j</em></sub> − <strong>r</strong><sub><em>i</em></sub>| 为两原子间距离，<strong>u</strong><sub><em>ij</em></sub> 为从 <em>i</em> 指向 <em>j</em> 的单位向量。由于原子只在 z 方向振动，弹簧在 z 方向的分量是 <strong>几何非线性</strong> 的——对于小振幅近似，z 方向等效于一个三次方恢复力（FPU 型非线性）。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.3 运动方程</h3>
+    <p>对于第 <em>i</em> 个自由原子（非受驱），牛顿第二定律给出：</p>
+    <div class="formula">
+      <em>m</em> · <strong>a</strong><sub><em>i</em></sub> = <strong>F</strong><sub><em>i</em></sub><sup>spring</sup> + <strong>F</strong><sub><em>i</em></sub><sup>driving</sup>
+    </div>
+    <p>本案例中 <strong>唯一的外力</strong> 来自驱动力（仅施加于原子 1）。无重力、无万有引力、无阻尼，系统总能量守恒。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.4 波传播</h3>
+    <p>原子 1 的受迫振动通过弹簧逐次传递给相邻原子，形成沿链传播的 <strong>横波</strong>。由于横向振动的几何非线性（弹簧大部分张力在 x 方向，z 方向的有效刚度远小于 1），波的传播速度较慢，且高阶频率成分会在链中产生复杂的非线性动力学行为（类似 FPU 回波现象）。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  2. Algorithm                                                 -->
+<!-- ============================================================ -->
+<section id="algorithm">
+  <h2>二、数值算法</h2>
+
+  <div class="card">
+    <h3>2.1 蛙跳法（Leapfrog / Velocity-Verlet）</h3>
+    <p>采用能量守恒特性优异的 <strong>蛙跳法</strong>（二阶辛积分器），更新公式为：</p>
+    <div class="formula">
+      <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) = <strong>v</strong>(<em>t</em>) + ½ <strong>a</strong>(<em>t</em>) · Δ<em>t</em><br>
+      <strong>r</strong>(<em>t</em> + Δ<em>t</em>) = <strong>r</strong>(<em>t</em>) + <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) · Δ<em>t</em><br>
+      <strong>a</strong>(<em>t</em> + Δ<em>t</em>) = <strong>F</strong>(<strong>r</strong>(<em>t</em> + Δ<em>t</em>), <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>)) / <em>m</em><br>
+      <strong>v</strong>(<em>t</em> + Δ<em>t</em>) = <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) + ½ <strong>a</strong>(<em>t</em> + Δ<em>t</em>) · Δ<em>t</em>
+    </div>
+    <p>蛙跳法在长时间模拟中能量漂移极小（本案例验证 <strong>&lt; 0.004%</strong>），适合无阻尼的保守系统。</p>
+  </div>
+
+  <div class="card">
+    <h3>2.2 时间步长与采样</h3>
+    <table>
+      <tr><th>参数</th><th>值</th><th>说明</th></tr>
+      <tr><td>DT</td><td>0.01 s</td><td>积分步长（远小于 1/ω ≈ 0.16 s，满足稳定性条件）</td></tr>
+      <tr><td>T_total</td><td>100 s</td><td>总模拟时间 → NT = 10000 步</td></tr>
+      <tr><td>NSTEP</td><td>50</td><td>每 NSTEP 步取一帧用于动画 → 200 帧</td></tr>
+      <tr><td>method</td><td>leapfrog</td><td>蛙跳法（Velocity-Verlet）</td></tr>
+    </table>
+  </div>
+
+  <div class="card">
+    <h3>2.3 计算流程</h3>
+    <div class="flow">
+      <span class="flow-step">读入 coord.txt<br>connection.txt<br>bond.txt</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">施加驱动力<br>（驱动原子 1）</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">记录轨迹</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">蛙跳法<br>更新位置/速度</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">固定约束<br>（x, y 锁定）</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step" style="background:#fef3c7;border-color:#f59e0b;">循环<br>NT 次</span>
+    </div>
+    <p style="margin-top:12px;">注意：驱动力在 <strong>每次积分前</strong> 施加，确保受驱原子的位置正确传递给弹簧力计算。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  3. Driving Force                                             -->
+<!-- ============================================================ -->
+<section id="driver">
+  <h2>三、驱动力模型</h2>
+
+  <div class="card">
+    <h3>3.1 定义文件</h3>
+    <p>驱动力由 <code>input/driver.txt</code> 定义，格式如下：</p>
+    <pre>n amp_x amp_y amp_z freq_x freq_y freq_z phi_x phi_y phi_z period
+1     0     0     5      0      0      1     0     0    90    all</pre>
+  </div>
+
+  <div class="card">
+    <h3>3.2 数学公式</h3>
+    <p>受驱原子的位置由下式决定（<strong>完全替换</strong> coord.txt 中的初始坐标和固定约束）：</p>
+    <div class="formula">
+      <strong>r</strong>(<em>t</em>) = <strong>A</strong> · cos(2π<em>f</em> · <em>t</em> + <strong>φ</strong>)
+    </div>
+    <p>速度由解析导数给出：</p>
+    <div class="formula">
+      <strong>v</strong>(<em>t</em>) = −<strong>A</strong> · 2π<em>f</em> · sin(2π<em>f</em> · <em>t</em> + <strong>φ</strong>)
+    </div>
+    <p>其中 <strong>A</strong> = (amp_x, amp_y, amp_z)，<strong>f</strong> = (freq_x, freq_y, freq_z) 为不同方向的驱动频率，<strong>φ</strong> = (phi_x, phi_y, phi_z) 为相位（<strong>角度制</strong>，代码自动转换为弧度）。</p>
+  </div>
+
+  <div class="card">
+    <h3>3.3 本案例驱动参数</h3>
+    <table>
+      <tr><th>参数</th><th>值</th><th>含义</th></tr>
+      <tr><td>amp_z</td><td>5.0</td><td>z 方向驱动振幅</td></tr>
+      <tr><td>freq_z</td><td>1.0 Hz</td><td>驱动频率（周期 1 s）</td></tr>
+      <tr><td>phi_z</td><td>90°</td><td>驱动相位 → z(0) = 5·cos(90°) = 0</td></tr>
+      <tr><td>period</td><td>all</td><td>全程驱动，永不停止</td></tr>
+    </table>
+    <div class="formula">
+      <em>z</em>(<em>t</em>) = 5.0 · cos(2π · 1.0 · <em>t</em> + 90°)
+    </div>
+  </div>
+
+  <div class="card">
+    <h3>3.4 有限周期驱动</h3>
+    <p><code>period</code> 参数支持三种模式：</p>
+    <ul>
+      <li><strong>all</strong> — 全程驱动</li>
+      <li><strong>数值</strong> — 驱动指定周期数后 <strong>静止</strong>（冻结在最终位置，速度归零）。例如 <code>period: 1</code> 表示驱动 1 个完整周期后停止。</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>3.5 驱动与固定约束的关系</h3>
+    <p>对于受驱原子（<code>driver.txt</code> 中 <code>n</code> 指定的原子），其在 <code>coord.txt</code> 中的初始坐标和 <code>fix_x/fix_y/fix_z</code> 约束被 <strong>完全忽略</strong>。原子的位置和速度完全由驱动力公式决定。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  4. Usage                                                     -->
+<!-- ============================================================ -->
+<section id="usage">
+  <h2>四、使用方法</h2>
+
+  <div class="card">
+    <h3>4.1 完整运行（模拟 + 动画）</h3>
+    <pre>cd examples/case06
+python run_dynamics.py</pre>
+    <p>这步会依次执行：物理模拟 → 抽帧 → 打开 VisPy 3D 动画窗口。</p>
+  </div>
+
+  <div class="card">
+    <h3>4.2 仅查看已有结果</h3>
+    <p>如果已经跑完模拟且生成了 <code>output/display.txt</code>，可以通过修改 <code>input.txt</code> 跳过计算，只开动画：</p>
+    <pre>step_simulate:  0   # 跳过模拟
+step_sample:    0   # 跳过抽帧
+step_animation: 1   # 播放动画</pre>
+    <p>然后运行：<code>python run_dynamics.py</code></p>
+  </div>
+
+  <div class="card">
+    <h3>4.3 手动 3D 动画</h3>
+    <p>也可以单独启动 VisPy 窗口：</p>
+    <pre>python ../../draw.py output/</pre>
+  </div>
+
+  <div class="card">
+    <h3>4.4 强制重新计算</h3>
+    <p>修改参数后需要重新运行模拟时，设置：</p>
+    <pre>force_calc: 1        # 忽略缓存，强制重新计算</pre>
+  </div>
+
+  <div class="card">
+    <h3>4.5 动画交互</h3>
+    <table>
+      <tr><th>操作</th><th>效果</th></tr>
+      <tr><td>鼠标拖动</td><td>旋转视角</td></tr>
+      <tr><td>滚轮</td><td>缩放</td></tr>
+      <tr><td>W / S 键</td><td>相机沿 Z 轴向前 / 向后移动（靠近/远离场景）</td></tr>
+      <tr><td>A / D 键</td><td>视角向右 / 向左平移</td></tr>
+      <tr><td>E / Q 键</td><td>视角上升 / 下降（屏幕方向）</td></tr>
+      <tr><td>C / X 键</td><td>增大 / 减小步长</td></tr>
+      <tr><td>V 键</td><td>切换透视 / 正交投影</td></tr>
+      <tr><td>左上角 <strong>reset</strong> 按钮</td><td>复位视角到初始位置</td></tr>
+      <tr><td>左上角 <strong>info</strong> 按钮</td><td>切换信息面板显示/隐藏</td></tr>
+      <tr><td>左上角 <strong>axes</strong> 按钮</td><td>切换坐标轴显示/隐藏</td></tr>
+    </table>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  5. Parameters                                                -->
+<!-- ============================================================ -->
+<section id="params">
+  <h2>五、参数参考</h2>
+
+  <div class="card">
+    <h3>5.1 input.txt 关键参数</h3>
+    <table>
+      <tr><th>参数</th><th>默认值</th><th>说明</th></tr>
+      <tr><td>gravity_field</td><td>0</td><td>均匀重力场（已关闭）</td></tr>
+      <tr><td>gravity_interaction</td><td>0</td><td>原子间万有引力（已关闭）</td></tr>
+      <tr><td>elastic_force</td><td>1</td><td>弹簧键力（已开启）</td></tr>
+      <tr><td>damping_force</td><td>0</td><td>阻尼（已关闭）</td></tr>
+      <tr><td><strong>driving_force</strong></td><td><strong>1</strong></td><td>驱动力开关（1=开启，需 driver.txt）</td></tr>
+      <tr><td>method</td><td>leapfrog</td><td>数值积分方法</td></tr>
+      <tr><td>DT</td><td>0.01</td><td>积分步长 (s)</td></tr>
+      <tr><td>T_total</td><td>100.0</td><td>总模拟时间 (s)</td></tr>
+      <tr><td>NSTEP</td><td>50</td><td>抽帧步数间隔</td></tr>
+      <tr><td>engine</td><td>python</td><td>计算引擎（python / c / cpp / fortran）</td></tr>
+      <tr><td>use_marker</td><td>1</td><td>渲染模式（0=Sphere 网格, 1=Marker GPU 实例化）</td></tr>
+    </table>
+  </div>
+
+  <div class="card">
+    <h3>5.2 流程控制参数</h3>
+    <table>
+      <tr><th>参数</th><th>0</th><th>1</th></tr>
+      <tr><td>step_simulate</td><td>跳过模拟（加载已有轨迹）</td><td>运行物理模拟</td></tr>
+      <tr><td>step_sample</td><td>跳过抽帧</td><td>从轨迹抽取显示帧</td></tr>
+      <tr><td>step_plot</td><td>不生成图表</td><td>生成轨迹/能量图</td></tr>
+      <tr><td><strong>step_plot_wave</strong></td><td>不生成波形图</td><td>生成波形能量动画 GIF</td></tr>
+      <tr><td>step_animation</td><td>不启动动画</td><td>自动打开 VisPy 3D 窗口</td></tr>
+      <tr><td>force_calc</td><td>自动检测缓存</td><td>强制重新计算</td></tr>
+    </table>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  6. File Structure                                            -->
+<!-- ============================================================ -->
+<section id="files">
+  <h2>六、文件结构</h2>
+
+  <pre>case06/
+├── input/
+│   ├── input.txt          # 主配置文件（YAML 格式）
+│   ├── coord.txt          # 原子坐标（120 个原子）
+│   ├── connection.txt     # 弹簧连接关系（59 条键）
+│   ├── bond.txt           # 弹簧参数（k=1.0, L₀=1.0）
+│   └── <strong>driver.txt</strong>       # <span class="cm">驱动力定义（本案例新增）</span>
+├── output/
+│   ├── trajectory.txt     # 全量轨迹数据（50000 步 × 120 原子）
+│   ├── display.txt        # 抽帧后的动画数据（500 帧 × 120 原子）
+│   ├── dynamics.log       # 计算日志
+│   ├── animation.log      # 动画启动日志（闪退时排查用）
+│   └── wave_animation.gif # 波形能量动画（step_plot_wave=1 时生成）
+├── doc/
+│   └── index.html         # <span class="cm">本文档</span>
+├── Readme.md              # 案例简介
+└── run_dynamics.py        # 案例运行入口</pre>
+</section>
+
+<!-- ============================================================ -->
+<!--  7. Troubleshooting                                           -->
+<!-- ============================================================ -->
+<section id="troubleshoot">
+  <h2>七、常见问题</h2>
+
+  <div class="card">
+    <h3>7.1 动画窗口闪退</h3>
+    <p>如果 VisPy 窗口一闪就消失，请检查：</p>
+    <ul>
+      <li><code>output/animation.log</code> 中是否有错误信息</li>
+      <li><code>output/display.txt</code> 是否存在（需先跑 <code>step_sample: 1</code>）</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>7.2 原子不振动</h3>
+    <p>可能原因：</p>
+    <ul>
+      <li><strong>NSTEP 过大</strong>：抽帧间隔大于驱动周期的一半时，动画会丢失振动细节。建议 NSTEP ≤ 1/(freq · DT · 10)</li>
+      <li><strong>相位 φ 使采样点落在零值</strong>：试试 <code>phi_z: 0</code> 让原子在 t=0 处于振幅峰值</li>
+      <li>确认 <code>driving_force: 1</code> 且 <code>driver.txt</code> 中 amp_z 不为 0</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>7.3 渲染性能慢</h3>
+    <p>原子数多时动画卡顿：</p>
+    <ul>
+      <li>设置 <code>use_marker: 1</code>（使用 GPU 实例化渲染替代独立网格球体）</li>
+      <li>增大 <code>NSTEP</code> 减少动画帧数</li>
+    </ul>
+  </div>
+</section>
+
+<hr style="border:none;border-top:1px solid var(--border);margin:40px 0;">
+
+<footer style="text-align:center;color:var(--muted);font-size:0.85rem;margin-bottom:40px;">
+  Dynamics Simulation Framework &nbsp;·&nbsp; 生成于 2026-06-10
+</footer>
+
+</div>
+</body>
+</html>

examples/case08/input/bond.txt

@@ -0,0 +1,2 @@
+bond_name k       rest_length
+k1        0.1     1.0

examples/case08/input/connection.txt

@@ -0,0 +1,2 @@
+n1 n2 bond_name
+1 2 k1

examples/case08/input/coord.txt

@@ -0,0 +1,3 @@
+n mass radius x y z vx vy vz fix_x fix_y fix_z
+1 1 0.1 0 0 0 0 0 0       0 1 0
+2 1 0.1 1 0 0 0 0 0       0 1 0

examples/case08/input/driver.txt

@@ -0,0 +1,2 @@
+  n amp_x amp_y amp_z freq_x freq_y  freq_z phi_x phi_y phi_z period
+  1   0.1     0   0.0   0.02      0       0    90     0     0    all

examples/case08/input/input.txt

@@ -0,0 +1,114 @@
+# 物理模拟参数配置
+# 格式：YAML
+# 用法：python run_dynamics.py
+
+# ── 流程控制 ──────────────────────────────────
+# 每步用 0/1 单独开关，1=执行，0=跳过
+# 依赖关系：抽帧依赖模拟结果，绘图依赖模拟+抽帧
+step_simulate:  1   # 运行物理模拟 → output/display.txt（引擎直接抽帧）
+step_sample:    0   # （旧版）从 trajectory.txt 重新抽帧，默认0=不执行
+step_plot:      0   # 绘制轨迹/能量图 → output/trajectory_plots.png
+step_animation: 0   # 自动播放 VisPy 3D 动画窗口（需安装 vispy）
+step_plot_wave: 1   # 绘制波形能量动画
+force_calc: 1       # 强制重新计算：1=跳过缓存强算，0=自动使用已有输出
+plot_wave_save_gif: 0  # 输出波形 GIF（需 step_plot_wave=1）
+plot_wave_save_mp4: 0  # 输出波形 MP4（需 step_plot_wave=1）
+
+# ── 文件保存 ──────────────────────────────────
+save_trajectory: 0  # 0=不保留完整轨迹文件, 1=保留 trajectory.txt（用于后续单独抽帧）
+
+# ── 计算引擎 ──────────────────────────────────
+# 可选: python, c, cpp, fortran, java
+engine: c # 默认使用 python 引擎
+
+# ── 盒子 ──────────────────────────────────────
+box_a: 300.0         # 立方体半边长，粒子被限制在 [-box_a, box_a]³ 内
+
+# ── 初始构型 ──────────────────────────────────
+# 坐标文件格式：
+#   第一行：n mass radius x y z vx vy vz fix_x fix_y fix_z
+#   后续行：原子序号 质量 半径 x y z vx vy vz fix_x fix_y fix_z
+coord_file: input/coord.txt
+connection_file: input/connection.txt
+bond_file: input/bond.txt
+driver_file: input/driver.txt     # 驱动力定义文件（driving_force=1 时生效）
+
+# 绘图/动画展示的原子序号（对应 coord_file 第一列 n）
+plot_atom: 1
+
+# ── 物理参数 ──────────────────────────────────
+# 三个方向分量分别对应 x, y, z
+G: [0.000, 0.000, 0.000]   # 重力场分量 (m/s²)
+B: [0.005, 0.000, 0.005]   # 阻尼分量
+
+# ── 力开关（0=关闭, 1=开启）──────────────────
+gravity_field: 0         # 均匀重力场 (G)
+gravity_interaction: 0   # 原子间万有引力
+elastic_force: 1         # 弹簧键力
+damping_force: 1         # 阻尼 (B)
+driving_force: 1         # 驱动力（需 driver_file 定义）
+#
+gravity_strength: 1.0    # 万有引力强度（仅 gravity_interaction=1 时有效）
+
+# ── 数值算法 ──────────────────────────────────
+# 可选：
+#   explicit_euler  显式欧拉法
+#   implicit_euler  隐式欧拉法
+#   midpoint        中点法
+#   leapfrog        蛙跳法
+method: leapfrog
+
+# ── 步骤控制 ──────────────────────────────────
+# 以下参数控制哪些步骤被执行和保存
+
+# 预热步数：模拟开始时跳过不保存的步数（用于稳定初始状态）
+warmup_steps: 0           # 默认 0（立即开始记录）
+
+# 总模拟时间（秒），程序自动计算 NT = T_total / DT
+# 如果同时指定了 NT，以 NT 为准
+T_total:  100.0
+
+# 抽帧间隔（每 NSTEP 步取一帧用于动画）
+NSTEP: 500
+
+# ── 时间步长 ──────────────────────────────────
+DT:    0.001         # 时间步长 (s)
+
+# 抽帧范围：只保存 [sample_start, sample_end) 区间内的帧
+sample_start: null        # null 表示从头开始（帧索引从 0 起）
+sample_end: null          # null 表示到末尾
+
+
+
+# ── 渲染方式 ──────────────────────────────────
+# 3D 动画中原子渲染方式：
+#   0 = Sphere （网格球体，效果精细，原子数少时推荐）
+#   1 = Marker （GPU 实例化点，原子数多时性能更佳）
+use_marker: 1
+
+# ── 显示参数 ──────────────────────────────────
+# 盒子透明度：单个数值（统一）或 6 个数的数组，按 [-x,+x,-y,+y,-z,+z] 顺序
+alpha: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+
+# 小球颜色
+# 小球半径从 coord_file 的 radius 列读取
+ball_color_r: 0.20  # R 分量 (0~1)
+ball_color_g: 0.60  # G 分量
+ball_color_b: 0.90  # B 分量
+
+# 盒子面颜色
+box_color_r:  0.80
+box_color_g:  0.80
+box_color_b:  0.85
+
+# ── 摄像机初始位置 ────────────────────────────
+camera_distance:    10.0    # 摄像机到场景中心的距离
+camera_elevation:    0.0    # 俯仰角（度），负值=俯视
+camera_azimuth:      0.0    # 方位角（度）
+camera_center_x:     0.0    # 摄像机注视点 x
+camera_center_y:     0.0    # 摄像机注视点 y
+camera_center_z:     0.0    # 摄像机注视点 z
+move_camera:         0      # 0=固定视角, 1=按 move_camera.txt 运动
+
+# ── 视觉放大 ──────────────────────────────────
+display_amp: [1.0, 1.0, 10.0]   # x/y/z 方向视觉位移放大倍数（不影响物理）

examples/case08/input/move_camera.txt

@@ -0,0 +1,9 @@
+# move_camera.txt — 摄像机速度段驱动
+# 格式: start-end  vx=f vy=f vz=f  rx=d ry=d rz=d
+#   vx/vy/vz: 平移速度（每帧移动单位）
+#   rx/ry/rz: 旋转速度（每帧度数）
+#     rx → elevation（俯仰）, ry → azimuth（方位）, rz → (预留)
+#
+# 示例：前60帧向右平移+绕x旋转，30-90帧向上平移+绕y绕z旋转
+all   vx=0.02
+# 30-90  vy=0.02  ry=1  rz=1

