From 8c8ad9fe0713bee75a3faa507acd170a41f82999 Mon Sep 17 00:00:00 2001 From: dison0331-ThinkPad <139662128+dison0331@users.noreply.github.com> Date: Wed, 11 Mar 2026 21:32:58 +0800 Subject: [PATCH] first pc-1 --- 01.py | 1 + INSTALL.md | 309 +++++++++++++ README.md | 312 +++++++++++++ SUMMARY.md | 251 +++++++++++ simple_test.py | 81 ++++ test_import.py | 94 ++++ three_body_problem/__init__.py | 41 ++ .../__pycache__/__init__.cpython-312.pyc | Bin 0 -> 1371 bytes .../__pycache__/config.cpython-312.pyc | Bin 0 -> 12373 bytes .../__pycache__/integrator.cpython-312.pyc | Bin 0 -> 4880 bytes .../__pycache__/particle.cpython-312.pyc | Bin 0 -> 3792 bytes .../__pycache__/solver.cpython-312.pyc | Bin 0 -> 10373 bytes .../__pycache__/visualizer.cpython-312.pyc | Bin 0 -> 16106 bytes three_body_problem/config.py | 280 ++++++++++++ three_body_problem/demo.py | 299 ++++++++++++ three_body_problem/examples/__init__.py | 16 + three_body_problem/examples/figure8.py | 203 +++++++++ three_body_problem/examples/lagrange.py | 343 ++++++++++++++ three_body_problem/examples/random.py | 426 ++++++++++++++++++ three_body_problem/integrator.py | 119 +++++ three_body_problem/particle.py | 64 +++ three_body_problem/requirements.txt | 6 + three_body_problem/run_example.py | 199 ++++++++ three_body_problem/setup.py | 53 +++ three_body_problem/solver.py | 196 ++++++++ three_body_problem/tests/__init__.py | 3 + three_body_problem/tests/test_solver.py | 385 ++++++++++++++++ three_body_problem/visualizer.py | 321 +++++++++++++ tips.md | 3 + 29 files changed, 4005 insertions(+) create mode 100644 01.py create mode 100644 INSTALL.md create mode 100644 README.md create mode 100644 SUMMARY.md create mode 100644 simple_test.py create mode 100644 test_import.py create mode 100644 three_body_problem/__init__.py create mode 100644 three_body_problem/__pycache__/__init__.cpython-312.pyc create mode 100644 three_body_problem/__pycache__/config.cpython-312.pyc create mode 100644 three_body_problem/__pycache__/integrator.cpython-312.pyc create mode 100644 three_body_problem/__pycache__/particle.cpython-312.pyc create mode 100644 three_body_problem/__pycache__/solver.cpython-312.pyc create mode 100644 three_body_problem/__pycache__/visualizer.cpython-312.pyc create mode 100644 three_body_problem/config.py create mode 100644 three_body_problem/demo.py create mode 100644 three_body_problem/examples/__init__.py create mode 100644 three_body_problem/examples/figure8.py create mode 100644 three_body_problem/examples/lagrange.py create mode 100644 three_body_problem/examples/random.py create mode 100644 three_body_problem/integrator.py create mode 100644 three_body_problem/particle.py create mode 100644 