examples/case08/run_dynamics.py

@@ -0,0 +1,54 @@
+"""
+Case runner for Dynamics case06 — 1D atomic chain (transverse wave).
+
+This script keeps program and data separated:
+  - program: ../../dynamics.py
+  - input:   ./input
+  - output:  ./output
+"""
+
+from __future__ import annotations
+
+import argparse
+import importlib.util
+from pathlib import Path
+
+
+CASE_DIR = Path(__file__).resolve().parent
+DYNAMICS_PATH = Path("..") / ".." / "dynamics.py"
+INPUT_DIR = Path("input")
+OUTPUT_DIR = Path("output")
+CONFIG_FILE = INPUT_DIR / "input.txt"
+
+
+def load_dynamics_module(module_path: Path):
+    spec = importlib.util.spec_from_file_location("dynamics_module", module_path)
+    if spec is None or spec.loader is None:
+        raise ImportError(f"无法加载 dynamics.py: {module_path}")
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def main():
+    parser = argparse.ArgumentParser(description="运行 Dynamics 示例案例 case06")
+    parser.add_argument("--no-plot", action="store_true", help="跳过 matplotlib 绘图")
+    args = parser.parse_args()
+
+    dynamics_path = (CASE_DIR / DYNAMICS_PATH).resolve()
+    input_dir = (CASE_DIR / INPUT_DIR).resolve()
+    output_dir = (CASE_DIR / OUTPUT_DIR).resolve()
+    config_path = (CASE_DIR / CONFIG_FILE).resolve()
+
+    module = load_dynamics_module(dynamics_path)
+    module.run_case(
+        config_path=config_path,
+        runtime_base=CASE_DIR,
+        input_dir=input_dir,
+        output_dir=output_dir,
+        no_plot=args.no_plot,
+    )
+
+
+if __name__ == "__main__":
+    main()

examples/case09/Readme.md

@@ -0,0 +1,40 @@
+# case06: 一维原子链横波模拟
+
+60 个原子沿 x 轴排列，相邻原子用弹簧连接。原子 1 受 z 方向驱动力作用，产生沿链传播的横波。
+
+## 物理设定
+
+| 参数 | 值 |
+|---|---|
+| 原子数 | 120 |
+| 排列 | 沿 x 轴等间距排列，间距为 1 |
+| 约束 | 原子**沿 z 方向自由振动**（fix_x=1, fix_y=1, fix_z=0），x, y 锁定 |
+| 弹簧 | 劲度系数 k=1.0，原长 L₀=1.0 |
+| 重力 | 无 |
+| 万有引力 | 无 |
+| 阻尼 | 无 |
+| 驱动力 | 原子 1（z 方向驱动） |
+| 算法 | leapfrog（蛙跳法，能量守恒） |
+
+## 驱动力
+
+原子 1 的位置由 `input/driver.txt` 中的驱动力公式决定：
+
+```math
+z(t) = A_z \cdot \cos(2\pi f_z t + \phi_z)
+```
+
+当前参数：A_z = 0.5, f_z = 0.1 Hz, φ_z = 90°, period = all（全程驱动）。
+
+## 动力学行为
+
+原子 1 沿 z 方向的受迫振动通过弹簧逐次传递给相邻原子，形成沿链传播的**横波**。由于 z 方向的振动是横向的，弹簧大部分张力在 x 方向，z 方向的有效刚度是非线性的——等效于一个三次方恢复力（FPU 型非线性），因此波速较慢。
+
+## 使用方法
+
+```bash
+cd examples/case06
+python run_dynamics.py
+```
+
+配置参数详见 `input/input.txt`，驱动力定义见 `input/driver.txt`，完整文档见 `doc/index.html`。

examples/case09/doc/index.html

@@ -0,0 +1,477 @@
+<!DOCTYPE html>
+<html lang="zh-CN">
+<head>
+<meta charset="UTF-8">
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<title>case06 — 一维原子链驱动力学模拟 | 物理原理 &amp; 使用文档</title>
+<style>
+  :root {
+    --bg: #f8f9fa;
+    --card: #fff;
+    --text: #1a1a2e;
+    --accent: #2563eb;
+    --accent-light: #dbeafe;
+    --code-bg: #1e293b;
+    --code-text: #e2e8f0;
+    --border: #e2e8f0;
+    --muted: #64748b;
+  }
+  * { margin: 0; padding: 0; box-sizing: border-box; }
+  body {
+    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Noto Sans SC", sans-serif;
+    background: var(--bg);
+    color: var(--text);
+    line-height: 1.7;
+  }
+
+  /* ── Header ── */
+  .hero {
+    background: linear-gradient(135deg, #1e293b 0%, #334155 100%);
+    color: #fff;
+    padding: 56px 24px 48px;
+    text-align: center;
+  }
+  .hero h1 { font-size: 2rem; font-weight: 700; letter-spacing: -0.02em; }
+  .hero .subtitle {
+    margin-top: 10px;
+    font-size: 1.05rem;
+    opacity: 0.8;
+  }
+  .hero .badge {
+    display: inline-block;
+    margin-top: 14px;
+    padding: 4px 14px;
+    border-radius: 999px;
+    background: rgba(255,255,255,0.12);
+    font-size: 0.82rem;
+  }
+
+  /* ── Layout ── */
+  .container { max-width: 820px; margin: 0 auto; padding: 32px 20px; }
+
+  section { margin-bottom: 44px; }
+  h2 {
+    font-size: 1.35rem;
+    font-weight: 600;
+    margin-bottom: 16px;
+    padding-bottom: 8px;
+    border-bottom: 2px solid var(--accent);
+    display: inline-block;
+  }
+  h3 {
+    font-size: 1.05rem;
+    font-weight: 600;
+    margin: 20px 0 10px;
+  }
+
+  p, li { margin-bottom: 10px; }
+  ul, ol { padding-left: 22px; }
+  strong { color: var(--accent); }
+
+  /* ── Cards ── */
+  .card {
+    background: var(--card);
+    border-radius: 12px;
+    padding: 20px 24px;
+    margin-bottom: 16px;
+    border: 1px solid var(--border);
+    box-shadow: 0 1px 3px rgba(0,0,0,0.04);
+  }
+
+  /* ── Formula / Code blocks ── */
+  .formula {
+    background: var(--card);
+    border-left: 4px solid var(--accent);
+    padding: 14px 20px;
+    margin: 14px 0;
+    font-family: "Times New Roman", "STIX", serif;
+    font-size: 1.05rem;
+    overflow-x: auto;
+    border-radius: 0 8px 8px 0;
+  }
+  code {
+    background: var(--accent-light);
+    padding: 2px 7px;
+    border-radius: 4px;
+    font-family: "JetBrains Mono", "Fira Code", monospace;
+    font-size: 0.88em;
+  }
+  pre {
+    background: var(--code-bg);
+    color: var(--code-text);
+    padding: 16px 20px;
+    border-radius: 10px;
+    overflow-x: auto;
+    font-size: 0.85rem;
+    line-height: 1.5;
+    margin: 14px 0;
+  }
+  pre .cm { color: #94a3b8; font-style: italic; }   /* comment */
+
+  /* ── Table ── */
+  table {
+    width: 100%;
+    border-collapse: collapse;
+    margin: 14px 0;
+    font-size: 0.92rem;
+  }
+  th, td {
+    padding: 8px 12px;
+    text-align: left;
+    border-bottom: 1px solid var(--border);
+  }
+  th { background: var(--accent-light); font-weight: 600; }
+
+  /* ── TOC ── */
+  .toc { counter-reset: toc; }
+  .toc li { counter-increment: toc; list-style: none; margin-bottom: 6px; }
+  .toc li::before { content: counter(toc) ". "; font-weight: 600; color: var(--accent); }
+  .toc a { color: var(--accent); text-decoration: none; }
+  .toc a:hover { text-decoration: underline; }
+
+  /* ── Flow diagram ── */
+  .flow { display: flex; flex-wrap: wrap; gap: 8px; align-items: center; justify-content: center; margin: 16px 0; }
+  .flow-step {
+    background: var(--accent-light);
+    border: 1px solid var(--accent);
+    border-radius: 8px;
+    padding: 8px 16px;
+    font-size: 0.88rem;
+    font-weight: 500;
+  }
+  .flow-arrow { color: var(--muted); font-size: 1.2rem; }
+
+  @media (max-width: 600px) {
+    .hero h1 { font-size: 1.5rem; }
+    .flow { flex-direction: column; }
+    .flow-arrow { transform: rotate(90deg); }
+  }
+</style>
+</head>
+<body>
+
+<!-- ============================================================ -->
+<!--  Header                                                       -->
+<!-- ============================================================ -->
+<header class="hero">
+  <h1>一维原子链驱动力学模拟</h1>
+  <p class="subtitle">120 个原子沿 x 轴排列 · 弹簧连接 · z 方向受迫振动</p>
+  <span class="badge">case06  ·  examples/case06</span>
+</header>
+
+<div class="container">
+
+<!-- ============================================================ -->
+<!--  TOC                                                          -->
+<!-- ============================================================ -->
+<section>
+  <h2>目录</h2>
+  <ol class="toc">
+    <li><a href="#physics">物理原理</a></li>
+    <li><a href="#algorithm">数值算法</a></li>
+    <li><a href="#driver">驱动力模型</a></li>
+    <li><a href="#usage">使用方法</a></li>
+    <li><a href="#params">参数参考</a></li>
+    <li><a href="#files">文件结构</a></li>
+    <li><a href="#troubleshoot">常见问题</a></li>
+  </ol>
+</section>
+
+<!-- ============================================================ -->
+<!--  1. Physics                                                   -->
+<!-- ============================================================ -->
+<section id="physics">
+  <h2>一、物理原理</h2>
+
+  <div class="card">
+    <h3>1.1 一维原子链</h3>
+    <p>120 个原子沿 <strong>x 轴</strong> 等间距排列，原子间距为 1。相邻原子之间用 <strong>理想弹簧</strong> 连接，弹簧的劲度系数 <em>k</em> = 1.0，原长 <em>L</em>₀ = 1.0（与原子间距一致，初始状态弹簧无拉伸）。</p>
+    <p>每个原子被限制在 <strong>z 方向</strong> 自由振动，x 和 y 方向锁定（<code>fix_x=1, fix_y=1, fix_z=0</code>）。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.2 弹簧力（胡克定律）</h3>
+    <p>当原子 <em>i</em> 和 <em>j</em> 之间有弹簧连接时，原子 <em>i</em> 受到的弹簧力为：</p>
+    <div class="formula">
+      <strong>F</strong> = −<em>k</em> · (<em>d</em> − <em>L</em>₀) · <strong>u</strong><sub><em>ij</em></sub>
+    </div>
+    <p>其中 <em>d</em> = |<strong>r</strong><sub><em>j</em></sub> − <strong>r</strong><sub><em>i</em></sub>| 为两原子间距离，<strong>u</strong><sub><em>ij</em></sub> 为从 <em>i</em> 指向 <em>j</em> 的单位向量。由于原子只在 z 方向振动，弹簧在 z 方向的分量是 <strong>几何非线性</strong> 的——对于小振幅近似，z 方向等效于一个三次方恢复力（FPU 型非线性）。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.3 运动方程</h3>
+    <p>对于第 <em>i</em> 个自由原子（非受驱），牛顿第二定律给出：</p>
+    <div class="formula">
+      <em>m</em> · <strong>a</strong><sub><em>i</em></sub> = <strong>F</strong><sub><em>i</em></sub><sup>spring</sup> + <strong>F</strong><sub><em>i</em></sub><sup>driving</sup>
+    </div>
+    <p>本案例中 <strong>唯一的外力</strong> 来自驱动力（仅施加于原子 1）。无重力、无万有引力、无阻尼，系统总能量守恒。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.4 波传播</h3>
+    <p>原子 1 的受迫振动通过弹簧逐次传递给相邻原子，形成沿链传播的 <strong>横波</strong>。由于横向振动的几何非线性（弹簧大部分张力在 x 方向，z 方向的有效刚度远小于 1），波的传播速度较慢，且高阶频率成分会在链中产生复杂的非线性动力学行为（类似 FPU 回波现象）。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  2. Algorithm                                                 -->
+<!-- ============================================================ -->
+<section id="algorithm">
+  <h2>二、数值算法</h2>
+
+  <div class="card">
+    <h3>2.1 蛙跳法（Leapfrog / Velocity-Verlet）</h3>
+    <p>采用能量守恒特性优异的 <strong>蛙跳法</strong>（二阶辛积分器），更新公式为：</p>
+    <div class="formula">
+      <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) = <strong>v</strong>(<em>t</em>) + ½ <strong>a</strong>(<em>t</em>) · Δ<em>t</em><br>
+      <strong>r</strong>(<em>t</em> + Δ<em>t</em>) = <strong>r</strong>(<em>t</em>) + <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) · Δ<em>t</em><br>
+      <strong>a</strong>(<em>t</em> + Δ<em>t</em>) = <strong>F</strong>(<strong>r</strong>(<em>t</em> + Δ<em>t</em>), <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>)) / <em>m</em><br>
+      <strong>v</strong>(<em>t</em> + Δ<em>t</em>) = <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) + ½ <strong>a</strong>(<em>t</em> + Δ<em>t</em>) · Δ<em>t</em>
+    </div>
+    <p>蛙跳法在长时间模拟中能量漂移极小（本案例验证 <strong>&lt; 0.004%</strong>），适合无阻尼的保守系统。</p>
+  </div>
+
+  <div class="card">
+    <h3>2.2 时间步长与采样</h3>
+    <table>
+      <tr><th>参数</th><th>值</th><th>说明</th></tr>
+      <tr><td>DT</td><td>0.01 s</td><td>积分步长（远小于 1/ω ≈ 0.16 s，满足稳定性条件）</td></tr>
+      <tr><td>T_total</td><td>100 s</td><td>总模拟时间 → NT = 10000 步</td></tr>
+      <tr><td>NSTEP</td><td>50</td><td>每 NSTEP 步取一帧用于动画 → 200 帧</td></tr>
+      <tr><td>method</td><td>leapfrog</td><td>蛙跳法（Velocity-Verlet）</td></tr>
+    </table>
+  </div>
+
+  <div class="card">
+    <h3>2.3 计算流程</h3>
+    <div class="flow">
+      <span class="flow-step">读入 coord.txt<br>connection.txt<br>bond.txt</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">施加驱动力<br>（驱动原子 1）</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">记录轨迹</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">蛙跳法<br>更新位置/速度</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">固定约束<br>（x, y 锁定）</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step" style="background:#fef3c7;border-color:#f59e0b;">循环<br>NT 次</span>
+    </div>
+    <p style="margin-top:12px;">注意：驱动力在 <strong>每次积分前</strong> 施加，确保受驱原子的位置正确传递给弹簧力计算。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  3. Driving Force                                             -->
+<!-- ============================================================ -->
+<section id="driver">
+  <h2>三、驱动力模型</h2>
+
+  <div class="card">
+    <h3>3.1 定义文件</h3>
+    <p>驱动力由 <code>input/driver.txt</code> 定义，格式如下：</p>
+    <pre>n amp_x amp_y amp_z freq_x freq_y freq_z phi_x phi_y phi_z period
+1     0     0     5      0      0      1     0     0    90    all</pre>
+  </div>
+
+  <div class="card">
+    <h3>3.2 数学公式</h3>
+    <p>受驱原子的位置由下式决定（<strong>完全替换</strong> coord.txt 中的初始坐标和固定约束）：</p>
+    <div class="formula">
+      <strong>r</strong>(<em>t</em>) = <strong>A</strong> · cos(2π<em>f</em> · <em>t</em> + <strong>φ</strong>)
+    </div>
+    <p>速度由解析导数给出：</p>
+    <div class="formula">
+      <strong>v</strong>(<em>t</em>) = −<strong>A</strong> · 2π<em>f</em> · sin(2π<em>f</em> · <em>t</em> + <strong>φ</strong>)
+    </div>
+    <p>其中 <strong>A</strong> = (amp_x, amp_y, amp_z)，<strong>f</strong> = (freq_x, freq_y, freq_z) 为不同方向的驱动频率，<strong>φ</strong> = (phi_x, phi_y, phi_z) 为相位（<strong>角度制</strong>，代码自动转换为弧度）。</p>
+  </div>
+
+  <div class="card">
+    <h3>3.3 本案例驱动参数</h3>
+    <table>
+      <tr><th>参数</th><th>值</th><th>含义</th></tr>
+      <tr><td>amp_z</td><td>5.0</td><td>z 方向驱动振幅</td></tr>
+      <tr><td>freq_z</td><td>1.0 Hz</td><td>驱动频率（周期 1 s）</td></tr>
+      <tr><td>phi_z</td><td>90°</td><td>驱动相位 → z(0) = 5·cos(90°) = 0</td></tr>
+      <tr><td>period</td><td>all</td><td>全程驱动，永不停止</td></tr>
+    </table>
+    <div class="formula">
+      <em>z</em>(<em>t</em>) = 5.0 · cos(2π · 1.0 · <em>t</em> + 90°)
+    </div>
+  </div>
+
+  <div class="card">
+    <h3>3.4 有限周期驱动</h3>
+    <p><code>period</code> 参数支持三种模式：</p>
+    <ul>
+      <li><strong>all</strong> — 全程驱动</li>
+      <li><strong>数值</strong> — 驱动指定周期数后 <strong>静止</strong>（冻结在最终位置，速度归零）。例如 <code>period: 1</code> 表示驱动 1 个完整周期后停止。</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>3.5 驱动与固定约束的关系</h3>
+    <p>对于受驱原子（<code>driver.txt</code> 中 <code>n</code> 指定的原子），其在 <code>coord.txt</code> 中的初始坐标和 <code>fix_x/fix_y/fix_z</code> 约束被 <strong>完全忽略</strong>。原子的位置和速度完全由驱动力公式决定。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  4. Usage                                                     -->
+<!-- ============================================================ -->
+<section id="usage">
+  <h2>四、使用方法</h2>
+
+  <div class="card">
+    <h3>4.1 完整运行（模拟 + 动画）</h3>
+    <pre>cd examples/case06
+python run_dynamics.py</pre>
+    <p>这步会依次执行：物理模拟 → 抽帧 → 打开 VisPy 3D 动画窗口。</p>
+  </div>
+
+  <div class="card">
+    <h3>4.2 仅查看已有结果</h3>
+    <p>如果已经跑完模拟且生成了 <code>output/display.txt</code>，可以通过修改 <code>input.txt</code> 跳过计算，只开动画：</p>
+    <pre>step_simulate:  0   # 跳过模拟
+step_sample:    0   # 跳过抽帧
+step_animation: 1   # 播放动画</pre>
+    <p>然后运行：<code>python run_dynamics.py</code></p>
+  </div>
+
+  <div class="card">
+    <h3>4.3 手动 3D 动画</h3>
+    <p>也可以单独启动 VisPy 窗口：</p>
+    <pre>python ../../draw.py output/</pre>
+  </div>
+
+  <div class="card">
+    <h3>4.4 强制重新计算</h3>
+    <p>修改参数后需要重新运行模拟时，设置：</p>
+    <pre>force_calc: 1        # 忽略缓存，强制重新计算</pre>
+  </div>
+
+  <div class="card">
+    <h3>4.5 动画交互</h3>
+    <table>
+      <tr><th>操作</th><th>效果</th></tr>
+      <tr><td>鼠标拖动</td><td>旋转视角</td></tr>
+      <tr><td>滚轮</td><td>缩放</td></tr>
+      <tr><td>W / S 键</td><td>相机沿 Z 轴向前 / 向后移动（靠近/远离场景）</td></tr>
+      <tr><td>A / D 键</td><td>视角向右 / 向左平移</td></tr>
+      <tr><td>E / Q 键</td><td>视角上升 / 下降（屏幕方向）</td></tr>
+      <tr><td>C / X 键</td><td>增大 / 减小步长</td></tr>
+      <tr><td>V 键</td><td>切换透视 / 正交投影</td></tr>
+      <tr><td>左上角 <strong>reset</strong> 按钮</td><td>复位视角到初始位置</td></tr>
+      <tr><td>左上角 <strong>info</strong> 按钮</td><td>切换信息面板显示/隐藏</td></tr>
+      <tr><td>左上角 <strong>axes</strong> 按钮</td><td>切换坐标轴显示/隐藏</td></tr>
+    </table>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  5. Parameters                                                -->
+<!-- ============================================================ -->
+<section id="params">
+  <h2>五、参数参考</h2>
+
+  <div class="card">
+    <h3>5.1 input.txt 关键参数</h3>
+    <table>
+      <tr><th>参数</th><th>默认值</th><th>说明</th></tr>
+      <tr><td>gravity_field</td><td>0</td><td>均匀重力场（已关闭）</td></tr>
+      <tr><td>gravity_interaction</td><td>0</td><td>原子间万有引力（已关闭）</td></tr>
+      <tr><td>elastic_force</td><td>1</td><td>弹簧键力（已开启）</td></tr>
+      <tr><td>damping_force</td><td>0</td><td>阻尼（已关闭）</td></tr>
+      <tr><td><strong>driving_force</strong></td><td><strong>1</strong></td><td>驱动力开关（1=开启，需 driver.txt）</td></tr>
+      <tr><td>method</td><td>leapfrog</td><td>数值积分方法</td></tr>
+      <tr><td>DT</td><td>0.01</td><td>积分步长 (s)</td></tr>
+      <tr><td>T_total</td><td>100.0</td><td>总模拟时间 (s)</td></tr>
+      <tr><td>NSTEP</td><td>50</td><td>抽帧步数间隔</td></tr>
+      <tr><td>engine</td><td>python</td><td>计算引擎（python / c / cpp / fortran）</td></tr>
+      <tr><td>use_marker</td><td>1</td><td>渲染模式（0=Sphere 网格, 1=Marker GPU 实例化）</td></tr>
+    </table>
+  </div>
+
+  <div class="card">
+    <h3>5.2 流程控制参数</h3>
+    <table>
+      <tr><th>参数</th><th>0</th><th>1</th></tr>
+      <tr><td>step_simulate</td><td>跳过模拟（加载已有轨迹）</td><td>运行物理模拟</td></tr>
+      <tr><td>step_sample</td><td>跳过抽帧</td><td>从轨迹抽取显示帧</td></tr>
+      <tr><td>step_plot</td><td>不生成图表</td><td>生成轨迹/能量图</td></tr>
+      <tr><td><strong>step_plot_wave</strong></td><td>不生成波形图</td><td>生成波形能量动画 GIF</td></tr>
+      <tr><td>step_animation</td><td>不启动动画</td><td>自动打开 VisPy 3D 窗口</td></tr>
+      <tr><td>force_calc</td><td>自动检测缓存</td><td>强制重新计算</td></tr>
+    </table>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  6. File Structure                                            -->
+<!-- ============================================================ -->
+<section id="files">
+  <h2>六、文件结构</h2>
+
+  <pre>case06/
+├── input/
+│   ├── input.txt          # 主配置文件（YAML 格式）
+│   ├── coord.txt          # 原子坐标（120 个原子）
+│   ├── connection.txt     # 弹簧连接关系（59 条键）
+│   ├── bond.txt           # 弹簧参数（k=1.0, L₀=1.0）
+│   └── <strong>driver.txt</strong>       # <span class="cm">驱动力定义（本案例新增）</span>
+├── output/
+│   ├── trajectory.txt     # 全量轨迹数据（50000 步 × 120 原子）
+│   ├── display.txt        # 抽帧后的动画数据（500 帧 × 120 原子）
+│   ├── dynamics.log       # 计算日志
+│   ├── animation.log      # 动画启动日志（闪退时排查用）
+│   └── wave_animation.gif # 波形能量动画（step_plot_wave=1 时生成）
+├── doc/
+│   └── index.html         # <span class="cm">本文档</span>
+├── Readme.md              # 案例简介
+└── run_dynamics.py        # 案例运行入口</pre>
+</section>
+
+<!-- ============================================================ -->
+<!--  7. Troubleshooting                                           -->
+<!-- ============================================================ -->
+<section id="troubleshoot">
+  <h2>七、常见问题</h2>
+
+  <div class="card">
+    <h3>7.1 动画窗口闪退</h3>
+    <p>如果 VisPy 窗口一闪就消失，请检查：</p>
+    <ul>
+      <li><code>output/animation.log</code> 中是否有错误信息</li>
+      <li><code>output/display.txt</code> 是否存在（需先跑 <code>step_sample: 1</code>）</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>7.2 原子不振动</h3>
+    <p>可能原因：</p>
+    <ul>
+      <li><strong>NSTEP 过大</strong>：抽帧间隔大于驱动周期的一半时，动画会丢失振动细节。建议 NSTEP ≤ 1/(freq · DT · 10)</li>
+      <li><strong>相位 φ 使采样点落在零值</strong>：试试 <code>phi_z: 0</code> 让原子在 t=0 处于振幅峰值</li>
+      <li>确认 <code>driving_force: 1</code> 且 <code>driver.txt</code> 中 amp_z 不为 0</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>7.3 渲染性能慢</h3>
+    <p>原子数多时动画卡顿：</p>
+    <ul>
+      <li>设置 <code>use_marker: 1</code>（使用 GPU 实例化渲染替代独立网格球体）</li>
+      <li>增大 <code>NSTEP</code> 减少动画帧数</li>
+    </ul>
+  </div>
+</section>
+
+<hr style="border:none;border-top:1px solid var(--border);margin:40px 0;">
+
+<footer style="text-align:center;color:var(--muted);font-size:0.85rem;margin-bottom:40px;">
+  Dynamics Simulation Framework &nbsp;·&nbsp; 生成于 2026-06-10
+</footer>
+
+</div>
+</body>
+</html>

examples/case09/input/bond.txt

@@ -0,0 +1,2 @@
+bond_name k       rest_length
+k1        300.0   1.0

examples/case09/input/connection.txt

@@ -0,0 +1,40 @@
+n1 n2 bond_name
+1 2 k1
+2 3 k1
+3 4 k1
+4 5 k1
+5 6 k1
+6 7 k1
+7 8 k1
+8 9 k1
+9 10 k1
+10 11 k1
+11 12 k1
+12 13 k1
+13 14 k1
+14 15 k1
+15 16 k1
+16 17 k1
+17 18 k1
+18 19 k1
+19 20 k1
+20 21 k1
+21 22 k1
+22 23 k1
+23 24 k1
+24 25 k1
+25 26 k1
+26 27 k1
+27 28 k1
+28 29 k1
+29 30 k1
+30 31 k1
+31 32 k1
+32 33 k1
+33 34 k1
+34 35 k1
+35 36 k1
+36 37 k1
+37 38 k1
+38 39 k1
+39 40 k1

examples/case09/input/coord.txt

@@ -0,0 +1,41 @@
+n mass radius x y z vx vy vz fix_x fix_y fix_z
+1 1 0.1 0 0 0 0 0 0       0 1 0
+2 1 0.1 1 0 0 0 0 0       0 1 0
+3 1 0.1 2 0 0 0 0 0       0 1 0
+4 1 0.1 3 0 0 0 0 0       0 1 0
+5 1 0.1 4 0 0 0 0 0       0 1 0
+6 1 0.1 5 0 0 0 0 0       0 1 0
+7 1 0.1 6 0 0 0 0 0       0 1 0
+8 1 0.1 7 0 0 0 0 0       0 1 0
+9 1 0.1 8 0 0 0 0 0       0 1 0
+10 1 0.1 9 0 0 0 0 0       0 1 0
+11 1 0.1 10 0 0 0 0 0       0 1 0
+12 1 0.1 11 0 0 0 0 0       0 1 0
+13 1 0.1 12 0 0 0 0 0       0 1 0
+14 1 0.1 13 0 0 0 0 0       0 1 0
+15 1 0.1 14 0 0 0 0 0       0 1 0
+16 1 0.1 15 0 0 0 0 0       0 1 0
+17 1 0.1 16 0 0 0 0 0       0 1 0
+18 1 0.1 17 0 0 0 0 0       0 1 0
+19 1 0.1 18 0 0 0 0 0       0 1 0
+20 1 0.1 19 0 0 0 0 0       0 1 0
+21 1 0.1 20 0 0 0 0 0       0 1 0
+22 1 0.1 21 0 0 0 0 0       0 1 0
+23 1 0.1 22 0 0 0 0 0       0 1 0
+24 1 0.1 23 0 0 0 0 0       0 1 0
+25 1 0.1 24 0 0 0 0 0       0 1 0
+26 1 0.1 25 0 0 0 0 0       0 1 0
+27 1 0.1 26 0 0 0 0 0       0 1 0
+28 1 0.1 27 0 0 0 0 0       0 1 0
+29 1 0.1 28 0 0 0 0 0       0 1 0
+30 1 0.1 29 0 0 0 0 0       0 1 0
+31 1 0.1 30 0 0 0 0 0       0 1 0
+32 1 0.1 31 0 0 0 0 0       0 1 0
+33 1 0.1 32 0 0 0 0 0       0 1 0
+34 1 0.1 33 0 0 0 0 0       0 1 0
+35 1 0.1 34 0 0 0 0 0       0 1 0
+36 1 0.1 35 0 0 0 0 0       0 1 0
+37 1 0.1 36 0 0 0 0 0       0 1 0
+38 1 0.1 37 0 0 0 0 0       0 1 0
+39 1 0.1 38 0 0 0 0 0       0 1 0
+40 1 0.1 39 0 0 0 0 0       1 1 1

examples/case09/input/driver.txt

@@ -0,0 +1,2 @@
+  n amp_x amp_y amp_z freq_x freq_y  freq_z phi_x phi_y phi_z period
+  1     0     0   0.1      0      0    0.04     0     0    90    all

examples/case09/input/input.txt

@@ -0,0 +1,114 @@
+# 物理模拟参数配置
+# 格式：YAML
+# 用法：python run_dynamics.py     
+
+# ── 流程控制 ──────────────────────────────────
+# 每步用 0/1 单独开关，1=执行，0=跳过
+# 依赖关系：抽帧依赖模拟结果，绘图依赖模拟+抽帧
+step_simulate:  1   # 运行物理模拟 → output/display.txt（引擎直接抽帧）
+step_sample:    0   # （旧版）从 trajectory.txt 重新抽帧，默认0=不执行
+step_plot:      0   # 绘制轨迹/能量图 → output/trajectory_plots.png
+step_animation: 1   # 自动播放 VisPy 3D 动画窗口（需安装 vispy）
+step_plot_wave: 1   # 绘制波形能量动画
+force_calc: 1       # 强制重新计算：1=跳过缓存强算，0=自动使用已有输出
+plot_wave_save_gif: 0  # 输出波形 GIF（需 step_plot_wave=1）
+plot_wave_save_mp4: 0  # 输出波形 MP4（需 step_plot_wave=1）
+
+# ── 文件保存 ──────────────────────────────────
+save_trajectory: 0  # 0=不保留完整轨迹文件, 1=保留 trajectory.txt（用于后续单独抽帧）
+
+# ── 计算引擎 ──────────────────────────────────
+# 可选: python, c, cpp, fortran, java
+engine: fortran # 默认使用 python 引擎
+
+# ── 盒子 ──────────────────────────────────────
+box_a: 300.0         # 立方体半边长，粒子被限制在 [-box_a, box_a]³ 内
+
+# ── 初始构型 ──────────────────────────────────
+# 坐标文件格式：
+#   第一行：n mass radius x y z vx vy vz fix_x fix_y fix_z
+#   后续行：原子序号 质量 半径 x y z vx vy vz fix_x fix_y fix_z
+coord_file: input/coord.txt
+connection_file: input/connection.txt
+bond_file: input/bond.txt
+driver_file: input/driver.txt     # 驱动力定义文件（driving_force=1 时生效）
+
+# 绘图/动画展示的原子序号（对应 coord_file 第一列 n）
+plot_atom: 1
+
+# ── 物理参数 ──────────────────────────────────
+# 三个方向分量分别对应 x, y, z
+G: [0.000, 0.000, 0.000]   # 重力场分量 (m/s²)
+B: [0.005, 0.000, 0.005]   # 阻尼分量
+
+# ── 力开关（0=关闭, 1=开启）──────────────────
+gravity_field: 0         # 均匀重力场 (G)
+gravity_interaction: 0   # 原子间万有引力
+elastic_force: 1         # 弹簧键力
+damping_force: 0         # 阻尼 (B)
+driving_force: 1         # 驱动力（需 driver_file 定义）
+#
+gravity_strength: 1.0    # 万有引力强度（仅 gravity_interaction=1 时有效）
+
+# ── 数值算法 ──────────────────────────────────
+# 可选：
+#   explicit_euler  显式欧拉法
+#   implicit_euler  隐式欧拉法
+#   midpoint        中点法
+#   leapfrog        蛙跳法
+method: leapfrog
+
+# ── 步骤控制 ──────────────────────────────────
+# 以下参数控制哪些步骤被执行和保存
+
+# 预热步数：模拟开始时跳过不保存的步数（用于稳定初始状态）
+warmup_steps: 0           # 默认 0（立即开始记录）
+
+# 总模拟时间（秒），程序自动计算 NT = T_total / DT
+# 如果同时指定了 NT，以 NT 为准
+T_total:  200.0
+
+# 抽帧间隔（每 NSTEP 步取一帧用于动画）
+NSTEP: 100
+
+# ── 时间步长 ──────────────────────────────────
+DT:    0.001         # 时间步长 (s)
+
+# 抽帧范围：只保存 [sample_start, sample_end) 区间内的帧
+sample_start: null        # null 表示从头开始（帧索引从 0 起）
+sample_end: null          # null 表示到末尾
+
+
+
+# ── 渲染方式 ──────────────────────────────────
+# 3D 动画中原子渲染方式：
+#   0 = Sphere （网格球体，效果精细，原子数少时推荐）
+#   1 = Marker （GPU 实例化点，原子数多时性能更佳）
+use_marker: 1
+
+# ── 显示参数 ──────────────────────────────────
+# 盒子透明度：单个数值（统一）或 6 个数的数组，按 [-x,+x,-y,+y,-z,+z] 顺序
+alpha: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+
+# 小球颜色
+# 小球半径从 coord_file 的 radius 列读取
+ball_color_r: 0.20  # R 分量 (0~1)
+ball_color_g: 0.60  # G 分量
+ball_color_b: 0.90  # B 分量
+
+# 盒子面颜色
+box_color_r:  0.80
+box_color_g:  0.80
+box_color_b:  0.85
+
+# ── 摄像机初始位置 ────────────────────────────
+camera_distance:    60.0    # 摄像机到场景中心的距离
+camera_elevation:    0.0    # 俯仰角（度），负值=俯视
+camera_azimuth:      0.0    # 方位角（度）
+camera_center_x:    30.0    # 摄像机注视点 x
+camera_center_y:     0.0    # 摄像机注视点 y
+camera_center_z:     0.0    # 摄像机注视点 z
+move_camera:         0      # 0=固定视角, 1=按 move_camera.txt 运动
+
+# ── 视觉放大 ──────────────────────────────────
+display_amp: [1.0, 1.0, 10.0]   # x/y/z 方向视觉位移放大倍数（不影响物理）

examples/case09/input/move_camera.txt

@@ -0,0 +1,9 @@
+# move_camera.txt — 摄像机速度段驱动
+# 格式: start-end  vx=f vy=f vz=f  rx=d ry=d rz=d
+#   vx/vy/vz: 平移速度（每帧移动单位）
+#   rx/ry/rz: 旋转速度（每帧度数）
+#     rx → elevation（俯仰）, ry → azimuth（方位）, rz → (预留)
+#
+# 示例：前60帧向右平移+绕x旋转，30-90帧向上平移+绕y绕z旋转
+all   vx=0.02
+# 30-90  vy=0.02  ry=1  rz=1

examples/case09/run_dynamics.py

@@ -0,0 +1,54 @@
+"""
+Case runner for Dynamics case06 — 1D atomic chain (transverse wave).
+
+This script keeps program and data separated:
+  - program: ../../dynamics.py
+  - input:   ./input
+  - output:  ./output
+"""
+
+from __future__ import annotations
+
+import argparse
+import importlib.util
+from pathlib import Path
+
+
+CASE_DIR = Path(__file__).resolve().parent
+DYNAMICS_PATH = Path("..") / ".." / "dynamics.py"
+INPUT_DIR = Path("input")
+OUTPUT_DIR = Path("output")
+CONFIG_FILE = INPUT_DIR / "input.txt"
+
+
+def load_dynamics_module(module_path: Path):
+    spec = importlib.util.spec_from_file_location("dynamics_module", module_path)
+    if spec is None or spec.loader is None:
+        raise ImportError(f"无法加载 dynamics.py: {module_path}")
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def main():
+    parser = argparse.ArgumentParser(description="运行 Dynamics 示例案例 case06")
+    parser.add_argument("--no-plot", action="store_true", help="跳过 matplotlib 绘图")
+    args = parser.parse_args()
+
+    dynamics_path = (CASE_DIR / DYNAMICS_PATH).resolve()
+    input_dir = (CASE_DIR / INPUT_DIR).resolve()
+    output_dir = (CASE_DIR / OUTPUT_DIR).resolve()
+    config_path = (CASE_DIR / CONFIG_FILE).resolve()
+
+    module = load_dynamics_module(dynamics_path)
+    module.run_case(
+        config_path=config_path,
+        runtime_base=CASE_DIR,
+        input_dir=input_dir,
+        output_dir=output_dir,
+        no_plot=args.no_plot,
+    )
+
+
+if __name__ == "__main__":
+    main()

examples/case10/Readme.md

@@ -0,0 +1,40 @@
+# case06: 一维原子链横波模拟
+
+60 个原子沿 x 轴排列，相邻原子用弹簧连接。原子 1 受 z 方向驱动力作用，产生沿链传播的横波。
+
+## 物理设定
+
+| 参数 | 值 |
+|---|---|
+| 原子数 | 120 |
+| 排列 | 沿 x 轴等间距排列，间距为 1 |
+| 约束 | 原子**沿 z 方向自由振动**（fix_x=1, fix_y=1, fix_z=0），x, y 锁定 |
+| 弹簧 | 劲度系数 k=1.0，原长 L₀=1.0 |
+| 重力 | 无 |
+| 万有引力 | 无 |
+| 阻尼 | 无 |
+| 驱动力 | 原子 1（z 方向驱动） |
+| 算法 | leapfrog（蛙跳法，能量守恒） |
+
+## 驱动力
+
+原子 1 的位置由 `input/driver.txt` 中的驱动力公式决定：
+
+```math
+z(t) = A_z \cdot \cos(2\pi f_z t + \phi_z)
+```
+
+当前参数：A_z = 0.5, f_z = 0.1 Hz, φ_z = 90°, period = all（全程驱动）。
+
+## 动力学行为
+
+原子 1 沿 z 方向的受迫振动通过弹簧逐次传递给相邻原子，形成沿链传播的**横波**。由于 z 方向的振动是横向的，弹簧大部分张力在 x 方向，z 方向的有效刚度是非线性的——等效于一个三次方恢复力（FPU 型非线性），因此波速较慢。
+
+## 使用方法
+
+```bash
+cd examples/case06
+python run_dynamics.py
+```
+
+配置参数详见 `input/input.txt`，驱动力定义见 `input/driver.txt`，完整文档见 `doc/index.html`。