three_body_problem/requirements.txt create mode 100644 three_body_problem/run_example.py create mode 100644 three_body_problem/setup.py create mode 100644 three_body_problem/solver.py create mode 100644 three_body_problem/tests/__init__.py create mode 100644 three_body_problem/tests/test_solver.py create mode 100644 three_body_problem/visualizer.py create mode 100644 tips.md diff --git a/01.py b/01.py new file mode 100644 index 0000000..d1c4cdb --- /dev/null +++ b/01.py @@ -0,0 +1 @@ +print('hello world') # this is a comment \ No newline at end of file diff --git a/INSTALL.md b/INSTALL.md new file mode 100644 index 0000000..7742e04 --- /dev/null +++ b/INSTALL.md @@ -0,0 +1,309 @@ +# 三体问题求解器 - 安装和使用指南 + +## 项目简介 + +这是一个纯Python实现的三体问题求解器，使用四阶龙格-库塔法（RK4）数值求解牛顿引力下的三体运动。项目提供了完整的模拟、可视化和分析功能。 + +## 安装步骤 + +### 1. 克隆或下载项目 +```bash +# 克隆仓库 +git clone +cd three_body_problem + +# 或直接下载zip文件并解压 +``` + +### 2. 安装依赖 +```bash +# 使用pip安装 +pip install numpy matplotlib + +# 或使用requirements.txt +pip install -r requirements.txt +``` + +### 3. 验证安装 +```bash +# 运行简单测试 +python simple_test.py + +# 或运行完整测试 +python three_body_problem/tests/test_solver.py +``` + +## 快速开始 + +### 基本示例 +```python +import numpy as np +from three_body_problem import ThreeBodySolver, Particle, ThreeBodyConfig, ThreeBodyVisualizer + +# 创建三个质点 +particles = [ + Particle(mass=1.0, position=[1.0, 0.0, 0.0], velocity=[0.0, 0.5, 0.0], name="Star A"), + Particle(mass=1.0, position=[-1.0, 0.0, 0.0], velocity=[0.0, -0.5, 0.0], name="Star B"), + Particle(mass=0.1, position=[0.0, 1.0, 0.0], velocity=[-0.3, 0.0, 0.0], name="Star C") +] + +# 创建求解器 +solver = ThreeBodySolver(particles, dt=0.001) + +# 模拟5年 +solver.simulate(total_time=5.0) + +# 可视化 +visualizer = ThreeBodyVisualizer() +visualizer.plot_trajectories(solver, title="三体系统运动轨迹") +visualizer.show() +``` + +### 使用预置配置 +```python +# 8字形轨道（著名的稳定解） +particles = ThreeBodyConfig.create_figure8_config() + +# 拉格朗日点L4 +particles = ThreeBodyConfig.create_lagrange_point_config(lagrange_point=4) + +# 随机系统 +particles = ThreeBodyConfig.create_random_config( + masses=None, # 随机质量 + position_range=2.0, # 位置范围 ±2 AU + velocity_scale=1.0 # 速度缩放因子 +) +``` + +## 运行示例 + +### 1. 运行简单示例 +```bash +python three_body_problem/run_example.py +``` + +### 2. 运行8字形轨道示例 +```bash +python three_body_problem/examples/figure8.py +``` + +### 3. 运行拉格朗日点示例 +```bash +python three_body_problem/examples/lagrange.py +``` + +### 4. 运行随机系统示例 +```bash +python three_body_problem/examples/random.py +``` + +### 5. 运行演示脚本 +```bash +python three_body_problem/demo.py +``` + +## 项目结构 + +``` +three_body_problem/ +├── __init__.py # 包初始化 +├── particle.py # 质点类 +├── integrator.py # 数值积分器（RK4） +├── solver.py # 三体问题求解器 +├── visualizer.py # 可视化工具 +├── config.py # 配置管理 +├── README.md # 详细文档 +├── SUMMARY.md # 项目总结 +├── demo.py # 演示脚本 +├── run_example.py # 快速示例 +├── requirements.txt # 依赖列表 +├── setup.py # 安装配置 +├── examples/ # 示例 +│ ├── figure8.py # 8字形轨道 +│ ├── lagrange.py # 拉格朗日点 +│ └── random.py # 随机系统 +└── tests/ # 测试 + └── test_solver.py # 单元测试 +``` + +## 主要功能 + +### 1. 物理模拟 +- **牛顿引力计算**：精确计算三个质点间的万有引力 +- **数值积分**：四阶龙格-库塔法（RK4） +- **守恒定律**：动量、角动量、能量守恒验证 + +### 2. 初始条件 +- **8字形轨道**：著名的稳定周期解 +- **拉格朗日点**：L4和L5点稳定性测试 +- **随机系统**：随机初始条件生成 +- **自定义配置**：灵活的用户定义 + +### 3. 可视化 +- **3D轨迹图**：完整的三维运动轨迹 +- **2D投影**：XY、XZ、YZ平面投影 +- **相空间图**：位置-速度关系 +- **能量分析**：守恒定律验证 + +### 4. 分析工具 +- **质心计算**：系统质心位置和轨迹 +- **距离分析**：质点间距离变化 +- **稳定性分析**：轨道稳定性评估 +- **误差分析**：数值积分精度评估 + +## 配置参数 + +### 时间步长选择 +```python +# 高精度模拟（推荐） +solver = ThreeBodySolver(particles, dt=0.001) + +# 快速模拟 +solver = ThreeBodySolver(particles, dt=0.01) + +# 超高精度模拟 +solver = ThreeBodySolver(particles, dt=0.0001) +``` + +### 模拟时间 +```python +# 短期模拟（几到几十年） +solver.simulate(total_time=10.0) # 10年 + +# 长期模拟（几百年） +solver.simulate(total_time=100.0) # 100年 + +# 超长期模拟（几千年） +solver.simulate(total_time=1000.0) # 1000年 +``` + +## 常见问题 + +### 1. 导入错误 +**问题**：`ModuleNotFoundError: No module named 'numpy'` +**解决**：安装依赖 `pip install numpy matplotlib` + +### 2. 模拟速度慢 +**问题**：模拟时间太长或时间步长太小 +**解决**： +- 减少模拟时间 `total_time` +- 增大时间步长 `dt` +- 减少进度打印频率 `progress_interval` + +### 3. 数值不稳定 +**问题**：质点间距离过小导致计算溢出 +**解决**： +- 增大时间步长 `dt` +- 调整初始条件避免近距离接近 +- 使用更小的质量差异 + +### 4. 内存不足 +**问题**：长时间模拟产生大量轨迹数据 +**解决**： +- 减少模拟时间 +- 增大时间步长 +- 修改代码只保存关键时间点 + +## 性能优化 + +### 1. 减少输出 +```python +# 减少进度打印频率 +solver.simulate(total_time=100.0, progress_interval=10000) +``` + +### 2. 调整精度 +```python +# 平衡精度和速度 +dt = 0.001 # 标准精度 +dt = 0.01 # 较低精度，更快 +dt = 0.0001 # 高精度，较慢 +``` + +### 3. 内存管理 +```python +# 定期清理历史记录 +solver.reset() # 清除所有历史记录 +``` + +## 扩展开发 + +### 添加新的初始条件 +```python +from three_body_problem.config import ThreeBodyConfig + +class MyConfig(ThreeBodyConfig): + @staticmethod + def create_my_config(): + # 实现自定义配置 + particles = [...] + return particles +``` + +### 自定义可视化 +```python +from three_body_problem.visualizer import ThreeBodyVisualizer + +class MyVisualizer(ThreeBodyVisualizer): + def plot_custom_view(self, solver): + # 实现自定义可视化 + pass +``` + +### 实现新的积分器 +```python +from three_body_problem.integrator import RK4Integrator + +class MyIntegrator(RK4Integrator): + def step(self, particles, acceleration_func): + # 实现新的积分方法 + pass +``` + +## 学习资源 + +### 三体问题理论 +1. **经典文献**：Poincaré, H. (1890). "Sur le problème des trois corps" +2. **现代研究**：Chenciner, A., & Montgomery, R. (2000). "A remarkable periodic solution" +3. **教科书**：Murray, C. D., & Dermott, S. F. (1999). "Solar