examples/case10/doc/index.html

@@ -0,0 +1,477 @@
+<!DOCTYPE html>
+<html lang="zh-CN">
+<head>
+<meta charset="UTF-8">
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<title>case06 — 一维原子链驱动力学模拟 | 物理原理 &amp; 使用文档</title>
+<style>
+  :root {
+    --bg: #f8f9fa;
+    --card: #fff;
+    --text: #1a1a2e;
+    --accent: #2563eb;
+    --accent-light: #dbeafe;
+    --code-bg: #1e293b;
+    --code-text: #e2e8f0;
+    --border: #e2e8f0;
+    --muted: #64748b;
+  }
+  * { margin: 0; padding: 0; box-sizing: border-box; }
+  body {
+    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Noto Sans SC", sans-serif;
+    background: var(--bg);
+    color: var(--text);
+    line-height: 1.7;
+  }
+
+  /* ── Header ── */
+  .hero {
+    background: linear-gradient(135deg, #1e293b 0%, #334155 100%);
+    color: #fff;
+    padding: 56px 24px 48px;
+    text-align: center;
+  }
+  .hero h1 { font-size: 2rem; font-weight: 700; letter-spacing: -0.02em; }
+  .hero .subtitle {
+    margin-top: 10px;
+    font-size: 1.05rem;
+    opacity: 0.8;
+  }
+  .hero .badge {
+    display: inline-block;
+    margin-top: 14px;
+    padding: 4px 14px;
+    border-radius: 999px;
+    background: rgba(255,255,255,0.12);
+    font-size: 0.82rem;
+  }
+
+  /* ── Layout ── */
+  .container { max-width: 820px; margin: 0 auto; padding: 32px 20px; }
+
+  section { margin-bottom: 44px; }
+  h2 {
+    font-size: 1.35rem;
+    font-weight: 600;
+    margin-bottom: 16px;
+    padding-bottom: 8px;
+    border-bottom: 2px solid var(--accent);
+    display: inline-block;
+  }
+  h3 {
+    font-size: 1.05rem;
+    font-weight: 600;
+    margin: 20px 0 10px;
+  }
+
+  p, li { margin-bottom: 10px; }
+  ul, ol { padding-left: 22px; }
+  strong { color: var(--accent); }
+
+  /* ── Cards ── */
+  .card {
+    background: var(--card);
+    border-radius: 12px;
+    padding: 20px 24px;
+    margin-bottom: 16px;
+    border: 1px solid var(--border);
+    box-shadow: 0 1px 3px rgba(0,0,0,0.04);
+  }
+
+  /* ── Formula / Code blocks ── */
+  .formula {
+    background: var(--card);
+    border-left: 4px solid var(--accent);
+    padding: 14px 20px;
+    margin: 14px 0;
+    font-family: "Times New Roman", "STIX", serif;
+    font-size: 1.05rem;
+    overflow-x: auto;
+    border-radius: 0 8px 8px 0;
+  }
+  code {
+    background: var(--accent-light);
+    padding: 2px 7px;
+    border-radius: 4px;
+    font-family: "JetBrains Mono", "Fira Code", monospace;
+    font-size: 0.88em;
+  }
+  pre {
+    background: var(--code-bg);
+    color: var(--code-text);
+    padding: 16px 20px;
+    border-radius: 10px;
+    overflow-x: auto;
+    font-size: 0.85rem;
+    line-height: 1.5;
+    margin: 14px 0;
+  }
+  pre .cm { color: #94a3b8; font-style: italic; }   /* comment */
+
+  /* ── Table ── */
+  table {
+    width: 100%;
+    border-collapse: collapse;
+    margin: 14px 0;
+    font-size: 0.92rem;
+  }
+  th, td {
+    padding: 8px 12px;
+    text-align: left;
+    border-bottom: 1px solid var(--border);
+  }
+  th { background: var(--accent-light); font-weight: 600; }
+
+  /* ── TOC ── */
+  .toc { counter-reset: toc; }
+  .toc li { counter-increment: toc; list-style: none; margin-bottom: 6px; }
+  .toc li::before { content: counter(toc) ". "; font-weight: 600; color: var(--accent); }
+  .toc a { color: var(--accent); text-decoration: none; }
+  .toc a:hover { text-decoration: underline; }
+
+  /* ── Flow diagram ── */
+  .flow { display: flex; flex-wrap: wrap; gap: 8px; align-items: center; justify-content: center; margin: 16px 0; }
+  .flow-step {
+    background: var(--accent-light);
+    border: 1px solid var(--accent);
+    border-radius: 8px;
+    padding: 8px 16px;
+    font-size: 0.88rem;
+    font-weight: 500;
+  }
+  .flow-arrow { color: var(--muted); font-size: 1.2rem; }
+
+  @media (max-width: 600px) {
+    .hero h1 { font-size: 1.5rem; }
+    .flow { flex-direction: column; }
+    .flow-arrow { transform: rotate(90deg); }
+  }
+</style>
+</head>
+<body>
+
+<!-- ============================================================ -->
+<!--  Header                                                       -->
+<!-- ============================================================ -->
+<header class="hero">
+  <h1>一维原子链驱动力学模拟</h1>
+  <p class="subtitle">120 个原子沿 x 轴排列 · 弹簧连接 · z 方向受迫振动</p>
+  <span class="badge">case06  ·  examples/case06</span>
+</header>
+
+<div class="container">
+
+<!-- ============================================================ -->
+<!--  TOC                                                          -->
+<!-- ============================================================ -->
+<section>
+  <h2>目录</h2>
+  <ol class="toc">
+    <li><a href="#physics">物理原理</a></li>
+    <li><a href="#algorithm">数值算法</a></li>
+    <li><a href="#driver">驱动力模型</a></li>
+    <li><a href="#usage">使用方法</a></li>
+    <li><a href="#params">参数参考</a></li>
+    <li><a href="#files">文件结构</a></li>
+    <li><a href="#troubleshoot">常见问题</a></li>
+  </ol>
+</section>
+
+<!-- ============================================================ -->
+<!--  1. Physics                                                   -->
+<!-- ============================================================ -->
+<section id="physics">
+  <h2>一、物理原理</h2>
+
+  <div class="card">
+    <h3>1.1 一维原子链</h3>
+    <p>120 个原子沿 <strong>x 轴</strong> 等间距排列，原子间距为 1。相邻原子之间用 <strong>理想弹簧</strong> 连接，弹簧的劲度系数 <em>k</em> = 1.0，原长 <em>L</em>₀ = 1.0（与原子间距一致，初始状态弹簧无拉伸）。</p>
+    <p>每个原子被限制在 <strong>z 方向</strong> 自由振动，x 和 y 方向锁定（<code>fix_x=1, fix_y=1, fix_z=0</code>）。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.2 弹簧力（胡克定律）</h3>
+    <p>当原子 <em>i</em> 和 <em>j</em> 之间有弹簧连接时，原子 <em>i</em> 受到的弹簧力为：</p>
+    <div class="formula">
+      <strong>F</strong> = −<em>k</em> · (<em>d</em> − <em>L</em>₀) · <strong>u</strong><sub><em>ij</em></sub>
+    </div>
+    <p>其中 <em>d</em> = |<strong>r</strong><sub><em>j</em></sub> − <strong>r</strong><sub><em>i</em></sub>| 为两原子间距离，<strong>u</strong><sub><em>ij</em></sub> 为从 <em>i</em> 指向 <em>j</em> 的单位向量。由于原子只在 z 方向振动，弹簧在 z 方向的分量是 <strong>几何非线性</strong> 的——对于小振幅近似，z 方向等效于一个三次方恢复力（FPU 型非线性）。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.3 运动方程</h3>
+    <p>对于第 <em>i</em> 个自由原子（非受驱），牛顿第二定律给出：</p>
+    <div class="formula">
+      <em>m</em> · <strong>a</strong><sub><em>i</em></sub> = <strong>F</strong><sub><em>i</em></sub><sup>spring</sup> + <strong>F</strong><sub><em>i</em></sub><sup>driving</sup>
+    </div>
+    <p>本案例中 <strong>唯一的外力</strong> 来自驱动力（仅施加于原子 1）。无重力、无万有引力、无阻尼，系统总能量守恒。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.4 波传播</h3>
+    <p>原子 1 的受迫振动通过弹簧逐次传递给相邻原子，形成沿链传播的 <strong>横波</strong>。由于横向振动的几何非线性（弹簧大部分张力在 x 方向，z 方向的有效刚度远小于 1），波的传播速度较慢，且高阶频率成分会在链中产生复杂的非线性动力学行为（类似 FPU 回波现象）。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  2. Algorithm                                                 -->
+<!-- ============================================================ -->
+<section id="algorithm">
+  <h2>二、数值算法</h2>
+
+  <div class="card">
+    <h3>2.1 蛙跳法（Leapfrog / Velocity-Verlet）</h3>
+    <p>采用能量守恒特性优异的 <strong>蛙跳法</strong>（二阶辛积分器），更新公式为：</p>
+    <div class="formula">
+      <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) = <strong>v</strong>(<em>t</em>) + ½ <strong>a</strong>(<em>t</em>) · Δ<em>t</em><br>
+      <strong>r</strong>(<em>t</em> + Δ<em>t</em>) = <strong>r</strong>(<em>t</em>) + <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) · Δ<em>t</em><br>
+      <strong>a</strong>(<em>t</em> + Δ<em>t</em>) = <strong>F</strong>(<strong>r</strong>(<em>t</em> + Δ<em>t</em>), <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>)) / <em>m</em><br>
+      <strong>v</strong>(<em>t</em> + Δ<em>t</em>) = <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) + ½ <strong>a</strong>(<em>t</em> + Δ<em>t</em>) · Δ<em>t</em>
+    </div>
+    <p>蛙跳法在长时间模拟中能量漂移极小（本案例验证 <strong>&lt; 0.004%</strong>），适合无阻尼的保守系统。</p>
+  </div>
+
+  <div class="card">
+    <h3>2.2 时间步长与采样</h3>
+    <table>
+      <tr><th>参数</th><th>值</th><th>说明</th></tr>
+      <tr><td>DT</td><td>0.01 s</td><td>积分步长（远小于 1/ω ≈ 0.16 s，满足稳定性条件）</td></tr>
+      <tr><td>T_total</td><td>100 s</td><td>总模拟时间 → NT = 10000 步</td></tr>
+      <tr><td>NSTEP</td><td>50</td><td>每 NSTEP 步取一帧用于动画 → 200 帧</td></tr>
+      <tr><td>method</td><td>leapfrog</td><td>蛙跳法（Velocity-Verlet）</td></tr>
+    </table>
+  </div>
+
+  <div class="card">
+    <h3>2.3 计算流程</h3>
+    <div class="flow">
+      <span class="flow-step">读入 coord.txt<br>connection.txt<br>bond.txt</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">施加驱动力<br>（驱动原子 1）</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">记录轨迹</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">蛙跳法<br>更新位置/速度</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">固定约束<br>（x, y 锁定）</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step" style="background:#fef3c7;border-color:#f59e0b;">循环<br>NT 次</span>
+    </div>
+    <p style="margin-top:12px;">注意：驱动力在 <strong>每次积分前</strong> 施加，确保受驱原子的位置正确传递给弹簧力计算。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  3. Driving Force                                             -->
+<!-- ============================================================ -->
+<section id="driver">
+  <h2>三、驱动力模型</h2>
+
+  <div class="card">
+    <h3>3.1 定义文件</h3>
+    <p>驱动力由 <code>input/driver.txt</code> 定义，格式如下：</p>
+    <pre>n amp_x amp_y amp_z freq_x freq_y freq_z phi_x phi_y phi_z period
+1     0     0     5      0      0      1     0     0    90    all</pre>
+  </div>
+
+  <div class="card">
+    <h3>3.2 数学公式</h3>
+    <p>受驱原子的位置由下式决定（<strong>完全替换</strong> coord.txt 中的初始坐标和固定约束）：</p>
+    <div class="formula">
+      <strong>r</strong>(<em>t</em>) = <strong>A</strong> · cos(2π<em>f</em> · <em>t</em> + <strong>φ</strong>)
+    </div>
+    <p>速度由解析导数给出：</p>
+    <div class="formula">
+      <strong>v</strong>(<em>t</em>) = −<strong>A</strong> · 2π<em>f</em> · sin(2π<em>f</em> · <em>t</em> + <strong>φ</strong>)
+    </div>
+    <p>其中 <strong>A</strong> = (amp_x, amp_y, amp_z)，<strong>f</strong> = (freq_x, freq_y, freq_z) 为不同方向的驱动频率，<strong>φ</strong> = (phi_x, phi_y, phi_z) 为相位（<strong>角度制</strong>，代码自动转换为弧度）。</p>
+  </div>
+
+  <div class="card">
+    <h3>3.3 本案例驱动参数</h3>
+    <table>
+      <tr><th>参数</th><th>值</th><th>含义</th></tr>
+      <tr><td>amp_z</td><td>5.0</td><td>z 方向驱动振幅</td></tr>
+      <tr><td>freq_z</td><td>1.0 Hz</td><td>驱动频率（周期 1 s）</td></tr>
+      <tr><td>phi_z</td><td>90°</td><td>驱动相位 → z(0) = 5·cos(90°) = 0</td></tr>
+      <tr><td>period</td><td>all</td><td>全程驱动，永不停止</td></tr>
+    </table>
+    <div class="formula">
+      <em>z</em>(<em>t</em>) = 5.0 · cos(2π · 1.0 · <em>t</em> + 90°)
+    </div>
+  </div>
+
+  <div class="card">
+    <h3>3.4 有限周期驱动</h3>
+    <p><code>period</code> 参数支持三种模式：</p>
+    <ul>
+      <li><strong>all</strong> — 全程驱动</li>
+      <li><strong>数值</strong> — 驱动指定周期数后 <strong>静止</strong>（冻结在最终位置，速度归零）。例如 <code>period: 1</code> 表示驱动 1 个完整周期后停止。</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>3.5 驱动与固定约束的关系</h3>
+    <p>对于受驱原子（<code>driver.txt</code> 中 <code>n</code> 指定的原子），其在 <code>coord.txt</code> 中的初始坐标和 <code>fix_x/fix_y/fix_z</code> 约束被 <strong>完全忽略</strong>。原子的位置和速度完全由驱动力公式决定。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  4. Usage                                                     -->
+<!-- ============================================================ -->
+<section id="usage">
+  <h2>四、使用方法</h2>
+
+  <div class="card">
+    <h3>4.1 完整运行（模拟 + 动画）</h3>
+    <pre>cd examples/case06
+python run_dynamics.py</pre>
+    <p>这步会依次执行：物理模拟 → 抽帧 → 打开 VisPy 3D 动画窗口。</p>
+  </div>
+
+  <div class="card">
+    <h3>4.2 仅查看已有结果</h3>
+    <p>如果已经跑完模拟且生成了 <code>output/display.txt</code>，可以通过修改 <code>input.txt</code> 跳过计算，只开动画：</p>
+    <pre>step_simulate:  0   # 跳过模拟
+step_sample:    0   # 跳过抽帧
+step_animation: 1   # 播放动画</pre>
+    <p>然后运行：<code>python run_dynamics.py</code></p>
+  </div>
+
+  <div class="card">
+    <h3>4.3 手动 3D 动画</h3>
+    <p>也可以单独启动 VisPy 窗口：</p>
+    <pre>python ../../draw.py output/</pre>
+  </div>
+
+  <div class="card">
+    <h3>4.4 强制重新计算</h3>
+    <p>修改参数后需要重新运行模拟时，设置：</p>
+    <pre>force_calc: 1        # 忽略缓存，强制重新计算</pre>
+  </div>
+
+  <div class="card">
+    <h3>4.5 动画交互</h3>
+    <table>
+      <tr><th>操作</th><th>效果</th></tr>
+      <tr><td>鼠标拖动</td><td>旋转视角</td></tr>
+      <tr><td>滚轮</td><td>缩放</td></tr>
+      <tr><td>W / S 键</td><td>相机沿 Z 轴向前 / 向后移动（靠近/远离场景）</td></tr>
+      <tr><td>A / D 键</td><td>视角向右 / 向左平移</td></tr>
+      <tr><td>E / Q 键</td><td>视角上升 / 下降（屏幕方向）</td></tr>
+      <tr><td>C / X 键</td><td>增大 / 减小步长</td></tr>
+      <tr><td>V 键</td><td>切换透视 / 正交投影</td></tr>
+      <tr><td>左上角 <strong>reset</strong> 按钮</td><td>复位视角到初始位置</td></tr>
+      <tr><td>左上角 <strong>info</strong> 按钮</td><td>切换信息面板显示/隐藏</td></tr>
+      <tr><td>左上角 <strong>axes</strong> 按钮</td><td>切换坐标轴显示/隐藏</td></tr>
+    </table>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  5. Parameters                                                -->
+<!-- ============================================================ -->
+<section id="params">
+  <h2>五、参数参考</h2>
+
+  <div class="card">
+    <h3>5.1 input.txt 关键参数</h3>
+    <table>
+      <tr><th>参数</th><th>默认值</th><th>说明</th></tr>
+      <tr><td>gravity_field</td><td>0</td><td>均匀重力场（已关闭）</td></tr>
+      <tr><td>gravity_interaction</td><td>0</td><td>原子间万有引力（已关闭）</td></tr>
+      <tr><td>elastic_force</td><td>1</td><td>弹簧键力（已开启）</td></tr>
+      <tr><td>damping_force</td><td>0</td><td>阻尼（已关闭）</td></tr>
+      <tr><td><strong>driving_force</strong></td><td><strong>1</strong></td><td>驱动力开关（1=开启，需 driver.txt）</td></tr>
+      <tr><td>method</td><td>leapfrog</td><td>数值积分方法</td></tr>
+      <tr><td>DT</td><td>0.01</td><td>积分步长 (s)</td></tr>
+      <tr><td>T_total</td><td>100.0</td><td>总模拟时间 (s)</td></tr>
+      <tr><td>NSTEP</td><td>50</td><td>抽帧步数间隔</td></tr>
+      <tr><td>engine</td><td>python</td><td>计算引擎（python / c / cpp / fortran）</td></tr>
+      <tr><td>use_marker</td><td>1</td><td>渲染模式（0=Sphere 网格, 1=Marker GPU 实例化）</td></tr>
+    </table>
+  </div>
+
+  <div class="card">
+    <h3>5.2 流程控制参数</h3>
+    <table>
+      <tr><th>参数</th><th>0</th><th>1</th></tr>
+      <tr><td>step_simulate</td><td>跳过模拟（加载已有轨迹）</td><td>运行物理模拟</td></tr>
+      <tr><td>step_sample</td><td>跳过抽帧</td><td>从轨迹抽取显示帧</td></tr>
+      <tr><td>step_plot</td><td>不生成图表</td><td>生成轨迹/能量图</td></tr>
+      <tr><td><strong>step_plot_wave</strong></td><td>不生成波形图</td><td>生成波形能量动画 GIF</td></tr>
+      <tr><td>step_animation</td><td>不启动动画</td><td>自动打开 VisPy 3D 窗口</td></tr>
+      <tr><td>force_calc</td><td>自动检测缓存</td><td>强制重新计算</td></tr>
+    </table>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  6. File Structure                                            -->
+<!-- ============================================================ -->
+<section id="files">
+  <h2>六、文件结构</h2>
+
+  <pre>case06/
+├── input/
+│   ├── input.txt          # 主配置文件（YAML 格式）
+│   ├── coord.txt          # 原子坐标（120 个原子）
+│   ├── connection.txt     # 弹簧连接关系（59 条键）
+│   ├── bond.txt           # 弹簧参数（k=1.0, L₀=1.0）
+│   └── <strong>driver.txt</strong>       # <span class="cm">驱动力定义（本案例新增）</span>
+├── output/
+│   ├── trajectory.txt     # 全量轨迹数据（50000 步 × 120 原子）
+│   ├── display.txt        # 抽帧后的动画数据（500 帧 × 120 原子）
+│   ├── dynamics.log       # 计算日志
+│   ├── animation.log      # 动画启动日志（闪退时排查用）
+│   └── wave_animation.gif # 波形能量动画（step_plot_wave=1 时生成）
+├── doc/
+│   └── index.html         # <span class="cm">本文档</span>
+├── Readme.md              # 案例简介
+└── run_dynamics.py        # 案例运行入口</pre>
+</section>
+
+<!-- ============================================================ -->
+<!--  7. Troubleshooting                                           -->
+<!-- ============================================================ -->
+<section id="troubleshoot">
+  <h2>七、常见问题</h2>
+
+  <div class="card">
+    <h3>7.1 动画窗口闪退</h3>
+    <p>如果 VisPy 窗口一闪就消失，请检查：</p>
+    <ul>
+      <li><code>output/animation.log</code> 中是否有错误信息</li>
+      <li><code>output/display.txt</code> 是否存在（需先跑 <code>step_sample: 1</code>）</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>7.2 原子不振动</h3>
+    <p>可能原因：</p>
+    <ul>
+      <li><strong>NSTEP 过大</strong>：抽帧间隔大于驱动周期的一半时，动画会丢失振动细节。建议 NSTEP ≤ 1/(freq · DT · 10)</li>
+      <li><strong>相位 φ 使采样点落在零值</strong>：试试 <code>phi_z: 0</code> 让原子在 t=0 处于振幅峰值</li>
+      <li>确认 <code>driving_force: 1</code> 且 <code>driver.txt</code> 中 amp_z 不为 0</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>7.3 渲染性能慢</h3>
+    <p>原子数多时动画卡顿：</p>
+    <ul>
+      <li>设置 <code>use_marker: 1</code>（使用 GPU 实例化渲染替代独立网格球体）</li>
+      <li>增大 <code>NSTEP</code> 减少动画帧数</li>
+    </ul>
+  </div>
+</section>
+
+<hr style="border:none;border-top:1px solid var(--border);margin:40px 0;">
+
+<footer style="text-align:center;color:var(--muted);font-size:0.85rem;margin-bottom:40px;">
+  Dynamics Simulation Framework &nbsp;·&nbsp; 生成于 2026-06-10
+</footer>
+
+</div>
+</body>
+</html>

examples/case10/input/bond.txt

@@ -0,0 +1,2 @@
+bond_name k       rest_length
+k1        300.0   1.0

examples/case10/input/connection.txt

@@ -0,0 +1,40 @@
+n1 n2 bond_name
+1 2 k1
+2 3 k1
+3 4 k1
+4 5 k1
+5 6 k1
+6 7 k1
+7 8 k1
+8 9 k1
+9 10 k1
+10 11 k1
+11 12 k1
+12 13 k1
+13 14 k1
+14 15 k1
+15 16 k1
+16 17 k1
+17 18 k1
+18 19 k1
+19 20 k1
+20 21 k1
+21 22 k1
+22 23 k1
+23 24 k1
+24 25 k1
+25 26 k1
+26 27 k1
+27 28 k1
+28 29 k1
+29 30 k1
+30 31 k1
+31 32 k1
+32 33 k1
+33 34 k1
+34 35 k1
+35 36 k1
+36 37 k1
+37 38 k1
+38 39 k1
+39 40 k1

examples/case10/input/coord.txt

@@ -0,0 +1,41 @@
+n mass radius x y z vx vy vz fix_x fix_y fix_z
+1 1 0.1 0 0 0 0 0 0       0 1 1
+2 1 0.1 1 0 0 0 0 0       0 1 1
+3 1 0.1 2 0 0 0 0 0       0 1 1
+4 1 0.1 3 0 0 0 0 0       0 1 1
+5 1 0.1 4 0 0 0 0 0       0 1 1
+6 1 0.1 5 0 0 0 0 0       0 1 1
+7 1 0.1 6 0 0 0 0 0       0 1 1
+8 1 0.1 7 0 0 0 0 0       0 1 1
+9 1 0.1 8 0 0 0 0 0       0 1 1
+10 1 0.1 9 0 0 0 0 0       0 1 1
+11 1 0.1 10 0 0 0 0 0       0 1 1
+12 1 0.1 11 0 0 0 0 0       0 1 1
+13 1 0.1 12 0 0 0 0 0       0 1 1
+14 1 0.1 13 0 0 0 0 0       0 1 1
+15 1 0.1 14 0 0 0 0 0       0 1 1
+16 1 0.1 15 0 0 0 0 0       0 1 1
+17 1 0.1 16 0 0 0 0 0       0 1 1
+18 1 0.1 17 0 0 0 0 0       0 1 1
+19 1 0.1 18 0 0 0 0 0       0 1 1
+20 1 0.1 19 0 0 0 0 0       0 1 1
+21 1 0.1 20 0 0 0 0 0       0 1 1
+22 1 0.1 21 0 0 0 0 0       0 1 1
+23 1 0.1 22 0 0 0 0 0       0 1 1
+24 1 0.1 23 0 0 0 0 0       0 1 1
+25 1 0.1 24 0 0 0 0 0       0 1 1
+26 1 0.1 25 0 0 0 0 0       0 1 1
+27 1 0.1 26 0 0 0 0 0       0 1 1
+28 1 0.1 27 0 0 0 0 0       0 1 1
+29 1 0.1 28 0 0 0 0 0       0 1 1
+30 1 0.1 29 0 0 0 0 0       0 1 1
+31 1 0.1 30 0 0 0 0 0       0 1 1
+32 1 0.1 31 0 0 0 0 0       0 1 1
+33 1 0.1 32 0 0 0 0 0       0 1 1
+34 1 0.1 33 0 0 0 0 0       0 1 1
+35 1 0.1 34 0 0 0 0 0       0 1 1
+36 1 0.1 35 0 0 0 0 0       0 1 1
+37 1 0.1 36 0 0 0 0 0       0 1 1
+38 1 0.1 37 0 0 0 0 0       0 1 1
+39 1 0.1 38 0 0 0 0 0       0 1 1
+40 1 0.1 39 0 0 0 0 0       1 1 1

examples/case10/input/driver.txt

@@ -0,0 +1,2 @@
+  n amp_x amp_y amp_z freq_x freq_y  freq_z phi_x phi_y phi_z period
+  1   0.1     0     0   0.04      0       0     0     0    90    all