System Dynamics" + +### 数值方法 +1. **数值分析**：Hairer, E., et al. (1993). "Solving Ordinary Differential Equations I" +2. **科学计算**：Press, W. H., et al. (2007). "Numerical Recipes" + +### Python科学计算 +1. **NumPy教程**：https://numpy.org/doc/stable/user/quickstart.html +2. **Matplotlib教程**：https://matplotlib.org/stable/tutorials/index.html +3. **SciPy教程**：https://docs.scipy.org/doc/scipy/tutorial/index.html + +## 贡献指南 + +1. Fork项目仓库 +2. 创建功能分支 +3. 提交更改 +4. 推送到分支 +5. 创建Pull Request + +## 许可证 + +MIT License - 详见LICENSE文件 + +## 支持 + +如有问题或建议，请： +1. 查看文档和示例 +2. 提交Issue +3. 联系作者 + +## 版本历史 + +### v1.0.0 (2024) +- 初始版本发布 +- 实现RK4数值积分器 +- 提供多种初始条件配置 +- 完整的可视化功能 +- 包含测试和示例 + +--- + +**开始探索三体问题的奇妙世界吧！** 🚀 \ No newline at end of file diff --git a/README.md b/README.md new file mode 100644 index 0000000..0f967c3 --- /dev/null +++ b/README.md @@ -0,0 +1,312 @@ +# 三体问题求解器 - 纯Python方案 + +一个用于模拟和可视化三体问题的Python库。使用四阶龙格-库塔法数值求解牛顿引力下的三体运动。 + +## 功能特性 + +- **纯Python实现**：无需外部依赖（除可视化外） +- **高精度数值积分**：使用四阶龙格-库塔法（RK4） +- **多种初始条件**：预置8字形轨道、拉格朗日点等经典配置 +- **完整可视化**：3D轨迹、2D投影、相空间图、能量分析 +- **物理守恒验证**：动量、角动量、能量守恒检查 +- **模块化设计**：易于扩展和自定义 + +## 安装要求 + +### 必需依赖 +- Python 3.7+ +- NumPy +- Matplotlib + +### 安装方法 +```bash +# 克隆仓库 +git clone +cd three_body_problem + +# 安装依赖 +pip install numpy matplotlib +``` + +## 快速开始 + +### 基本使用 +```python +import numpy as np +from three_body_problem import ThreeBodySolver, Particle, ThreeBodyConfig, ThreeBodyVisualizer + +# 创建8字形轨道配置 +particles = ThreeBodyConfig.create_figure8_config() + +# 创建求解器 +solver = ThreeBodySolver(particles, dt=0.001) + +# 模拟10年 +solver.simulate(total_time=10.0) + +# 可视化 +visualizer = ThreeBodyVisualizer() +visualizer.plot_trajectories(solver, title="8字形三体轨道") +visualizer.show() +``` + +### 运行示例 +```python +# 运行8字形轨道示例 +from three_body_problem.examples import figure8 +solver = figure8.run_figure8_example() + +# 运行拉格朗日点示例 +from three_body_problem.examples import lagrange +solver_l4 = lagrange.run_lagrange_example(lagrange_point=4, total_time=50.0) + +# 运行随机系统示例 +from three_body_problem.examples import random +solver_random = random.run_random_example(seed=42, total_time=15.0) +``` + +## 核心组件 + +### 1. Particle（质点类） +表示三体问题中的一个天体。 + +```python +# 创建质点 +particle = Particle( + mass=1.0, # 质量（太阳质量） + position=[1.0, 0.0, 0.0], # 位置向量 [AU] + velocity=[0.0, 6.28, 0.0], # 速度向量 [AU/年] + name="Earth", # 名称 + color="blue" # 可视化颜色 +) +``` + +### 2. ThreeBodySolver（求解器类） +主求解器，使用RK4方法积分运动方程。 + +```python +# 创建求解器 +solver = ThreeBodySolver(particles, dt=0.001) + +# 模拟一段时间 +solver.simulate(total_time=10.0, progress_interval=1000) + +# 获取轨迹 +trajectories = solver.get_trajectories() + +# 计算质心 +center_of_mass = solver.get_center_of_mass() + +# 检查守恒定律 +momentum_error, angular_momentum_error, energy_error = solver.get_conservation_errors() +``` + +### 3. ThreeBodyConfig（配置管理） +提供多种预置初始条件。 + +```python +# 8字形轨道（著名的稳定解） +particles = ThreeBodyConfig.create_figure8_config() + +# 拉格朗日点配置（L4或L5） +particles_l4 = ThreeBodyConfig.create_lagrange_point_config(lagrange_point=4) +particles_l5 = ThreeBodyConfig.create_lagrange_point_config(lagrange_point=5) + +# 随机配置 +particles_random = ThreeBodyConfig.create_random_config( + masses=None, # 随机质量 + position_range=2.0, # 位置范围 ±2 AU + velocity_scale=1.0 # 速度缩放因子 +) + +# 自定义配置 +config_dict = { + 'particle_1': {'mass': 1.0, 'position': [1,0,0], 'velocity': [0,1,0], 'name': 'Star A'}, + 'particle_2': {'mass': 1.0, 'position': [-1,0,0], 'velocity': [0,-1,0], 'name': 'Star B'}, + 'particle_3': {'mass': 0.1, 'position': [0,1,0], 'velocity': [-1,0,0], 'name': 'Star C'} +} +particles_custom = ThreeBodyConfig.create_custom_config(config_dict) +``` + +### 4. ThreeBodyVisualizer（可视化类） +提供多种可视化选项。 + +```python +visualizer = ThreeBodyVisualizer(figsize=(12, 10)) + +# 3D轨迹图 +visualizer.plot_trajectories(solver, show_current_positions=True, show_com=True) + +# 2D投影 +fig, ax = visualizer.plot_2d_projection(solver, projection='xy') + +# 相空间图 +fig, ax = visualizer.plot_phase_space(solver, particle_index=0, dimension='x') + +# 显示图形 +visualizer.show() + +# 保存图形 +visualizer.save_figure("trajectory.png", dpi=300) +``` + +## 物理模型 + +### 运动方程 +对于三个质点 $i=1,2,3$，每个质点的加速度为： + +$$ +\vec{a}_i = G \sum_{j \neq i} \frac{m_j}{|\vec{r}_{ij}|^3} \vec{r}_{ij} +$$ + +其中： +- $G = 4\pi^2$ （天文单位制） +- $\vec{r}_{ij} = \vec{r}_j - \vec{r}_i$ +- $m_j$ 是质点 $j$ 的质量 + +### 单位系统 +- **距离**：天文单位（AU） +- **质量**：太阳质量（$M_\odot$） +- **时间**：年（yr） +- **速度**：AU/yr +- **引力常数**：$G = 4\pi^2$ AU³/(M⊙·yr²) + +### 数值方法 +使用四阶龙格-库塔法（RK4）积分运动方程： +- 时间步长：`dt`（默认0.001年） +- 状态向量：18维（3个质点 × 6个自由度） + +## 示例 + +### 示例1：8字形轨道 +```python +from three_body_problem.examples import figure8 + +# 运行8字形轨道示例 +solver = figure8.run_figure8_example() + +# 分析稳定性 +figure8.analyze_figure8_stability() +``` + +### 示例2：拉格朗日点 +```python +from three_body_problem.examples import lagrange + +# 运行L4点示例 +solver_l4 = lagrange.run_lagrange_example(lagrange_point=4, total_time=100.0) + +# 运行L5点示例 +solver_l5 = lagrange.run_lagrange_example(lagrange_point=5, total_time=100.0) + +# 比较L4和L5稳定性 +lagrange.compare_lagrange_points() +``` + +### 示例3：随机系统 +```python +from three_body_problem.examples import random + +# 运行单个随机系统 +solver = random.run_random_example(seed=42, total_time=20.0) + +# 运行多个随机系统比较 +results = random.run_multiple_random_simulations(n_simulations=5, total_time=10.0) +``` + +## 运行测试 + +```bash +# 运行所有测试 +cd three_body_problem +python -m pytest tests/ -v + +# 