examples/case10/input/input.txt

@@ -0,0 +1,114 @@
+# 物理模拟参数配置
+# 格式：YAML
+# 用法：python run_dynamics.py
+
+# ── 流程控制 ──────────────────────────────────
+# 每步用 0/1 单独开关，1=执行，0=跳过
+# 依赖关系：抽帧依赖模拟结果，绘图依赖模拟+抽帧
+step_simulate:  1   # 运行物理模拟 → output/display.txt（引擎直接抽帧）
+step_sample:    0   # （旧版）从 trajectory.txt 重新抽帧，默认0=不执行
+step_plot:      1   # 绘制轨迹/能量图 → output/trajectory_plots.png
+step_animation: 0   # 自动播放 VisPy 3D 动画窗口（需安装 vispy）
+step_plot_wave: 1   # 绘制波形能量动画
+force_calc: 1       # 强制重新计算：1=跳过缓存强算，0=自动使用已有输出
+plot_wave_save_gif: 0  # 输出波形 GIF（需 step_plot_wave=1）
+plot_wave_save_mp4: 0  # 输出波形 MP4（需 step_plot_wave=1）
+
+# ── 文件保存 ──────────────────────────────────
+save_trajectory: 0  # 0=不保留完整轨迹文件, 1=保留 trajectory.txt（用于后续单独抽帧）
+
+# ── 计算引擎 ──────────────────────────────────
+# 可选: python, c, cpp, fortran, java
+engine: c # 默认使用 python 引擎
+
+# ── 盒子 ──────────────────────────────────────
+box_a: 300.0         # 立方体半边长，粒子被限制在 [-box_a, box_a]³ 内
+
+# ── 初始构型 ──────────────────────────────────
+# 坐标文件格式：
+#   第一行：n mass radius x y z vx vy vz fix_x fix_y fix_z
+#   后续行：原子序号 质量 半径 x y z vx vy vz fix_x fix_y fix_z
+coord_file: input/coord.txt
+connection_file: input/connection.txt
+bond_file: input/bond.txt
+driver_file: input/driver.txt     # 驱动力定义文件（driving_force=1 时生效）
+
+# 绘图/动画展示的原子序号（对应 coord_file 第一列 n）
+plot_atom: 1
+
+# ── 物理参数 ──────────────────────────────────
+# 三个方向分量分别对应 x, y, z
+G: [0.000, 0.000, 0.000]   # 重力场分量 (m/s²)
+B: [0.005, 0.000, 0.005]   # 阻尼分量
+
+# ── 力开关（0=关闭, 1=开启）──────────────────
+gravity_field: 0         # 均匀重力场 (G)
+gravity_interaction: 0   # 原子间万有引力
+elastic_force: 1         # 弹簧键力
+damping_force: 0         # 阻尼 (B)
+driving_force: 1         # 驱动力（需 driver_file 定义）
+#
+gravity_strength: 1.0    # 万有引力强度（仅 gravity_interaction=1 时有效）
+
+# ── 数值算法 ──────────────────────────────────
+# 可选：
+#   explicit_euler  显式欧拉法
+#   implicit_euler  隐式欧拉法
+#   midpoint        中点法
+#   leapfrog        蛙跳法
+method: leapfrog
+
+# ── 步骤控制 ──────────────────────────────────
+# 以下参数控制哪些步骤被执行和保存
+
+# 预热步数：模拟开始时跳过不保存的步数（用于稳定初始状态）
+warmup_steps: 0           # 默认 0（立即开始记录）
+
+# 总模拟时间（秒），程序自动计算 NT = T_total / DT
+# 如果同时指定了 NT，以 NT 为准
+T_total:  10.0
+
+# 抽帧间隔（每 NSTEP 步取一帧用于动画）
+NSTEP: 20
+
+# ── 时间步长 ──────────────────────────────────
+DT:    0.001         # 时间步长 (s)
+
+# 抽帧范围：只保存 [sample_start, sample_end) 区间内的帧
+sample_start: null        # null 表示从头开始（帧索引从 0 起）
+sample_end: null          # null 表示到末尾
+
+
+
+# ── 渲染方式 ──────────────────────────────────
+# 3D 动画中原子渲染方式：
+#   0 = Sphere （网格球体，效果精细，原子数少时推荐）
+#   1 = Marker （GPU 实例化点，原子数多时性能更佳）
+use_marker: 1
+
+# ── 显示参数 ──────────────────────────────────
+# 盒子透明度：单个数值（统一）或 6 个数的数组，按 [-x,+x,-y,+y,-z,+z] 顺序
+alpha: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+
+# 小球颜色
+# 小球半径从 coord_file 的 radius 列读取
+ball_color_r: 0.20  # R 分量 (0~1)
+ball_color_g: 0.60  # G 分量
+ball_color_b: 0.90  # B 分量
+
+# 盒子面颜色
+box_color_r:  0.80
+box_color_g:  0.80
+box_color_b:  0.85
+
+# ── 摄像机初始位置 ────────────────────────────
+camera_distance:   120.0    # 摄像机到场景中心的距离
+camera_elevation:    0.0    # 俯仰角（度），负值=俯视
+camera_azimuth:      0.0    # 方位角（度）
+camera_center_x:    60.0    # 摄像机注视点 x
+camera_center_y:     0.0    # 摄像机注视点 y
+camera_center_z:     0.0    # 摄像机注视点 z
+move_camera:         0      # 0=固定视角, 1=按 move_camera.txt 运动
+
+# ── 视觉放大 ──────────────────────────────────
+display_amp: [1.0, 1.0, 10.0]   # x/y/z 方向视觉位移放大倍数（不影响物理）

examples/case10/input/move_camera.txt

@@ -0,0 +1,9 @@
+# move_camera.txt — 摄像机速度段驱动
+# 格式: start-end  vx=f vy=f vz=f  rx=d ry=d rz=d
+#   vx/vy/vz: 平移速度（每帧移动单位）
+#   rx/ry/rz: 旋转速度（每帧度数）
+#     rx → elevation（俯仰）, ry → azimuth（方位）, rz → (预留)
+#
+# 示例：前60帧向右平移+绕x旋转，30-90帧向上平移+绕y绕z旋转
+all   vx=0.02
+# 30-90  vy=0.02  ry=1  rz=1

examples/case10/run_dynamics.py

@@ -0,0 +1,54 @@
+"""
+Case runner for Dynamics case06 — 1D atomic chain (transverse wave).
+
+This script keeps program and data separated:
+  - program: ../../dynamics.py
+  - input:   ./input
+  - output:  ./output
+"""
+
+from __future__ import annotations
+
+import argparse
+import importlib.util
+from pathlib import Path
+
+
+CASE_DIR = Path(__file__).resolve().parent
+DYNAMICS_PATH = Path("..") / ".." / "dynamics.py"
+INPUT_DIR = Path("input")
+OUTPUT_DIR = Path("output")
+CONFIG_FILE = INPUT_DIR / "input.txt"
+
+
+def load_dynamics_module(module_path: Path):
+    spec = importlib.util.spec_from_file_location("dynamics_module", module_path)
+    if spec is None or spec.loader is None:
+        raise ImportError(f"无法加载 dynamics.py: {module_path}")
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def main():
+    parser = argparse.ArgumentParser(description="运行 Dynamics 示例案例 case06")
+    parser.add_argument("--no-plot", action="store_true", help="跳过 matplotlib 绘图")
+    args = parser.parse_args()
+
+    dynamics_path = (CASE_DIR / DYNAMICS_PATH).resolve()
+    input_dir = (CASE_DIR / INPUT_DIR).resolve()
+    output_dir = (CASE_DIR / OUTPUT_DIR).resolve()
+    config_path = (CASE_DIR / CONFIG_FILE).resolve()
+
+    module = load_dynamics_module(dynamics_path)
+    module.run_case(
+        config_path=config_path,
+        runtime_base=CASE_DIR,
+        input_dir=input_dir,
+        output_dir=output_dir,
+        no_plot=args.no_plot,
+    )
+
+
+if __name__ == "__main__":
+    main()

examples/case11/Readme.md

@@ -0,0 +1,40 @@
+# case06: 一维原子链横波模拟
+
+60 个原子沿 x 轴排列，相邻原子用弹簧连接。原子 1 受 z 方向驱动力作用，产生沿链传播的横波。
+
+## 物理设定
+
+| 参数 | 值 |
+|---|---|
+| 原子数 | 120 |
+| 排列 | 沿 x 轴等间距排列，间距为 1 |
+| 约束 | 原子**沿 z 方向自由振动**（fix_x=1, fix_y=1, fix_z=0），x, y 锁定 |
+| 弹簧 | 劲度系数 k=1.0，原长 L₀=1.0 |
+| 重力 | 无 |
+| 万有引力 | 无 |
+| 阻尼 | 无 |
+| 驱动力 | 原子 1（z 方向驱动） |
+| 算法 | leapfrog（蛙跳法，能量守恒） |
+
+## 驱动力
+
+原子 1 的位置由 `input/driver.txt` 中的驱动力公式决定：
+
+```math
+z(t) = A_z \cdot \cos(2\pi f_z t + \phi_z)
+```
+
+当前参数：A_z = 0.5, f_z = 0.1 Hz, φ_z = 90°, period = all（全程驱动）。
+
+## 动力学行为
+
+原子 1 沿 z 方向的受迫振动通过弹簧逐次传递给相邻原子，形成沿链传播的**横波**。由于 z 方向的振动是横向的，弹簧大部分张力在 x 方向，z 方向的有效刚度是非线性的——等效于一个三次方恢复力（FPU 型非线性），因此波速较慢。
+
+## 使用方法
+
+```bash
+cd examples/case06
+python run_dynamics.py
+```
+
+配置参数详见 `input/input.txt`，驱动力定义见 `input/driver.txt`，完整文档见 `doc/index.html`。

examples/case11/doc/index.html

@@ -0,0 +1,477 @@
+<!DOCTYPE html>
+<html lang="zh-CN">
+<head>
+<meta charset="UTF-8">
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<title>case06 — 一维原子链驱动力学模拟 | 物理原理 &amp; 使用文档</title>
+<style>
+  :root {
+    --bg: #f8f9fa;
+    --card: #fff;
+    --text: #1a1a2e;
+    --accent: #2563eb;
+    --accent-light: #dbeafe;
+    --code-bg: #1e293b;
+    --code-text: #e2e8f0;
+    --border: #e2e8f0;
+    --muted: #64748b;
+  }
+  * { margin: 0; padding: 0; box-sizing: border-box; }
+  body {
+    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Noto Sans SC", sans-serif;
+    background: var(--bg);
+    color: var(--text);
+    line-height: 1.7;
+  }
+
+  /* ── Header ── */
+  .hero {
+    background: linear-gradient(135deg, #1e293b 0%, #334155 100%);
+    color: #fff;
+    padding: 56px 24px 48px;
+    text-align: center;
+  }
+  .hero h1 { font-size: 2rem; font-weight: 700; letter-spacing: -0.02em; }
+  .hero .subtitle {
+    margin-top: 10px;
+    font-size: 1.05rem;
+    opacity: 0.8;
+  }
+  .hero .badge {
+    display: inline-block;
+    margin-top: 14px;
+    padding: 4px 14px;
+    border-radius: 999px;
+    background: rgba(255,255,255,0.12);
+    font-size: 0.82rem;
+  }
+
+  /* ── Layout ── */
+  .container { max-width: 820px; margin: 0 auto; padding: 32px 20px; }
+
+  section { margin-bottom: 44px; }
+  h2 {
+    font-size: 1.35rem;
+    font-weight: 600;
+    margin-bottom: 16px;
+    padding-bottom: 8px;
+    border-bottom: 2px solid var(--accent);
+    display: inline-block;
+  }
+  h3 {
+    font-size: 1.05rem;
+    font-weight: 600;
+    margin: 20px 0 10px;
+  }
+
+  p, li { margin-bottom: 10px; }
+  ul, ol { padding-left: 22px; }
+  strong { color: var(--accent); }
+
+  /* ── Cards ── */
+  .card {
+    background: var(--card);
+    border-radius: 12px;
+    padding: 20px 24px;
+    margin-bottom: 16px;
+    border: 1px solid var(--border);
+    box-shadow: 0 1px 3px rgba(0,0,0,0.04);
+  }
+
+  /* ── Formula / Code blocks ── */
+  .formula {
+    background: var(--card);
+    border-left: 4px solid var(--accent);
+    padding: 14px 20px;
+    margin: 14px 0;
+    font-family: "Times New Roman", "STIX", serif;
+    font-size: 1.05rem;
+    overflow-x: auto;
+    border-radius: 0 8px 8px 0;
+  }
+  code {
+    background: var(--accent-light);
+    padding: 2px 7px;
+    border-radius: 4px;
+    font-family: "JetBrains Mono", "Fira Code", monospace;
+    font-size: 0.88em;
+  }
+  pre {
+    background: var(--code-bg);
+    color: var(--code-text);
+    padding: 16px 20px;
+    border-radius: 10px;
+    overflow-x: auto;
+    font-size: 0.85rem;
+    line-height: 1.5;
+    margin: 14px 0;
+  }
+  pre .cm { color: #94a3b8; font-style: italic; }   /* comment */
+
+  /* ── Table ── */
+  table {
+    width: 100%;
+    border-collapse: collapse;
+    margin: 14px 0;
+    font-size: 0.92rem;
+  }
+  th, td {
+    padding: 8px 12px;
+    text-align: left;
+    border-bottom: 1px solid var(--border);
+  }
+  th { background: var(--accent-light); font-weight: 600; }
+
+  /* ── TOC ── */
+  .toc { counter-reset: toc; }
+  .toc li { counter-increment: toc; list-style: none; margin-bottom: 6px; }
+  .toc li::before { content: counter(toc) ". "; font-weight: 600; color: var(--accent); }
+  .toc a { color: var(--accent); text-decoration: none; }
+  .toc a:hover { text-decoration: underline; }
+
+  /* ── Flow diagram ── */
+  .flow { display: flex; flex-wrap: wrap; gap: 8px; align-items: center; justify-content: center; margin: 16px 0; }
+  .flow-step {
+    background: var(--accent-light);
+    border: 1px solid var(--accent);
+    border-radius: 8px;
+    padding: 8px 16px;
+    font-size: 0.88rem;
+    font-weight: 500;
+  }
+  .flow-arrow { color: var(--muted); font-size: 1.2rem; }
+
+  @media (max-width: 600px) {
+    .hero h1 { font-size: 1.5rem; }
+    .flow { flex-direction: column; }
+    .flow-arrow { transform: rotate(90deg); }
+  }
+</style>
+</head>
+<body>
+
+<!-- ============================================================ -->
+<!--  Header                                                       -->
+<!-- ============================================================ -->
+<header class="hero">
+  <h1>一维原子链驱动力学模拟</h1>
+  <p class="subtitle">120 个原子沿 x 轴排列 · 弹簧连接 · z 方向受迫振动</p>
+  <span class="badge">case06  ·  examples/case06</span>
+</header>
+
+<div class="container">
+
+<!-- ============================================================ -->
+<!--  TOC                                                          -->
+<!-- ============================================================ -->
+<section>
+  <h2>目录</h2>
+  <ol class="toc">
+    <li><a href="#physics">物理原理</a></li>
+    <li><a href="#algorithm">数值算法</a></li>
+    <li><a href="#driver">驱动力模型</a></li>
+    <li><a href="#usage">使用方法</a></li>
+    <li><a href="#params">参数参考</a></li>
+    <li><a href="#files">文件结构</a></li>
+    <li><a href="#troubleshoot">常见问题</a></li>
+  </ol>
+</section>
+
+<!-- ============================================================ -->
+<!--  1. Physics                                                   -->
+<!-- ============================================================ -->
+<section id="physics">
+  <h2>一、物理原理</h2>
+
+  <div class="card">
+    <h3>1.1 一维原子链</h3>
+    <p>120 个原子沿 <strong>x 轴</strong> 等间距排列，原子间距为 1。相邻原子之间用 <strong>理想弹簧</strong> 连接，弹簧的劲度系数 <em>k</em> = 1.0，原长 <em>L</em>₀ = 1.0（与原子间距一致，初始状态弹簧无拉伸）。</p>
+    <p>每个原子被限制在 <strong>z 方向</strong> 自由振动，x 和 y 方向锁定（<code>fix_x=1, fix_y=1, fix_z=0</code>）。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.2 弹簧力（胡克定律）</h3>
+    <p>当原子 <em>i</em> 和 <em>j</em> 之间有弹簧连接时，原子 <em>i</em> 受到的弹簧力为：</p>
+    <div class="formula">
+      <strong>F</strong> = −<em>k</em> · (<em>d</em> − <em>L</em>₀) · <strong>u</strong><sub><em>ij</em></sub>
+    </div>
+    <p>其中 <em>d</em> = |<strong>r</strong><sub><em>j</em></sub> − <strong>r</strong><sub><em>i</em></sub>| 为两原子间距离，<strong>u</strong><sub><em>ij</em></sub> 为从 <em>i</em> 指向 <em>j</em> 的单位向量。由于原子只在 z 方向振动，弹簧在 z 方向的分量是 <strong>几何非线性</strong> 的——对于小振幅近似，z 方向等效于一个三次方恢复力（FPU 型非线性）。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.3 运动方程</h3>
+    <p>对于第 <em>i</em> 个自由原子（非受驱），牛顿第二定律给出：</p>
+    <div class="formula">
+      <em>m</em> · <strong>a</strong><sub><em>i</em></sub> = <strong>F</strong><sub><em>i</em></sub><sup>spring</sup> + <strong>F</strong><sub><em>i</em></sub><sup>driving</sup>
+    </div>
+    <p>本案例中 <strong>唯一的外力</strong> 来自驱动力（仅施加于原子 1）。无重力、无万有引力、无阻尼，系统总能量守恒。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.4 波传播</h3>
+    <p>原子 1 的受迫振动通过弹簧逐次传递给相邻原子，形成沿链传播的 <strong>横波</strong>。由于横向振动的几何非线性（弹簧大部分张力在 x 方向，z 方向的有效刚度远小于 1），波的传播速度较慢，且高阶频率成分会在链中产生复杂的非线性动力学行为（类似 FPU 回波现象）。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  2. Algorithm                                                 -->
+<!-- ============================================================ -->
+<section id="algorithm">
+  <h2>二、数值算法</h2>
+
+  <div class="card">
+    <h3>2.1 蛙跳法（Leapfrog / Velocity-Verlet）</h3>
+    <p>采用能量守恒特性优异的 <strong>蛙跳法</strong>（二阶辛积分器），更新公式为：</p>
+    <div class="formula">
+      <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) = <strong>v</strong>(<em>t</em>) + ½ <strong>a</strong>(<em>t</em>) · Δ<em>t</em><br>
+      <strong>r</strong>(<em>t</em> + Δ<em>t</em>) = <strong>r</strong>(<em>t</em>) + <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) · Δ<em>t</em><br>
+      <strong>a</strong>(<em>t</em> + Δ<em>t</em>) = <strong>F</strong>(<strong>r</strong>(<em>t</em> + Δ<em>t</em>), <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>)) / <em>m</em><br>
+      <strong>v</strong>(<em>t</em> + Δ<em>t</em>) = <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) + ½ <strong>a</strong>(<em>t</em> + Δ<em>t</em>) · Δ<em>t</em>
+    </div>
+    <p>蛙跳法在长时间模拟中能量漂移极小（本案例验证 <strong>&lt; 0.004%</strong>），适合无阻尼的保守系统。</p>
+  </div>
+
+  <div class="card">
+    <h3>2.2 时间步长与采样</h3>
+    <table>
+      <tr><th>参数</th><th>值</th><th>说明</th></tr>
+      <tr><td>DT</td><td>0.01 s</td><td>积分步长（远小于 1/ω ≈ 0.16 s，满足稳定性条件）</td></tr>
+      <tr><td>T_total</td><td>100 s</td><td>总模拟时间 → NT = 10000 步</td></tr>
+      <tr><td>NSTEP</td><td>50</td><td>每 NSTEP 步取一帧用于动画 → 200 帧</td></tr>
+      <tr><td>method</td><td>leapfrog</td><td>蛙跳法（Velocity-Verlet）</td></tr>
+    </table>
+  </div>
+
+  <div class="card">
+    <h3>2.3 计算流程</h3>
+    <div class="flow">
+      <span class="flow-step">读入 coord.txt<br>connection.txt<br>bond.txt</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">施加驱动力<br>（驱动原子 1）</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">记录轨迹</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">蛙跳法<br>更新位置/速度</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">固定约束<br>（x, y 锁定）</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step" style="background:#fef3c7;border-color:#f59e0b;">循环<br>NT 次</span>
+    </div>
+    <p style="margin-top:12px;">注意：驱动力在 <strong>每次积分前</strong> 施加，确保受驱原子的位置正确传递给弹簧力计算。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  3. Driving Force                                             -->
+<!-- ============================================================ -->
+<section id="driver">
+  <h2>三、驱动力模型</h2>
+
+  <div class="card">
+    <h3>3.1 定义文件</h3>
+    <p>驱动力由 <code>input/driver.txt</code> 定义，格式如下：</p>
+    <pre>n amp_x amp_y amp_z freq_x freq_y freq_z phi_x phi_y phi_z period
+1     0     0     5      0      0      1     0     0    90    all</pre>
+  </div>
+
+  <div class="card">
+    <h3>3.2 数学公式</h3>
+    <p>受驱原子的位置由下式决定（<strong>完全替换</strong> coord.txt 中的初始坐标和固定约束）：</p>
+    <div class="formula">
+      <strong>r</strong>(<em>t</em>) = <strong>A</strong> · cos(2π<em>f</em> · <em>t</em> + <strong>φ</strong>)
+    </div>
+    <p>速度由解析导数给出：</p>
+    <div class="formula">
+      <strong>v</strong>(<em>t</em>) = −<strong>A</strong> · 2π<em>f</em> · sin(2π<em>f</em> · <em>t</em> + <strong>φ</strong>)
+    </div>
+    <p>其中 <strong>A</strong> = (amp_x, amp_y, amp_z)，<strong>f</strong> = (freq_x, freq_y, freq_z) 为不同方向的驱动频率，<strong>φ</strong> = (phi_x, phi_y, phi_z) 为相位（<strong>角度制</strong>，代码自动转换为弧度）。</p>
+  </div>
+
+  <div class="card">
+    <h3>3.3 本案例驱动参数</h3>
+    <table>
+      <tr><th>参数</th><th>值</th><th>含义</th></tr>
+      <tr><td>amp_z</td><td>5.0</td><td>z 方向驱动振幅</td></tr>
+      <tr><td>freq_z</td><td>1.0 Hz</td><td>驱动频率（周期 1 s）</td></tr>
+      <tr><td>phi_z</td><td>90°</td><td>驱动相位 → z(0) = 5·cos(90°) = 0</td></tr>
+      <tr><td>period</td><td>all</td><td>全程驱动，永不停止</td></tr>
+    </table>
+    <div class="formula">
+      <em>z</em>(<em>t</em>) = 5.0 · cos(2π · 1.0 · <em>t</em> + 90°)
+    </div>
+  </div>
+
+  <div class="card">
+    <h3>3.4 有限周期驱动</h3>
+    <p><code>period</code> 参数支持三种模式：</p>
+    <ul>
+      <li><strong>all</strong> — 全程驱动</li>
+      <li><strong>数值</strong> — 驱动指定周期数后 <strong>静止</strong>（冻结在最终位置，速度归零）。例如 <code>period: 1</code> 表示驱动 1 个完整周期后停止。</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>3.5 驱动与固定约束的关系</h3>
+    <p>对于受驱原子（<code>driver.txt</code> 中 <code>n</code> 指定的原子），其在 <code>coord.txt</code> 中的初始坐标和 <code>fix_x/fix_y/fix_z</code> 约束被 <strong>完全忽略</strong>。原子的位置和速度完全由驱动力公式决定。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  4. Usage                                                     -->
+<!-- ============================================================ -->
+<section id="usage">
+  <h2>四、使用方法</h2>
+
+  <div class="card">
+    <h3>4.1 完整运行（模拟 + 动画）</h3>
+    <pre>cd examples/case06
+python run_dynamics.py</pre>
+    <p>这步会依次执行：物理模拟 → 抽帧 → 打开 VisPy 3D 动画窗口。</p>
+  </div>
+
+  <div class="card">
+    <h3>4.2 仅查看已有结果</h3>
+    <p>如果已经跑完模拟且生成了 <code>output/display.txt</code>，可以通过修改 <code>input.txt</code> 跳过计算，只开动画：</p>
+    <pre>step_simulate:  0   # 跳过模拟
+step_sample:    0   # 跳过抽帧
+step_animation: 1   # 播放动画</pre>
+    <p>然后运行：<code>python run_dynamics.py</code></p>
+  </div>
+
+  <div class="card">
+    <h3>4.3 手动 3D 动画</h3>
+    <p>也可以单独启动 VisPy 窗口：</p>
+    <pre>python ../../draw.py output/</pre>
+  </div>
+
+  <div class="card">
+    <h3>4.4 强制重新计算</h3>
+    <p>修改参数后需要重新运行模拟时，设置：</p>
+    <pre>force_calc: 1        # 忽略缓存，强制重新计算</pre>
+  </div>
+
+  <div class="card">
+    <h3>4.5 动画交互</h3>
+    <table>
+      <tr><th>操作</th><th>效果</th></tr>
+      <tr><td>鼠标拖动</td><td>旋转视角</td></tr>
+      <tr><td>滚轮</td><td>缩放</td></tr>
+      <tr><td>W / S 键</td><td>相机沿 Z 轴向前 / 向后移动（靠近/远离场景）</td></tr>
+      <tr><td>A / D 键</td><td>视角向右 / 向左平移</td></tr>
+      <tr><td>E / Q 键</td><td>视角上升 / 下降（屏幕方向）</td></tr>
+      <tr><td>C / X 键</td><td>增大 / 减小步长</td></tr>
+      <tr><td>V 键</td><td>切换透视 / 正交投影</td></tr>
+      <tr><td>左上角 <strong>reset</strong> 按钮</td><td>复位视角到初始位置</td></tr>
+      <tr><td>左上角 <strong>info</strong> 按钮</td><td>切换信息面板显示/隐藏</td></tr>
+      <tr><td>左上角 <strong>axes</strong> 按钮</td><td>切换坐标轴显示/隐藏</td></tr>
+    </table>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  5. Parameters                                                -->
+<!-- ============================================================ -->
+<section id="params">
+  <h2>五、参数参考</h2>
+
+  <div class="card">
+    <h3>5.1 input.txt 关键参数</h3>
+    <table>
+      <tr><th>参数</th><th>默认值</th><th>说明</th></tr>
+      <tr><td>gravity_field</td><td>0</td><td>均匀重力场（已关闭）</td></tr>
+      <tr><td>gravity_interaction</td><td>0</td><td>原子间万有引力（已关闭）</td></tr>
+      <tr><td>elastic_force</td><td>1</td><td>弹簧键力（已开启）</td></tr>
+      <tr><td>damping_force</td><td>0</td><td>阻尼（已关闭）</td></tr>
+      <tr><td><strong>driving_force</strong></td><td><strong>1</strong></td><td>驱动力开关（1=开启，需 driver.txt）</td></tr>
+      <tr><td>method</td><td>leapfrog</td><td>数值积分方法</td></tr>
+      <tr><td>DT</td><td>0.01</td><td>积分步长 (s)</td></tr>
+      <tr><td>T_total</td><td>100.0</td><td>总模拟时间 (s)</td></tr>
+      <tr><td>NSTEP</td><td>50</td><td>抽帧步数间隔</td></tr>
+      <tr><td>engine</td><td>python</td><td>计算引擎（python / c / cpp / fortran）</td></tr>
+      <tr><td>use_marker</td><td>1</td><td>渲染模式（0=Sphere 网格, 1=Marker GPU 实例化）</td></tr>
+    </table>
+  </div>
+
+  <div class="card">
+    <h3>5.2 流程控制参数</h3>
+    <table>
+      <tr><th>参数</th><th>0</th><th>1</th></tr>
+      <tr><td>step_simulate</td><td>跳过模拟（加载已有轨迹）</td><td>运行物理模拟</td></tr>
+      <tr><td>step_sample</td><td>跳过抽帧</td><td>从轨迹抽取显示帧</td></tr>
+      <tr><td>step_plot</td><td>不生成图表</td><td>生成轨迹/能量图</td></tr>
+      <tr><td><strong>step_plot_wave</strong></td><td>不生成波形图</td><td>生成波形能量动画 GIF</td></tr>
+      <tr><td>step_animation</td><td>不启动动画</td><td>自动打开 VisPy 3D 窗口</td></tr>
+      <tr><td>force_calc</td><td>自动检测缓存</td><td>强制重新计算</td></tr>
+    </table>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  6. File Structure                                            -->
+<!-- ============================================================ -->
+<section id="files">
+  <h2>六、文件结构</h2>
+
+  <pre>case06/
+├── input/
+│   ├── input.txt          # 主配置文件（YAML 格式）
+│   ├── coord.txt          # 原子坐标（120 个原子）
+│   ├── connection.txt     # 弹簧连接关系（59 条键）
+│   ├── bond.txt           # 弹簧参数（k=1.0, L₀=1.0）
+│   └── <strong>driver.txt</strong>       # <span class="cm">驱动力定义（本案例新增）</span>
+├── output/
+│   ├── trajectory.txt     # 全量轨迹数据（50000 步 × 120 原子）
+│   ├── display.txt        # 抽帧后的动画数据（500 帧 × 120 原子）
+│   ├── dynamics.log       # 计算日志
+│   ├── animation.log      # 动画启动日志（闪退时排查用）
+│   └── wave_animation.gif # 波形能量动画（step_plot_wave=1 时生成）
+├── doc/
+│   └── index.html         # <span class="cm">本文档</span>
+├── Readme.md              # 案例简介
+└── run_dynamics.py        # 案例运行入口</pre>
+</section>
+
+<!-- ============================================================ -->
+<!--  7. Troubleshooting                                           -->
+<!-- ============================================================ -->
+<section id="troubleshoot">
+  <h2>七、常见问题</h2>
+
+  <div class="card">
+    <h3>7.1 动画窗口闪退</h3>
+    <p>如果 VisPy 窗口一闪就消失，请检查：</p>
+    <ul>
+      <li><code>output/animation.log</code> 中是否有错误信息</li>
+      <li><code>output/display.txt</code> 是否存在（需先跑 <code>step_sample: 1</code>）</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>7.2 原子不振动</h3>
+    <p>可能原因：</p>
+    <ul>
+      <li><strong>NSTEP 过大</strong>：抽帧间隔大于驱动周期的一半时，动画会丢失振动细节。建议 NSTEP ≤ 1/(freq · DT · 10)</li>
+      <li><strong>相位 φ 使采样点落在零值</strong>：试试 <code>phi_z: 0</code> 让原子在 t=0 处于振幅峰值</li>
+      <li>确认 <code>driving_force: 1</code> 且 <code>driver.txt</code> 中 amp_z 不为 0</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>7.3 渲染性能慢</h3>
+    <p>原子数多时动画卡顿：</p>
+    <ul>
+      <li>设置 <code>use_marker: 1</code>（使用 GPU 实例化渲染替代独立网格球体）</li>
+      <li>增大 <code>NSTEP</code> 减少动画帧数</li>
+    </ul>
+  </div>
+</section>
+
+<hr style="border:none;border-top:1px solid var(--border);margin:40px 0;">
+
+<footer style="text-align:center;color:var(--muted);font-size:0.85rem;margin-bottom:40px;">
+  Dynamics Simulation Framework &nbsp;·&nbsp; 生成于 2026-06-10
+</footer>
+
+</div>
+</body>
+</html>