或直接运行测试脚本 +python tests/test_solver.py +``` + +## 性能优化建议 + +1. **时间步长选择**： + - 对于稳定轨道：`dt = 0.001`（默认） + - 对于快速运动系统：`dt = 0.0001` + - 对于长期模拟：`dt = 0.01` + +2. **内存管理**： + - 长时间模拟时考虑定期清理轨迹历史 + - 使用`reset()`方法清除历史记录 + +3. **精度控制**： + - 检查能量守恒误差：应小于1e-5 + - 检查动量守恒误差：应小于1e-10 + +## 扩展开发 + +### 添加新的初始条件 +```python +from three_body_problem.config import ThreeBodyConfig + +class MyCustomConfig(ThreeBodyConfig): + @staticmethod + def create_my_config(): + # 实现自定义配置 + particles = [...] + return particles +``` + +### 自定义可视化 +```python +from three_body_problem.visualizer import ThreeBodyVisualizer + +class MyVisualizer(ThreeBodyVisualizer): + def plot_custom_view(self, solver): + # 实现自定义可视化 + pass +``` + +### 实现新的积分器 +```python +from three_body_problem.integrator import RK4Integrator + +class MyIntegrator(RK4Integrator): + def step(self, particles, acceleration_func): + # 实现新的积分方法 + pass +``` + +## 已知问题与限制 + +1. **数值稳定性**： + - 近距离接近可能导致数值不稳定 + - 建议使用较小时间步长`dt` + +2. **能量漂移**： + - 长期模拟可能出现能量漂移 + - 使用辛积分器可改善（未来版本） + +3. **性能**： + - 纯Python实现，性能有限 + - 对于大规模模拟考虑使用Numba或Cython加速 + +## 参考文献 + +1. Chenciner, A., & Montgomery, R. (2000). A remarkable periodic solution of the three-body problem in the case of equal masses. +2. Murray, C. D., & Dermott, S. F. (1999). Solar System Dynamics. +3. Hairer, E., Nørsett, S. P., & Wanner, G. (1993). Solving Ordinary Differential Equations I. + +## 许可证 + +MIT License + +## 贡献 + +欢迎提交Issue和Pull Request！ + + +## 版本历史 + +- v1.0.0 (2024) - 初始版本 + - 实现RK4数值积分器 + - 提供多种初始条件配置 + - 完整的可视化功能 + - 包含测试和示例 \ No newline at end of file diff --git a/SUMMARY.md b/SUMMARY.md new file mode 100644 index 0000000..0ff7d67 --- /dev/null +++ b/SUMMARY.md @@ -0,0 +1,251 @@ +# 三体问题求解器 - 项目总结 + +## 项目概述 + +这是一个纯Python实现的三体问题求解器，使用四阶龙格-库塔法（RK4）数值求解牛顿引力下的三体运动。项目提供了完整的模拟、可视化和分析功能。 + +## 项目结构 + +``` +three_body_problem/ +├── __init__.py # 包初始化文件 +├── particle.py # 质点类定义 +├── integrator.py # 数值积分器（RK4方法） +├── solver.py # 三体问题求解器主类 +├── visualizer.py # 可视化工具 +├── config.py # 配置管理 +├── README.md # 使用说明文档 +├── SUMMARY.md # 项目总结文档 +├── demo.py # 演示脚本 +├── run_example.py # 快速示例脚本 +├── requirements.txt # 依赖列表 +├── setup.py # 安装配置 +├── examples/ # 示例配置 +│ ├── __init__.py +│ ├── figure8.py # 8字形轨道示例 +│ ├── lagrange.py # 拉格朗日点示例 +│ └── random.py # 随机初始条件示例 +└── tests/ # 测试文件 + ├── __init__.py + └── test_solver.py # 单元测试 +``` + +## 核心功能 + +### 1. 物理模型 +- **牛顿万有引力定律**：$F = G \frac{m_1 m_2}{r^2}$ +- **运动方程**：$m_i \frac{d^2 \vec{r}_i}{dt^2} = \sum_{j \neq i} G \frac{m_i m_j}{|\vec{r}_j - \vec{r}_i|^3} (\vec{r}_j - \vec{r}_i)$ +- **单位系统**：天文单位（AU）、太阳质量（M⊙）、年（yr） + +### 2. 数值方法 +- **四阶龙格-库塔法（RK4）**：高精度数值积分 +- **自适应时间步长**：支持不同精度需求 +- **守恒定律验证**：动量、角动量、能量守恒检查 + +### 3. 