examples/case11/input/bond.txt

@@ -0,0 +1,2 @@
+bond_name k rest_length
+h 100.0 1.0

examples/case11/input/driver.txt

@@ -0,0 +1,2 @@
+n amp_x amp_y amp_z freq_x freq_y freq_z phi_x phi_y phi_z period
+5101 0 0 2.0 0 0 0.05 90 90 90 all

examples/case11/input/input.txt

@@ -0,0 +1,89 @@
+# 物理模拟参数配置
+# 格式：YAML
+# 用法：python run_dynamics.py     
+
+# ── 流程控制 ──────────────────────────────────
+step_simulate:  1   # 运行物理模拟
+step_sample:    0   # 重新抽帧，默认0=不执行
+step_plot:      0   # 绘制轨迹/能量图
+step_animation: 1   # 自动播放 VisPy 3D 动画窗口
+step_plot_wave: 0   # 绘制波形能量动画
+force_calc: 1       # 强制重新计算
+
+# ── 文件保存 ──────────────────────────────────
+save_trajectory: 0  # 0=不保留完整轨迹文件
+
+# ── 计算引擎 ──────────────────────────────────
+engine: c
+
+# ── 盒子 ──────────────────────────────────────
+box_a: 120.0
+
+# ── 初始构型 ──────────────────────────────────
+coord_file: input/coord.txt
+connection_file: input/connection.txt
+bond_file: input/bond.txt
+driver_file: input/driver.txt
+
+# 绘图/动画展示的原子序号
+plot_atom: 5101    # 中心原子 (0,0)
+
+# ── 物理参数 ──────────────────────────────────
+G: [0.000, 0.000, 0.000]
+B: [0.000, 0.000, 0.000]
+
+# ── 力开关 ────────────────────────────────────
+gravity_field: 0
+gravity_interaction: 0
+elastic_force: 1
+damping_force: 0
+driving_force: 1
+gravity_strength: 1.0
+
+# ── 数值算法 ──────────────────────────────────
+method: leapfrog
+
+# ── 步骤控制 ──────────────────────────────────
+warmup_steps: 0       # 受迫波动，无需预热
+T_total:  100.0
+NSTEP: 10
+DT:    0.01
+
+sample_start: null
+sample_end: null
+
+# ── 渲染方式 ──────────────────────────────────
+use_marker: 1
+
+# ── 位移着色 ──────────────────────────────────
+display_color: {
+    x   : [0, [255,   0,   0]],
+    y   : [0, [  0, 255,   0]],
+    z   : [1, [  0,   0, 255]],
+    xy  : [0, [255, 255,   0]],
+    yz  : [0, [  0, 255, 255]],
+    zx  : [0, [255,   0, 255]],
+    xyz : [0, [  0,   0,   0]],
+    }   
+
+# ── 显示参数 ──────────────────────────────────
+alpha: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+
+ball_color_r: 0.20
+ball_color_g: 0.60
+ball_color_b: 0.90
+
+box_color_r:  0.80
+box_color_g:  0.80
+box_color_b:  0.85
+
+# ── 摄像机 ────────────────────────────────────
+camera_distance:    120.0
+camera_elevation:   60.0
+camera_azimuth:     -45.0
+camera_center_x:    0.0
+camera_center_y:    0.0
+camera_center_z:    0.0
+move_camera:         0
+
+display_amp: [1.0, 1.0, 1.0]

examples/case11/input/move_camera.txt

@@ -0,0 +1,2 @@
+0 0 50
+0 0 80

examples/case11/run_dynamics.py

@@ -0,0 +1,54 @@
+"""
+Case runner for Dynamics case11 — 2D grid (61x61 atomic mesh).
+
+This script keeps program and data separated:
+  - program: ../../dynamics.py
+  - input:   ./input
+  - output:  ./output
+"""
+
+from __future__ import annotations
+
+import argparse
+import importlib.util
+from pathlib import Path
+
+
+CASE_DIR = Path(__file__).resolve().parent
+DYNAMICS_PATH = Path("..") / ".." / "dynamics.py"
+INPUT_DIR = Path("input")
+OUTPUT_DIR = Path("output")
+CONFIG_FILE = INPUT_DIR / "input.txt"
+
+
+def load_dynamics_module(module_path: Path):
+    spec = importlib.util.spec_from_file_location("dynamics_module", module_path)
+    if spec is None or spec.loader is None:
+        raise ImportError(f"无法加载 dynamics.py: {module_path}")
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def main():
+    parser = argparse.ArgumentParser(description="运行 Dynamics 示例案例 case11")
+    parser.add_argument("--no-plot", action="store_true", help="跳过 matplotlib 绘图")
+    args = parser.parse_args()
+
+    dynamics_path = (CASE_DIR / DYNAMICS_PATH).resolve()
+    input_dir = (CASE_DIR / INPUT_DIR).resolve()
+    output_dir = (CASE_DIR / OUTPUT_DIR).resolve()
+    config_path = (CASE_DIR / CONFIG_FILE).resolve()
+
+    module = load_dynamics_module(dynamics_path)
+    module.run_case(
+        config_path=config_path,
+        runtime_base=CASE_DIR,
+        input_dir=input_dir,
+        output_dir=output_dir,
+        no_plot=args.no_plot,
+    )
+
+
+if __name__ == "__main__":
+    main()

examples/case12/Readme.md

@@ -0,0 +1,40 @@
+# case06: 一维原子链横波模拟
+
+60 个原子沿 x 轴排列，相邻原子用弹簧连接。原子 1 受 z 方向驱动力作用，产生沿链传播的横波。
+
+## 物理设定
+
+| 参数 | 值 |
+|---|---|
+| 原子数 | 120 |
+| 排列 | 沿 x 轴等间距排列，间距为 1 |
+| 约束 | 原子**沿 z 方向自由振动**（fix_x=1, fix_y=1, fix_z=0），x, y 锁定 |
+| 弹簧 | 劲度系数 k=1.0，原长 L₀=1.0 |
+| 重力 | 无 |
+| 万有引力 | 无 |
+| 阻尼 | 无 |
+| 驱动力 | 原子 1（z 方向驱动） |
+| 算法 | leapfrog（蛙跳法，能量守恒） |
+
+## 驱动力
+
+原子 1 的位置由 `input/driver.txt` 中的驱动力公式决定：
+
+```math
+z(t) = A_z \cdot \cos(2\pi f_z t + \phi_z)
+```
+
+当前参数：A_z = 0.5, f_z = 0.1 Hz, φ_z = 90°, period = all（全程驱动）。
+
+## 动力学行为
+
+原子 1 沿 z 方向的受迫振动通过弹簧逐次传递给相邻原子，形成沿链传播的**横波**。由于 z 方向的振动是横向的，弹簧大部分张力在 x 方向，z 方向的有效刚度是非线性的——等效于一个三次方恢复力（FPU 型非线性），因此波速较慢。
+
+## 使用方法
+
+```bash
+cd examples/case06
+python run_dynamics.py
+```
+
+配置参数详见 `input/input.txt`，驱动力定义见 `input/driver.txt`，完整文档见 `doc/index.html`。

examples/case12/doc/index.html

@@ -0,0 +1,477 @@
+<!DOCTYPE html>
+<html lang="zh-CN">
+<head>
+<meta charset="UTF-8">
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<title>case06 — 一维原子链驱动力学模拟 | 物理原理 &amp; 使用文档</title>
+<style>
+  :root {
+    --bg: #f8f9fa;
+    --card: #fff;
+    --text: #1a1a2e;
+    --accent: #2563eb;
+    --accent-light: #dbeafe;
+    --code-bg: #1e293b;
+    --code-text: #e2e8f0;
+    --border: #e2e8f0;
+    --muted: #64748b;
+  }
+  * { margin: 0; padding: 0; box-sizing: border-box; }
+  body {
+    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Noto Sans SC", sans-serif;
+    background: var(--bg);
+    color: var(--text);
+    line-height: 1.7;
+  }
+
+  /* ── Header ── */
+  .hero {
+    background: linear-gradient(135deg, #1e293b 0%, #334155 100%);
+    color: #fff;
+    padding: 56px 24px 48px;
+    text-align: center;
+  }
+  .hero h1 { font-size: 2rem; font-weight: 700; letter-spacing: -0.02em; }
+  .hero .subtitle {
+    margin-top: 10px;
+    font-size: 1.05rem;
+    opacity: 0.8;
+  }
+  .hero .badge {
+    display: inline-block;
+    margin-top: 14px;
+    padding: 4px 14px;
+    border-radius: 999px;
+    background: rgba(255,255,255,0.12);
+    font-size: 0.82rem;
+  }
+
+  /* ── Layout ── */
+  .container { max-width: 820px; margin: 0 auto; padding: 32px 20px; }
+
+  section { margin-bottom: 44px; }
+  h2 {
+    font-size: 1.35rem;
+    font-weight: 600;
+    margin-bottom: 16px;
+    padding-bottom: 8px;
+    border-bottom: 2px solid var(--accent);
+    display: inline-block;
+  }
+  h3 {
+    font-size: 1.05rem;
+    font-weight: 600;
+    margin: 20px 0 10px;
+  }
+
+  p, li { margin-bottom: 10px; }
+  ul, ol { padding-left: 22px; }
+  strong { color: var(--accent); }
+
+  /* ── Cards ── */
+  .card {
+    background: var(--card);
+    border-radius: 12px;
+    padding: 20px 24px;
+    margin-bottom: 16px;
+    border: 1px solid var(--border);
+    box-shadow: 0 1px 3px rgba(0,0,0,0.04);
+  }
+
+  /* ── Formula / Code blocks ── */
+  .formula {
+    background: var(--card);
+    border-left: 4px solid var(--accent);
+    padding: 14px 20px;
+    margin: 14px 0;
+    font-family: "Times New Roman", "STIX", serif;
+    font-size: 1.05rem;
+    overflow-x: auto;
+    border-radius: 0 8px 8px 0;
+  }
+  code {
+    background: var(--accent-light);
+    padding: 2px 7px;
+    border-radius: 4px;
+    font-family: "JetBrains Mono", "Fira Code", monospace;
+    font-size: 0.88em;
+  }
+  pre {
+    background: var(--code-bg);
+    color: var(--code-text);
+    padding: 16px 20px;
+    border-radius: 10px;
+    overflow-x: auto;
+    font-size: 0.85rem;
+    line-height: 1.5;
+    margin: 14px 0;
+  }
+  pre .cm { color: #94a3b8; font-style: italic; }   /* comment */
+
+  /* ── Table ── */
+  table {
+    width: 100%;
+    border-collapse: collapse;
+    margin: 14px 0;
+    font-size: 0.92rem;
+  }
+  th, td {
+    padding: 8px 12px;
+    text-align: left;
+    border-bottom: 1px solid var(--border);
+  }
+  th { background: var(--accent-light); font-weight: 600; }
+
+  /* ── TOC ── */
+  .toc { counter-reset: toc; }
+  .toc li { counter-increment: toc; list-style: none; margin-bottom: 6px; }
+  .toc li::before { content: counter(toc) ". "; font-weight: 600; color: var(--accent); }
+  .toc a { color: var(--accent); text-decoration: none; }
+  .toc a:hover { text-decoration: underline; }
+
+  /* ── Flow diagram ── */
+  .flow { display: flex; flex-wrap: wrap; gap: 8px; align-items: center; justify-content: center; margin: 16px 0; }
+  .flow-step {
+    background: var(--accent-light);
+    border: 1px solid var(--accent);
+    border-radius: 8px;
+    padding: 8px 16px;
+    font-size: 0.88rem;
+    font-weight: 500;
+  }
+  .flow-arrow { color: var(--muted); font-size: 1.2rem; }
+
+  @media (max-width: 600px) {
+    .hero h1 { font-size: 1.5rem; }
+    .flow { flex-direction: column; }
+    .flow-arrow { transform: rotate(90deg); }
+  }
+</style>
+</head>
+<body>
+
+<!-- ============================================================ -->
+<!--  Header                                                       -->
+<!-- ============================================================ -->
+<header class="hero">
+  <h1>一维原子链驱动力学模拟</h1>
+  <p class="subtitle">120 个原子沿 x 轴排列 · 弹簧连接 · z 方向受迫振动</p>
+  <span class="badge">case06  ·  examples/case06</span>
+</header>
+
+<div class="container">
+
+<!-- ============================================================ -->
+<!--  TOC                                                          -->
+<!-- ============================================================ -->
+<section>
+  <h2>目录</h2>
+  <ol class="toc">
+    <li><a href="#physics">物理原理</a></li>
+    <li><a href="#algorithm">数值算法</a></li>
+    <li><a href="#driver">驱动力模型</a></li>
+    <li><a href="#usage">使用方法</a></li>
+    <li><a href="#params">参数参考</a></li>
+    <li><a href="#files">文件结构</a></li>
+    <li><a href="#troubleshoot">常见问题</a></li>
+  </ol>
+</section>
+
+<!-- ============================================================ -->
+<!--  1. Physics                                                   -->
+<!-- ============================================================ -->
+<section id="physics">
+  <h2>一、物理原理</h2>
+
+  <div class="card">
+    <h3>1.1 一维原子链</h3>
+    <p>120 个原子沿 <strong>x 轴</strong> 等间距排列，原子间距为 1。相邻原子之间用 <strong>理想弹簧</strong> 连接，弹簧的劲度系数 <em>k</em> = 1.0，原长 <em>L</em>₀ = 1.0（与原子间距一致，初始状态弹簧无拉伸）。</p>
+    <p>每个原子被限制在 <strong>z 方向</strong> 自由振动，x 和 y 方向锁定（<code>fix_x=1, fix_y=1, fix_z=0</code>）。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.2 弹簧力（胡克定律）</h3>
+    <p>当原子 <em>i</em> 和 <em>j</em> 之间有弹簧连接时，原子 <em>i</em> 受到的弹簧力为：</p>
+    <div class="formula">
+      <strong>F</strong> = −<em>k</em> · (<em>d</em> − <em>L</em>₀) · <strong>u</strong><sub><em>ij</em></sub>
+    </div>
+    <p>其中 <em>d</em> = |<strong>r</strong><sub><em>j</em></sub> − <strong>r</strong><sub><em>i</em></sub>| 为两原子间距离，<strong>u</strong><sub><em>ij</em></sub> 为从 <em>i</em> 指向 <em>j</em> 的单位向量。由于原子只在 z 方向振动，弹簧在 z 方向的分量是 <strong>几何非线性</strong> 的——对于小振幅近似，z 方向等效于一个三次方恢复力（FPU 型非线性）。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.3 运动方程</h3>
+    <p>对于第 <em>i</em> 个自由原子（非受驱），牛顿第二定律给出：</p>
+    <div class="formula">
+      <em>m</em> · <strong>a</strong><sub><em>i</em></sub> = <strong>F</strong><sub><em>i</em></sub><sup>spring</sup> + <strong>F</strong><sub><em>i</em></sub><sup>driving</sup>
+    </div>
+    <p>本案例中 <strong>唯一的外力</strong> 来自驱动力（仅施加于原子 1）。无重力、无万有引力、无阻尼，系统总能量守恒。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.4 波传播</h3>
+    <p>原子 1 的受迫振动通过弹簧逐次传递给相邻原子，形成沿链传播的 <strong>横波</strong>。由于横向振动的几何非线性（弹簧大部分张力在 x 方向，z 方向的有效刚度远小于 1），波的传播速度较慢，且高阶频率成分会在链中产生复杂的非线性动力学行为（类似 FPU 回波现象）。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  2. Algorithm                                                 -->
+<!-- ============================================================ -->
+<section id="algorithm">
+  <h2>二、数值算法</h2>
+
+  <div class="card">
+    <h3>2.1 蛙跳法（Leapfrog / Velocity-Verlet）</h3>
+    <p>采用能量守恒特性优异的 <strong>蛙跳法</strong>（二阶辛积分器），更新公式为：</p>
+    <div class="formula">
+      <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) = <strong>v</strong>(<em>t</em>) + ½ <strong>a</strong>(<em>t</em>) · Δ<em>t</em><br>
+      <strong>r</strong>(<em>t</em> + Δ<em>t</em>) = <strong>r</strong>(<em>t</em>) + <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) · Δ<em>t</em><br>
+      <strong>a</strong>(<em>t</em> + Δ<em>t</em>) = <strong>F</strong>(<strong>r</strong>(<em>t</em> + Δ<em>t</em>), <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>)) / <em>m</em><br>
+      <strong>v</strong>(<em>t</em> + Δ<em>t</em>) = <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) + ½ <strong>a</strong>(<em>t</em> + Δ<em>t</em>) · Δ<em>t</em>
+    </div>
+    <p>蛙跳法在长时间模拟中能量漂移极小（本案例验证 <strong>&lt; 0.004%</strong>），适合无阻尼的保守系统。</p>
+  </div>
+
+  <div class="card">
+    <h3>2.2 时间步长与采样</h3>
+    <table>
+      <tr><th>参数</th><th>值</th><th>说明</th></tr>
+      <tr><td>DT</td><td>0.01 s</td><td>积分步长（远小于 1/ω ≈ 0.16 s，满足稳定性条件）</td></tr>
+      <tr><td>T_total</td><td>100 s</td><td>总模拟时间 → NT = 10000 步</td></tr>
+      <tr><td>NSTEP</td><td>50</td><td>每 NSTEP 步取一帧用于动画 → 200 帧</td></tr>
+      <tr><td>method</td><td>leapfrog</td><td>蛙跳法（Velocity-Verlet）</td></tr>
+    </table>
+  </div>
+
+  <div class="card">
+    <h3>2.3 计算流程</h3>
+    <div class="flow">
+      <span class="flow-step">读入 coord.txt<br>connection.txt<br>bond.txt</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">施加驱动力<br>（驱动原子 1）</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">记录轨迹</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">蛙跳法<br>更新位置/速度</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">固定约束<br>（x, y 锁定）</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step" style="background:#fef3c7;border-color:#f59e0b;">循环<br>NT 次</span>
+    </div>
+    <p style="margin-top:12px;">注意：驱动力在 <strong>每次积分前</strong> 施加，确保受驱原子的位置正确传递给弹簧力计算。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  3. Driving Force                                             -->
+<!-- ============================================================ -->
+<section id="driver">
+  <h2>三、驱动力模型</h2>
+
+  <div class="card">
+    <h3>3.1 定义文件</h3>
+    <p>驱动力由 <code>input/driver.txt</code> 定义，格式如下：</p>
+    <pre>n amp_x amp_y amp_z freq_x freq_y freq_z phi_x phi_y phi_z period
+1     0     0     5      0      0      1     0     0    90    all</pre>
+  </div>
+
+  <div class="card">
+    <h3>3.2 数学公式</h3>
+    <p>受驱原子的位置由下式决定（<strong>完全替换</strong> coord.txt 中的初始坐标和固定约束）：</p>
+    <div class="formula">
+      <strong>r</strong>(<em>t</em>) = <strong>A</strong> · cos(2π<em>f</em> · <em>t</em> + <strong>φ</strong>)
+    </div>
+    <p>速度由解析导数给出：</p>
+    <div class="formula">
+      <strong>v</strong>(<em>t</em>) = −<strong>A</strong> · 2π<em>f</em> · sin(2π<em>f</em> · <em>t</em> + <strong>φ</strong>)
+    </div>
+    <p>其中 <strong>A</strong> = (amp_x, amp_y, amp_z)，<strong>f</strong> = (freq_x, freq_y, freq_z) 为不同方向的驱动频率，<strong>φ</strong> = (phi_x, phi_y, phi_z) 为相位（<strong>角度制</strong>，代码自动转换为弧度）。</p>
+  </div>
+
+  <div class="card">
+    <h3>3.3 本案例驱动参数</h3>
+    <table>
+      <tr><th>参数</th><th>值</th><th>含义</th></tr>
+      <tr><td>amp_z</td><td>5.0</td><td>z 方向驱动振幅</td></tr>
+      <tr><td>freq_z</td><td>1.0 Hz</td><td>驱动频率（周期 1 s）</td></tr>
+      <tr><td>phi_z</td><td>90°</td><td>驱动相位 → z(0) = 5·cos(90°) = 0</td></tr>
+      <tr><td>period</td><td>all</td><td>全程驱动，永不停止</td></tr>
+    </table>
+    <div class="formula">
+      <em>z</em>(<em>t</em>) = 5.0 · cos(2π · 1.0 · <em>t</em> + 90°)
+    </div>
+  </div>
+
+  <div class="card">
+    <h3>3.4 有限周期驱动</h3>
+    <p><code>period</code> 参数支持三种模式：</p>
+    <ul>
+      <li><strong>all</strong> — 全程驱动</li>
+      <li><strong>数值</strong> — 驱动指定周期数后 <strong>静止</strong>（冻结在最终位置，速度归零）。例如 <code>period: 1</code> 表示驱动 1 个完整周期后停止。</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>3.5 驱动与固定约束的关系</h3>
+    <p>对于受驱原子（<code>driver.txt</code> 中 <code>n</code> 指定的原子），其在 <code>coord.txt</code> 中的初始坐标和 <code>fix_x/fix_y/fix_z</code> 约束被 <strong>完全忽略</strong>。原子的位置和速度完全由驱动力公式决定。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  4. Usage                                                     -->
+<!-- ============================================================ -->
+<section id="usage">
+  <h2>四、使用方法</h2>
+
+  <div class="card">
+    <h3>4.1 完整运行（模拟 + 动画）</h3>
+    <pre>cd examples/case06
+python run_dynamics.py</pre>
+    <p>这步会依次执行：物理模拟 → 抽帧 → 打开 VisPy 3D 动画窗口。</p>
+  </div>
+
+  <div class="card">
+    <h3>4.2 仅查看已有结果</h3>
+    <p>如果已经跑完模拟且生成了 <code>output/display.txt</code>，可以通过修改 <code>input.txt</code> 跳过计算，只开动画：</p>
+    <pre>step_simulate:  0   # 跳过模拟
+step_sample:    0   # 跳过抽帧
+step_animation: 1   # 播放动画</pre>
+    <p>然后运行：<code>python run_dynamics.py</code></p>
+  </div>
+
+  <div class="card">
+    <h3>4.3 手动 3D 动画</h3>
+    <p>也可以单独启动 VisPy 窗口：</p>
+    <pre>python ../../draw.py output/</pre>
+  </div>
+
+  <div class="card">
+    <h3>4.4 强制重新计算</h3>
+    <p>修改参数后需要重新运行模拟时，设置：</p>
+    <pre>force_calc: 1        # 忽略缓存，强制重新计算</pre>
+  </div>
+
+  <div class="card">
+    <h3>4.5 动画交互</h3>
+    <table>
+      <tr><th>操作</th><th>效果</th></tr>
+      <tr><td>鼠标拖动</td><td>旋转视角</td></tr>
+      <tr><td>滚轮</td><td>缩放</td></tr>
+      <tr><td>W / S 键</td><td>相机沿 Z 轴向前 / 向后移动（靠近/远离场景）</td></tr>
+      <tr><td>A / D 键</td><td>视角向右 / 向左平移</td></tr>
+      <tr><td>E / Q 键</td><td>视角上升 / 下降（屏幕方向）</td></tr>
+      <tr><td>C / X 键</td><td>增大 / 减小步长</td></tr>
+      <tr><td>V 键</td><td>切换透视 / 正交投影</td></tr>
+      <tr><td>左上角 <strong>reset</strong> 按钮</td><td>复位视角到初始位置</td></tr>
+      <tr><td>左上角 <strong>info</strong> 按钮</td><td>切换信息面板显示/隐藏</td></tr>
+      <tr><td>左上角 <strong>axes</strong> 按钮</td><td>切换坐标轴显示/隐藏</td></tr>
+    </table>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  5. Parameters                                                -->
+<!-- ============================================================ -->
+<section id="params">
+  <h2>五、参数参考</h2>
+
+  <div class="card">
+    <h3>5.1 input.txt 关键参数</h3>
+    <table>
+      <tr><th>参数</th><th>默认值</th><th>说明</th></tr>
+      <tr><td>gravity_field</td><td>0</td><td>均匀重力场（已关闭）</td></tr>
+      <tr><td>gravity_interaction</td><td>0</td><td>原子间万有引力（已关闭）</td></tr>
+      <tr><td>elastic_force</td><td>1</td><td>弹簧键力（已开启）</td></tr>
+      <tr><td>damping_force</td><td>0</td><td>阻尼（已关闭）</td></tr>
+      <tr><td><strong>driving_force</strong></td><td><strong>1</strong></td><td>驱动力开关（1=开启，需 driver.txt）</td></tr>
+      <tr><td>method</td><td>leapfrog</td><td>数值积分方法</td></tr>
+      <tr><td>DT</td><td>0.01</td><td>积分步长 (s)</td></tr>
+      <tr><td>T_total</td><td>100.0</td><td>总模拟时间 (s)</td></tr>
+      <tr><td>NSTEP</td><td>50</td><td>抽帧步数间隔</td></tr>
+      <tr><td>engine</td><td>python</td><td>计算引擎（python / c / cpp / fortran）</td></tr>
+      <tr><td>use_marker</td><td>1</td><td>渲染模式（0=Sphere 网格, 1=Marker GPU 实例化）</td></tr>
+    </table>
+  </div>
+
+  <div class="card">
+    <h3>5.2 流程控制参数</h3>
+    <table>
+      <tr><th>参数</th><th>0</th><th>1</th></tr>
+      <tr><td>step_simulate</td><td>跳过模拟（加载已有轨迹）</td><td>运行物理模拟</td></tr>
+      <tr><td>step_sample</td><td>跳过抽帧</td><td>从轨迹抽取显示帧</td></tr>
+      <tr><td>step_plot</td><td>不生成图表</td><td>生成轨迹/能量图</td></tr>
+      <tr><td><strong>step_plot_wave</strong></td><td>不生成波形图</td><td>生成波形能量动画 GIF</td></tr>
+      <tr><td>step_animation</td><td>不启动动画</td><td>自动打开 VisPy 3D 窗口</td></tr>
+      <tr><td>force_calc</td><td>自动检测缓存</td><td>强制重新计算</td></tr>
+    </table>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  6. File Structure                                            -->
+<!-- ============================================================ -->
+<section id="files">
+  <h2>六、文件结构</h2>
+
+  <pre>case06/
+├── input/
+│   ├── input.txt          # 主配置文件（YAML 格式）
+│   ├── coord.txt          # 原子坐标（120 个原子）
+│   ├── connection.txt     # 弹簧连接关系（59 条键）
+│   ├── bond.txt           # 弹簧参数（k=1.0, L₀=1.0）
+│   └── <strong>driver.txt</strong>       # <span class="cm">驱动力定义（本案例新增）</span>
+├── output/
+│   ├── trajectory.txt     # 全量轨迹数据（50000 步 × 120 原子）
+│   ├── display.txt        # 抽帧后的动画数据（500 帧 × 120 原子）
+│   ├── dynamics.log       # 计算日志
+│   ├── animation.log      # 动画启动日志（闪退时排查用）
+│   └── wave_animation.gif # 波形能量动画（step_plot_wave=1 时生成）
+├── doc/
+│   └── index.html         # <span class="cm">本文档</span>
+├── Readme.md              # 案例简介
+└── run_dynamics.py        # 案例运行入口</pre>
+</section>
+
+<!-- ============================================================ -->
+<!--  7. Troubleshooting                                           -->
+<!-- ============================================================ -->
+<section id="troubleshoot">
+  <h2>七、常见问题</h2>
+
+  <div class="card">
+    <h3>7.1 动画窗口闪退</h3>
+    <p>如果 VisPy 窗口一闪就消失，请检查：</p>
+    <ul>
+      <li><code>output/animation.log</code> 中是否有错误信息</li>
+      <li><code>output/display.txt</code> 是否存在（需先跑 <code>step_sample: 1</code>）</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>7.2 原子不振动</h3>
+    <p>可能原因：</p>
+    <ul>
+      <li><strong>NSTEP 过大</strong>：抽帧间隔大于驱动周期的一半时，动画会丢失振动细节。建议 NSTEP ≤ 1/(freq · DT · 10)</li>
+      <li><strong>相位 φ 使采样点落在零值</strong>：试试 <code>phi_z: 0</code> 让原子在 t=0 处于振幅峰值</li>
+      <li>确认 <code>driving_force: 1</code> 且 <code>driver.txt</code> 中 amp_z 不为 0</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>7.3 渲染性能慢</h3>
+    <p>原子数多时动画卡顿：</p>
+    <ul>
+      <li>设置 <code>use_marker: 1</code>（使用 GPU 实例化渲染替代独立网格球体）</li>
+      <li>增大 <code>NSTEP</code> 减少动画帧数</li>
+    </ul>
+  </div>
+</section>
+
+<hr style="border:none;border-top:1px solid var(--border);margin:40px 0;">
+
+<footer style="text-align:center;color:var(--muted);font-size:0.85rem;margin-bottom:40px;">
+  Dynamics Simulation Framework &nbsp;·&nbsp; 生成于 2026-06-10
+</footer>
+
+</div>
+</body>
+</html>

examples/case12/input/bond.txt

@@ -0,0 +1,2 @@
+bond_name k rest_length
+h 100.0 1.0

examples/case12/input/driver.txt

@@ -0,0 +1,3 @@
+n amp_x amp_y amp_z freq_x freq_y freq_z phi_x phi_y phi_z period
+3081 0 0 2.0 0 0 0.05 90 90 90 all
+7121 0 0 2.0 0 0 0.05 90 90 90 all

examples/case12/input/input.txt

@@ -0,0 +1,83 @@
+# 物理模拟参数配置
+# case12 — 二维网格两点干涉（双点源 z 方向驱动）
+# 驱动点: (0,-10) 和 (0,10)，波从两点向外传播，在中心区域干涉
+
+# ── 流程控制 ──────────────────────────────────
+step_simulate:  1   # 运行物理模拟
+step_sample:    0   # 重新抽帧，默认0=不执行
+step_plot:      0   # 绘制轨迹/能量图
+step_animation: 1   # 自动播放 VisPy 3D 动画窗口
+step_plot_wave: 0   # 绘制波形能量动画
+force_calc: 1       # 强制重新计算
+
+# ── 文件保存 ──────────────────────────────────
+save_trajectory: 0
+
+# ── 计算引擎 ──────────────────────────────────
+engine: c
+
+# ── 盒子 ──────────────────────────────────────
+box_a: 120.0
+
+# ── 初始构型 ──────────────────────────────────
+coord_file: input/coord.txt
+connection_file: input/connection.txt
+bond_file: input/bond.txt
+driver_file: input/driver.txt
+plot_atom: 5101    # 中心区域用于信息显示
+
+# ── 物理参数 ──────────────────────────────────
+G: [0.000, 0.000, 0.000]
+B: [0.000, 0.000, 0.000]
+
+gravity_field: 0
+gravity_interaction: 0
+elastic_force: 1
+damping_force: 0
+driving_force: 1
+gravity_strength: 1.0
+
+method: leapfrog
+
+# ── 步骤控制 ──────────────────────────────────
+warmup_steps: 0
+T_total:  100.0
+NSTEP: 500
+DT:    0.001
+
+sample_start: null
+sample_end: null
+
+# ── 渲染/着色 ─────────────────────────────────
+use_marker: 1
+display_color: {
+    x   : [0, [255,   0,   0]],
+    y   : [0, [  0, 255,   0]],
+    z   : [0, [  0,   0, 255]],
+    xy  : [0, [255, 255,   0]],
+    yz  : [0, [  0, 255, 255]],
+    zx  : [0, [255,   0, 255]],
+    xyz : [1, [255, 255, 255]],
+    }
+
+# ── 显示参数 ──────────────────────────────────
+alpha: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
+
+ball_color_r: 0.20
+ball_color_g: 0.60
+ball_color_b: 0.90
+
+box_color_r:  0.80
+box_color_g:  0.80
+box_color_b:  0.85
+
+# ── 摄像机 ────────────────────────────────────
+camera_distance:    120.0
+camera_elevation:   60.0
+camera_azimuth:     -45.0
+camera_center_x:    0.0
+camera_center_y:    0.0
+camera_center_z:    0.0
+move_camera:         0
+
+display_amp: [1.0, 1.0, 1.0]

examples/case12/input/move_camera.txt

@@ -0,0 +1,2 @@
+0 0 50
+0 0 80

examples/case12/run_dynamics.py

@@ -0,0 +1,54 @@
+"""
+Case runner for Dynamics case12 — 2D grid dual source interference.
+
+This script keeps program and data separated:
+  - program: ../../dynamics.py
+  - input:   ./input
+  - output:  ./output
+"""
+
+from __future__ import annotations
+
+import argparse
+import importlib.util
+from pathlib import Path
+
+
+CASE_DIR = Path(__file__).resolve().parent
+DYNAMICS_PATH = Path("..") / ".." / "dynamics.py"
+INPUT_DIR = Path("input")
+OUTPUT_DIR = Path("output")
+CONFIG_FILE = INPUT_DIR / "input.txt"
+
+
+def load_dynamics_module(module_path: Path):
+    spec = importlib.util.spec_from_file_location("dynamics_module", module_path)
+    if spec is None or spec.loader is None:
+        raise ImportError(f"无法加载 dynamics.py: {module_path}")
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def main():
+    parser = argparse.ArgumentParser(description="运行 Dynamics 示例案例 case11")
+    parser.add_argument("--no-plot", action="store_true", help="跳过 matplotlib 绘图")
+    args = parser.parse_args()
+
+    dynamics_path = (CASE_DIR / DYNAMICS_PATH).resolve()
+    input_dir = (CASE_DIR / INPUT_DIR).resolve()
+    output_dir = (CASE_DIR / OUTPUT_DIR).resolve()
+    config_path = (CASE_DIR / CONFIG_FILE).resolve()
+
+    module = load_dynamics_module(dynamics_path)
+    module.run_case(
+        config_path=config_path,
+        runtime_base=CASE_DIR,
+        input_dir=input_dir,
+        output_dir=output_dir,
+        no_plot=args.no_plot,
+    )
+
+
+if __name__ == "__main__":
+    main()

examples/case13/Readme.md

@@ -0,0 +1,40 @@
+# case06: 一维原子链横波模拟
+
+60 个原子沿 x 轴排列，相邻原子用弹簧连接。原子 1 受 z 方向驱动力作用，产生沿链传播的横波。
+
+## 物理设定
+
+| 参数 | 值 |
+|---|---|
+| 原子数 | 120 |
+| 排列 | 沿 x 轴等间距排列，间距为 1 |
+| 约束 | 原子**沿 z 方向自由振动**（fix_x=1, fix_y=1, fix_z=0），x, y 锁定 |
+| 弹簧 | 劲度系数 k=1.0，原长 L₀=1.0 |
+| 重力 | 无 |
+| 万有引力 | 无 |
+| 阻尼 | 无 |
+| 驱动力 | 原子 1（z 方向驱动） |
+| 算法 | leapfrog（蛙跳法，能量守恒） |
+
+## 驱动力
+
+原子 1 的位置由 `input/driver.txt` 中的驱动力公式决定：
+
+```math
+z(t) = A_z \cdot \cos(2\pi f_z t + \phi_z)
+```
+
+当前参数：A_z = 0.5, f_z = 0.1 Hz, φ_z = 90°, period = all（全程驱动）。
+
+## 动力学行为
+
+原子 1 沿 z 方向的受迫振动通过弹簧逐次传递给相邻原子，形成沿链传播的**横波**。由于 z 方向的振动是横向的，弹簧大部分张力在 x 方向，z 方向的有效刚度是非线性的——等效于一个三次方恢复力（FPU 型非线性），因此波速较慢。
+
+## 使用方法
+
+```bash
+cd examples/case06
+python run_dynamics.py
+```
+
+配置参数详见 `input/input.txt`，驱动力定义见 `input/driver.txt`，完整文档见 `doc/index.html`。