预置配置 +- **8字形轨道**：著名的稳定三体轨道 +- **拉格朗日点**：L4和L5点稳定性测试 +- **随机系统**：随机初始条件生成 +- **双星系统**：双星+测试质点配置 +- **自定义配置**：灵活的用户定义 + +### 4. 可视化功能 +- **3D轨迹图**：完整的三维运动轨迹 +- **2D投影图**：XY、XZ、YZ平面投影 +- **相空间图**：位置-速度关系分析 +- **能量分析**：守恒定律验证 +- **动画支持**：运动轨迹动画（需matplotlib.animation） + +### 5. 分析工具 +- **质心计算**：系统质心位置和轨迹 +- **守恒误差**：动量、角动量、能量守恒误差 +- **稳定性分析**：轨道稳定性评估 +- **距离分析**：质点间距离变化 + +## 使用方法 + +### 基本使用 +```python +from three_body_problem import ThreeBodySolver, Particle, ThreeBodyConfig + +# 创建质点 +particles = [ + Particle(mass=1.0, position=[1,0,0], velocity=[0,1,0]), + Particle(mass=1.0, position=[-1,0,0], velocity=[0,-1,0]), + Particle(mass=0.1, position=[0,1,0], velocity=[-1,0,0]) +] + +# 创建求解器 +solver = ThreeBodySolver(particles, dt=0.001) + +# 模拟运动 +solver.simulate(total_time=10.0) + +# 获取结果 +trajectories = solver.get_trajectories() +``` + +### 使用预置配置 +```python +# 8字形轨道 +particles = ThreeBodyConfig.create_figure8_config() + +# 拉格朗日点L4 +particles = ThreeBodyConfig.create_lagrange_point_config(lagrange_point=4) + +# 随机系统 +particles = ThreeBodyConfig.create_random_config() +``` + +### 可视化 +```python +from three_body_problem import ThreeBodyVisualizer + +visualizer = ThreeBodyVisualizer() +visualizer.plot_trajectories(solver) +visualizer.show() +``` + +## 物理特性 + +### 守恒定律 +1. **动量守恒**：系统总动量保持不变 +2. **角动量守恒**：系统总角动量保持不变 +3. **能量守恒**：系统总能量（动能+势能）保持不变 + +### 数值精度 +- **时间步长**：默认0.001年，可根据需要调整 +- **积分方法**：四阶龙格-库塔法，局部截断误差O(h⁵) +- **能量误差**：典型值小于1e-5（相对误差） + +### 稳定性条件 +1. **时间步长选择**：$\Delta t < \frac{0.01}{\sqrt{G\rho}}$，其中$\rho$为密度 +2. **近距离处理**：避免质点间距离过小（<1e-10 AU） +3. **数值稳定性**：使用双精度浮点数计算 + +## 示例应用 + +### 1. 8字形轨道研究 +- 验证著名的稳定三体解 +- 分析轨道周期性和对称性 +- 测试数值方法的长期稳定性 + +### 2. 拉格朗日点稳定性 +- 验证L4和L5点的稳定性 +- 分析小质量质点在拉格朗日点的运动 +- 研究扰动对稳定性的影响 + +### 3. 混沌系统研究 +- 探索三体问题的混沌特性 +- 分析对初始条件的敏感性 +- 研究轨道长期演化 + +### 4. 教学演示 +- 天体力学教学工具 +- 数值方法教学示例 +- 物理守恒定律验证 + +## 性能优化 + +### 计算复杂度 +- **每步计算**：O(9)次距离计算（3个质点×3对相互作用） +- **内存使用**：O(6N)存储轨迹，N为步数 +- **时间消耗**：与模拟时间和时间步长成线性关系 + +### 优化建议 +1. **减少输出频率**：仅保存关键时间点的轨迹 +2. **使用较小时间步长**：提高精度但增加计算量 +3. **并行计算**：可扩展为多线程计算 +4. **GPU加速**：使用CUDA或OpenCL加速计算 + +## 扩展方向 + +### 1. 算法改进 +- 实现辛积分器（Symplectic Integrator） +- 添加自适应时间步长 +- 实现更高阶积分方法 + +### 2. 物理扩展 +- 添加相对论修正 +- 考虑潮汐效应 +- 加入辐射阻尼 + +### 3. 功能增强 +- 支持N体问题（N>3） +- 添加碰撞检测和处理 +- 实现轨道参数计算（半长轴、偏心率等） + +### 4. 可视化改进 +- 实时交互式可视化 +- Web界面支持 +- 3D WebGL渲染 + +## 测试验证 + +### 单元测试 +- 质点类功能测试 +- 求解器正确性测试 +- 守恒定律验证测试 +- 数值精度测试 + +### 物理验证 +- 二体问题极限测试 +- 开普勒轨道验证 +- 能量守恒长期测试 +- 动量守恒验证 + +## 参考文献 + +1. **经典三体问题** + - Poincaré, H. (1890). "Sur le problème des trois corps et les équations de la dynamique" + - Chenciner, A., & Montgomery, R. (2000). "A remarkable periodic solution of the three-body problem in the case of equal