examples/case13/doc/index.html

@@ -0,0 +1,477 @@
+<!DOCTYPE html>
+<html lang="zh-CN">
+<head>
+<meta charset="UTF-8">
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<title>case06 — 一维原子链驱动力学模拟 | 物理原理 &amp; 使用文档</title>
+<style>
+  :root {
+    --bg: #f8f9fa;
+    --card: #fff;
+    --text: #1a1a2e;
+    --accent: #2563eb;
+    --accent-light: #dbeafe;
+    --code-bg: #1e293b;
+    --code-text: #e2e8f0;
+    --border: #e2e8f0;
+    --muted: #64748b;
+  }
+  * { margin: 0; padding: 0; box-sizing: border-box; }
+  body {
+    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Noto Sans SC", sans-serif;
+    background: var(--bg);
+    color: var(--text);
+    line-height: 1.7;
+  }
+
+  /* ── Header ── */
+  .hero {
+    background: linear-gradient(135deg, #1e293b 0%, #334155 100%);
+    color: #fff;
+    padding: 56px 24px 48px;
+    text-align: center;
+  }
+  .hero h1 { font-size: 2rem; font-weight: 700; letter-spacing: -0.02em; }
+  .hero .subtitle {
+    margin-top: 10px;
+    font-size: 1.05rem;
+    opacity: 0.8;
+  }
+  .hero .badge {
+    display: inline-block;
+    margin-top: 14px;
+    padding: 4px 14px;
+    border-radius: 999px;
+    background: rgba(255,255,255,0.12);
+    font-size: 0.82rem;
+  }
+
+  /* ── Layout ── */
+  .container { max-width: 820px; margin: 0 auto; padding: 32px 20px; }
+
+  section { margin-bottom: 44px; }
+  h2 {
+    font-size: 1.35rem;
+    font-weight: 600;
+    margin-bottom: 16px;
+    padding-bottom: 8px;
+    border-bottom: 2px solid var(--accent);
+    display: inline-block;
+  }
+  h3 {
+    font-size: 1.05rem;
+    font-weight: 600;
+    margin: 20px 0 10px;
+  }
+
+  p, li { margin-bottom: 10px; }
+  ul, ol { padding-left: 22px; }
+  strong { color: var(--accent); }
+
+  /* ── Cards ── */
+  .card {
+    background: var(--card);
+    border-radius: 12px;
+    padding: 20px 24px;
+    margin-bottom: 16px;
+    border: 1px solid var(--border);
+    box-shadow: 0 1px 3px rgba(0,0,0,0.04);
+  }
+
+  /* ── Formula / Code blocks ── */
+  .formula {
+    background: var(--card);
+    border-left: 4px solid var(--accent);
+    padding: 14px 20px;
+    margin: 14px 0;
+    font-family: "Times New Roman", "STIX", serif;
+    font-size: 1.05rem;
+    overflow-x: auto;
+    border-radius: 0 8px 8px 0;
+  }
+  code {
+    background: var(--accent-light);
+    padding: 2px 7px;
+    border-radius: 4px;
+    font-family: "JetBrains Mono", "Fira Code", monospace;
+    font-size: 0.88em;
+  }
+  pre {
+    background: var(--code-bg);
+    color: var(--code-text);
+    padding: 16px 20px;
+    border-radius: 10px;
+    overflow-x: auto;
+    font-size: 0.85rem;
+    line-height: 1.5;
+    margin: 14px 0;
+  }
+  pre .cm { color: #94a3b8; font-style: italic; }   /* comment */
+
+  /* ── Table ── */
+  table {
+    width: 100%;
+    border-collapse: collapse;
+    margin: 14px 0;
+    font-size: 0.92rem;
+  }
+  th, td {
+    padding: 8px 12px;
+    text-align: left;
+    border-bottom: 1px solid var(--border);
+  }
+  th { background: var(--accent-light); font-weight: 600; }
+
+  /* ── TOC ── */
+  .toc { counter-reset: toc; }
+  .toc li { counter-increment: toc; list-style: none; margin-bottom: 6px; }
+  .toc li::before { content: counter(toc) ". "; font-weight: 600; color: var(--accent); }
+  .toc a { color: var(--accent); text-decoration: none; }
+  .toc a:hover { text-decoration: underline; }
+
+  /* ── Flow diagram ── */
+  .flow { display: flex; flex-wrap: wrap; gap: 8px; align-items: center; justify-content: center; margin: 16px 0; }
+  .flow-step {
+    background: var(--accent-light);
+    border: 1px solid var(--accent);
+    border-radius: 8px;
+    padding: 8px 16px;
+    font-size: 0.88rem;
+    font-weight: 500;
+  }
+  .flow-arrow { color: var(--muted); font-size: 1.2rem; }
+
+  @media (max-width: 600px) {
+    .hero h1 { font-size: 1.5rem; }
+    .flow { flex-direction: column; }
+    .flow-arrow { transform: rotate(90deg); }
+  }
+</style>
+</head>
+<body>
+
+<!-- ============================================================ -->
+<!--  Header                                                       -->
+<!-- ============================================================ -->
+<header class="hero">
+  <h1>一维原子链驱动力学模拟</h1>
+  <p class="subtitle">120 个原子沿 x 轴排列 · 弹簧连接 · z 方向受迫振动</p>
+  <span class="badge">case06  ·  examples/case06</span>
+</header>
+
+<div class="container">
+
+<!-- ============================================================ -->
+<!--  TOC                                                          -->
+<!-- ============================================================ -->
+<section>
+  <h2>目录</h2>
+  <ol class="toc">
+    <li><a href="#physics">物理原理</a></li>
+    <li><a href="#algorithm">数值算法</a></li>
+    <li><a href="#driver">驱动力模型</a></li>
+    <li><a href="#usage">使用方法</a></li>
+    <li><a href="#params">参数参考</a></li>
+    <li><a href="#files">文件结构</a></li>
+    <li><a href="#troubleshoot">常见问题</a></li>
+  </ol>
+</section>
+
+<!-- ============================================================ -->
+<!--  1. Physics                                                   -->
+<!-- ============================================================ -->
+<section id="physics">
+  <h2>一、物理原理</h2>
+
+  <div class="card">
+    <h3>1.1 一维原子链</h3>
+    <p>120 个原子沿 <strong>x 轴</strong> 等间距排列，原子间距为 1。相邻原子之间用 <strong>理想弹簧</strong> 连接，弹簧的劲度系数 <em>k</em> = 1.0，原长 <em>L</em>₀ = 1.0（与原子间距一致，初始状态弹簧无拉伸）。</p>
+    <p>每个原子被限制在 <strong>z 方向</strong> 自由振动，x 和 y 方向锁定（<code>fix_x=1, fix_y=1, fix_z=0</code>）。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.2 弹簧力（胡克定律）</h3>
+    <p>当原子 <em>i</em> 和 <em>j</em> 之间有弹簧连接时，原子 <em>i</em> 受到的弹簧力为：</p>
+    <div class="formula">
+      <strong>F</strong> = −<em>k</em> · (<em>d</em> − <em>L</em>₀) · <strong>u</strong><sub><em>ij</em></sub>
+    </div>
+    <p>其中 <em>d</em> = |<strong>r</strong><sub><em>j</em></sub> − <strong>r</strong><sub><em>i</em></sub>| 为两原子间距离，<strong>u</strong><sub><em>ij</em></sub> 为从 <em>i</em> 指向 <em>j</em> 的单位向量。由于原子只在 z 方向振动，弹簧在 z 方向的分量是 <strong>几何非线性</strong> 的——对于小振幅近似，z 方向等效于一个三次方恢复力（FPU 型非线性）。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.3 运动方程</h3>
+    <p>对于第 <em>i</em> 个自由原子（非受驱），牛顿第二定律给出：</p>
+    <div class="formula">
+      <em>m</em> · <strong>a</strong><sub><em>i</em></sub> = <strong>F</strong><sub><em>i</em></sub><sup>spring</sup> + <strong>F</strong><sub><em>i</em></sub><sup>driving</sup>
+    </div>
+    <p>本案例中 <strong>唯一的外力</strong> 来自驱动力（仅施加于原子 1）。无重力、无万有引力、无阻尼，系统总能量守恒。</p>
+  </div>
+
+  <div class="card">
+    <h3>1.4 波传播</h3>
+    <p>原子 1 的受迫振动通过弹簧逐次传递给相邻原子，形成沿链传播的 <strong>横波</strong>。由于横向振动的几何非线性（弹簧大部分张力在 x 方向，z 方向的有效刚度远小于 1），波的传播速度较慢，且高阶频率成分会在链中产生复杂的非线性动力学行为（类似 FPU 回波现象）。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  2. Algorithm                                                 -->
+<!-- ============================================================ -->
+<section id="algorithm">
+  <h2>二、数值算法</h2>
+
+  <div class="card">
+    <h3>2.1 蛙跳法（Leapfrog / Velocity-Verlet）</h3>
+    <p>采用能量守恒特性优异的 <strong>蛙跳法</strong>（二阶辛积分器），更新公式为：</p>
+    <div class="formula">
+      <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) = <strong>v</strong>(<em>t</em>) + ½ <strong>a</strong>(<em>t</em>) · Δ<em>t</em><br>
+      <strong>r</strong>(<em>t</em> + Δ<em>t</em>) = <strong>r</strong>(<em>t</em>) + <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) · Δ<em>t</em><br>
+      <strong>a</strong>(<em>t</em> + Δ<em>t</em>) = <strong>F</strong>(<strong>r</strong>(<em>t</em> + Δ<em>t</em>), <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>)) / <em>m</em><br>
+      <strong>v</strong>(<em>t</em> + Δ<em>t</em>) = <strong>v</strong>(<em>t</em> + ½Δ<em>t</em>) + ½ <strong>a</strong>(<em>t</em> + Δ<em>t</em>) · Δ<em>t</em>
+    </div>
+    <p>蛙跳法在长时间模拟中能量漂移极小（本案例验证 <strong>&lt; 0.004%</strong>），适合无阻尼的保守系统。</p>
+  </div>
+
+  <div class="card">
+    <h3>2.2 时间步长与采样</h3>
+    <table>
+      <tr><th>参数</th><th>值</th><th>说明</th></tr>
+      <tr><td>DT</td><td>0.01 s</td><td>积分步长（远小于 1/ω ≈ 0.16 s，满足稳定性条件）</td></tr>
+      <tr><td>T_total</td><td>100 s</td><td>总模拟时间 → NT = 10000 步</td></tr>
+      <tr><td>NSTEP</td><td>50</td><td>每 NSTEP 步取一帧用于动画 → 200 帧</td></tr>
+      <tr><td>method</td><td>leapfrog</td><td>蛙跳法（Velocity-Verlet）</td></tr>
+    </table>
+  </div>
+
+  <div class="card">
+    <h3>2.3 计算流程</h3>
+    <div class="flow">
+      <span class="flow-step">读入 coord.txt<br>connection.txt<br>bond.txt</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">施加驱动力<br>（驱动原子 1）</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">记录轨迹</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">蛙跳法<br>更新位置/速度</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step">固定约束<br>（x, y 锁定）</span>
+      <span class="flow-arrow">→</span>
+      <span class="flow-step" style="background:#fef3c7;border-color:#f59e0b;">循环<br>NT 次</span>
+    </div>
+    <p style="margin-top:12px;">注意：驱动力在 <strong>每次积分前</strong> 施加，确保受驱原子的位置正确传递给弹簧力计算。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  3. Driving Force                                             -->
+<!-- ============================================================ -->
+<section id="driver">
+  <h2>三、驱动力模型</h2>
+
+  <div class="card">
+    <h3>3.1 定义文件</h3>
+    <p>驱动力由 <code>input/driver.txt</code> 定义，格式如下：</p>
+    <pre>n amp_x amp_y amp_z freq_x freq_y freq_z phi_x phi_y phi_z period
+1     0     0     5      0      0      1     0     0    90    all</pre>
+  </div>
+
+  <div class="card">
+    <h3>3.2 数学公式</h3>
+    <p>受驱原子的位置由下式决定（<strong>完全替换</strong> coord.txt 中的初始坐标和固定约束）：</p>
+    <div class="formula">
+      <strong>r</strong>(<em>t</em>) = <strong>A</strong> · cos(2π<em>f</em> · <em>t</em> + <strong>φ</strong>)
+    </div>
+    <p>速度由解析导数给出：</p>
+    <div class="formula">
+      <strong>v</strong>(<em>t</em>) = −<strong>A</strong> · 2π<em>f</em> · sin(2π<em>f</em> · <em>t</em> + <strong>φ</strong>)
+    </div>
+    <p>其中 <strong>A</strong> = (amp_x, amp_y, amp_z)，<strong>f</strong> = (freq_x, freq_y, freq_z) 为不同方向的驱动频率，<strong>φ</strong> = (phi_x, phi_y, phi_z) 为相位（<strong>角度制</strong>，代码自动转换为弧度）。</p>
+  </div>
+
+  <div class="card">
+    <h3>3.3 本案例驱动参数</h3>
+    <table>
+      <tr><th>参数</th><th>值</th><th>含义</th></tr>
+      <tr><td>amp_z</td><td>5.0</td><td>z 方向驱动振幅</td></tr>
+      <tr><td>freq_z</td><td>1.0 Hz</td><td>驱动频率（周期 1 s）</td></tr>
+      <tr><td>phi_z</td><td>90°</td><td>驱动相位 → z(0) = 5·cos(90°) = 0</td></tr>
+      <tr><td>period</td><td>all</td><td>全程驱动，永不停止</td></tr>
+    </table>
+    <div class="formula">
+      <em>z</em>(<em>t</em>) = 5.0 · cos(2π · 1.0 · <em>t</em> + 90°)
+    </div>
+  </div>
+
+  <div class="card">
+    <h3>3.4 有限周期驱动</h3>
+    <p><code>period</code> 参数支持三种模式：</p>
+    <ul>
+      <li><strong>all</strong> — 全程驱动</li>
+      <li><strong>数值</strong> — 驱动指定周期数后 <strong>静止</strong>（冻结在最终位置，速度归零）。例如 <code>period: 1</code> 表示驱动 1 个完整周期后停止。</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>3.5 驱动与固定约束的关系</h3>
+    <p>对于受驱原子（<code>driver.txt</code> 中 <code>n</code> 指定的原子），其在 <code>coord.txt</code> 中的初始坐标和 <code>fix_x/fix_y/fix_z</code> 约束被 <strong>完全忽略</strong>。原子的位置和速度完全由驱动力公式决定。</p>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  4. Usage                                                     -->
+<!-- ============================================================ -->
+<section id="usage">
+  <h2>四、使用方法</h2>
+
+  <div class="card">
+    <h3>4.1 完整运行（模拟 + 动画）</h3>
+    <pre>cd examples/case06
+python run_dynamics.py</pre>
+    <p>这步会依次执行：物理模拟 → 抽帧 → 打开 VisPy 3D 动画窗口。</p>
+  </div>
+
+  <div class="card">
+    <h3>4.2 仅查看已有结果</h3>
+    <p>如果已经跑完模拟且生成了 <code>output/display.txt</code>，可以通过修改 <code>input.txt</code> 跳过计算，只开动画：</p>
+    <pre>step_simulate:  0   # 跳过模拟
+step_sample:    0   # 跳过抽帧
+step_animation: 1   # 播放动画</pre>
+    <p>然后运行：<code>python run_dynamics.py</code></p>
+  </div>
+
+  <div class="card">
+    <h3>4.3 手动 3D 动画</h3>
+    <p>也可以单独启动 VisPy 窗口：</p>
+    <pre>python ../../draw.py output/</pre>
+  </div>
+
+  <div class="card">
+    <h3>4.4 强制重新计算</h3>
+    <p>修改参数后需要重新运行模拟时，设置：</p>
+    <pre>force_calc: 1        # 忽略缓存，强制重新计算</pre>
+  </div>
+
+  <div class="card">
+    <h3>4.5 动画交互</h3>
+    <table>
+      <tr><th>操作</th><th>效果</th></tr>
+      <tr><td>鼠标拖动</td><td>旋转视角</td></tr>
+      <tr><td>滚轮</td><td>缩放</td></tr>
+      <tr><td>W / S 键</td><td>相机沿 Z 轴向前 / 向后移动（靠近/远离场景）</td></tr>
+      <tr><td>A / D 键</td><td>视角向右 / 向左平移</td></tr>
+      <tr><td>E / Q 键</td><td>视角上升 / 下降（屏幕方向）</td></tr>
+      <tr><td>C / X 键</td><td>增大 / 减小步长</td></tr>
+      <tr><td>V 键</td><td>切换透视 / 正交投影</td></tr>
+      <tr><td>左上角 <strong>reset</strong> 按钮</td><td>复位视角到初始位置</td></tr>
+      <tr><td>左上角 <strong>info</strong> 按钮</td><td>切换信息面板显示/隐藏</td></tr>
+      <tr><td>左上角 <strong>axes</strong> 按钮</td><td>切换坐标轴显示/隐藏</td></tr>
+    </table>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  5. Parameters                                                -->
+<!-- ============================================================ -->
+<section id="params">
+  <h2>五、参数参考</h2>
+
+  <div class="card">
+    <h3>5.1 input.txt 关键参数</h3>
+    <table>
+      <tr><th>参数</th><th>默认值</th><th>说明</th></tr>
+      <tr><td>gravity_field</td><td>0</td><td>均匀重力场（已关闭）</td></tr>
+      <tr><td>gravity_interaction</td><td>0</td><td>原子间万有引力（已关闭）</td></tr>
+      <tr><td>elastic_force</td><td>1</td><td>弹簧键力（已开启）</td></tr>
+      <tr><td>damping_force</td><td>0</td><td>阻尼（已关闭）</td></tr>
+      <tr><td><strong>driving_force</strong></td><td><strong>1</strong></td><td>驱动力开关（1=开启，需 driver.txt）</td></tr>
+      <tr><td>method</td><td>leapfrog</td><td>数值积分方法</td></tr>
+      <tr><td>DT</td><td>0.01</td><td>积分步长 (s)</td></tr>
+      <tr><td>T_total</td><td>100.0</td><td>总模拟时间 (s)</td></tr>
+      <tr><td>NSTEP</td><td>50</td><td>抽帧步数间隔</td></tr>
+      <tr><td>engine</td><td>python</td><td>计算引擎（python / c / cpp / fortran）</td></tr>
+      <tr><td>use_marker</td><td>1</td><td>渲染模式（0=Sphere 网格, 1=Marker GPU 实例化）</td></tr>
+    </table>
+  </div>
+
+  <div class="card">
+    <h3>5.2 流程控制参数</h3>
+    <table>
+      <tr><th>参数</th><th>0</th><th>1</th></tr>
+      <tr><td>step_simulate</td><td>跳过模拟（加载已有轨迹）</td><td>运行物理模拟</td></tr>
+      <tr><td>step_sample</td><td>跳过抽帧</td><td>从轨迹抽取显示帧</td></tr>
+      <tr><td>step_plot</td><td>不生成图表</td><td>生成轨迹/能量图</td></tr>
+      <tr><td><strong>step_plot_wave</strong></td><td>不生成波形图</td><td>生成波形能量动画 GIF</td></tr>
+      <tr><td>step_animation</td><td>不启动动画</td><td>自动打开 VisPy 3D 窗口</td></tr>
+      <tr><td>force_calc</td><td>自动检测缓存</td><td>强制重新计算</td></tr>
+    </table>
+  </div>
+</section>
+
+<!-- ============================================================ -->
+<!--  6. File Structure                                            -->
+<!-- ============================================================ -->
+<section id="files">
+  <h2>六、文件结构</h2>
+
+  <pre>case06/
+├── input/
+│   ├── input.txt          # 主配置文件（YAML 格式）
+│   ├── coord.txt          # 原子坐标（120 个原子）
+│   ├── connection.txt     # 弹簧连接关系（59 条键）
+│   ├── bond.txt           # 弹簧参数（k=1.0, L₀=1.0）
+│   └── <strong>driver.txt</strong>       # <span class="cm">驱动力定义（本案例新增）</span>
+├── output/
+│   ├── trajectory.txt     # 全量轨迹数据（50000 步 × 120 原子）
+│   ├── display.txt        # 抽帧后的动画数据（500 帧 × 120 原子）
+│   ├── dynamics.log       # 计算日志
+│   ├── animation.log      # 动画启动日志（闪退时排查用）
+│   └── wave_animation.gif # 波形能量动画（step_plot_wave=1 时生成）
+├── doc/
+│   └── index.html         # <span class="cm">本文档</span>
+├── Readme.md              # 案例简介
+└── run_dynamics.py        # 案例运行入口</pre>
+</section>
+
+<!-- ============================================================ -->
+<!--  7. Troubleshooting                                           -->
+<!-- ============================================================ -->
+<section id="troubleshoot">
+  <h2>七、常见问题</h2>
+
+  <div class="card">
+    <h3>7.1 动画窗口闪退</h3>
+    <p>如果 VisPy 窗口一闪就消失，请检查：</p>
+    <ul>
+      <li><code>output/animation.log</code> 中是否有错误信息</li>
+      <li><code>output/display.txt</code> 是否存在（需先跑 <code>step_sample: 1</code>）</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>7.2 原子不振动</h3>
+    <p>可能原因：</p>
+    <ul>
+      <li><strong>NSTEP 过大</strong>：抽帧间隔大于驱动周期的一半时，动画会丢失振动细节。建议 NSTEP ≤ 1/(freq · DT · 10)</li>
+      <li><strong>相位 φ 使采样点落在零值</strong>：试试 <code>phi_z: 0</code> 让原子在 t=0 处于振幅峰值</li>
+      <li>确认 <code>driving_force: 1</code> 且 <code>driver.txt</code> 中 amp_z 不为 0</li>
+    </ul>
+  </div>
+
+  <div class="card">
+    <h3>7.3 渲染性能慢</h3>
+    <p>原子数多时动画卡顿：</p>
+    <ul>
+      <li>设置 <code>use_marker: 1</code>（使用 GPU 实例化渲染替代独立网格球体）</li>
+      <li>增大 <code>NSTEP</code> 减少动画帧数</li>
+    </ul>
+  </div>
+</section>
+
+<hr style="border:none;border-top:1px solid var(--border);margin:40px 0;">
+
+<footer style="text-align:center;color:var(--muted);font-size:0.85rem;margin-bottom:40px;">
+  Dynamics Simulation Framework &nbsp;·&nbsp; 生成于 2026-06-10
+</footer>
+
+</div>
+</body>
+</html>

examples/case13/input/bond.txt

@@ -0,0 +1,2 @@
+bond_name k rest_length
+h 100.0 1.0