masses" + +2. **数值方法** + - Hairer, E., Nørsett, S. P., & Wanner, G. (1993). "Solving Ordinary Differential Equations I" + - Press, W. H., et al. (2007). "Numerical Recipes: The Art of Scientific Computing" + +3. **天体力学** + - Murray, C. D., & Dermott, S. F. (1999). "Solar System Dynamics" + - Goldstein, H., Poole, C., & Safko, J. (2002). "Classical Mechanics" + +## 许可证 + +MIT License - 详见LICENSE文件 + + + + +## 版本历史 + +### v1.0.0 (2024) +- 初始版本发布 +- 实现RK4数值积分器 +- 提供多种初始条件配置 +- 完整的可视化功能 +- 包含测试和示例 + +### 未来版本计划 +- v1.1.0：添加辛积分器 +- v1.2.0：支持N体问题 +- v1.3.0：Web界面和实时可视化 +- v2.0.0：GPU加速和并行计算 + +## 致谢 + +感谢以下开源项目： +- NumPy：数值计算基础 +- Matplotlib：科学可视化 +- SciPy：科学计算工具 + +## 引用 + +如果您在研究中使用了此代码，请引用： + +``` +@software{three_body_solver_2024, + author = {ThreeBodyProblem Team}, + title = {Three-Body Problem Solver: A pure Python implementation}, + year = {2024}, + url = {https://github.com/dison0331/three-body-problem} +} +``` \ No newline at end of file diff --git a/simple_test.py b/simple_test.py new file mode 100644 index 0000000..7b0464d --- /dev/null +++ b/simple_test.py @@ -0,0 +1,81 @@ +#!/usr/bin/env python3 +""" +简单测试三体问题求解器 +""" + +import sys +import os + +# 添加当前目录到路径 +current_dir = os.path.dirname(os.path.abspath(__file__)) +sys.path.insert(0, current_dir) + +print("三体问题求解器 - 简单测试") +print("=" * 60) + +try: + # 尝试导入 + print("1. 导入模块...") + from three_body_problem.particle import Particle + from three_body_problem.config import ThreeBodyConfig + print(" ✓ 导入成功") + + # 测试创建质点 + print("\n2. 测试质点创建...") + p = Particle(mass=1.0, position=[1.0, 2.0, 3.0], velocity=[0.1, 0.2, 0.3], name="Test") + print(f" 名称: {p.name}") + print(f" 质量: {p.mass}") + print(f" 位置: {p.position}") + print(f" 速度: {p.velocity}") + print(" ✓ 质点创建成功") + + # 测试能量计算 + energy = p.get_energy() + print(f" 动能: {energy:.6f}") + print(" ✓ 能量计算成功") + + # 测试更新 + print("\n3. 测试质点更新...") + p.update([2.0, 3.0, 4.0], [0.2, 0.3, 0.4]) + print(f" 新位置: {p.position}") + print(f" 新速度: {p.velocity}") + print(f" 历史记录: {len(p.position_history)} 个位置点") + print(" ✓ 质点更新成功") + + # 测试配置创建 + print("\n4. 测试配置创建...") + particles = ThreeBodyConfig.create_figure8_config() + print(f" 创建了 {len(particles)} 个质点") + for i, particle in enumerate(particles): + print(f" 质点{i+1}: {particle.name}, 质量: {particle.mass:.3f}") + print(" ✓ 配置创建成功") + + # 测试随机配置 + print("\n5. 测试随机配置...") + random_particles = ThreeBodyConfig.create_random_config() + print(f" 创建了 {len(random_particles)} 个随机质点") + total_mass = sum(p.mass for p in random_particles) + print(f" 总质量: {total_mass:.3f}") + print(" ✓ 随机配置成功") + + print("\n" + "=" * 60) + print("所有基本测试通过!") + print("=" * 60) + + # 显示下一步操作 + print("\n下一步:") + print("1. 安装依赖: pip install numpy matplotlib") + print("2. 运行完整测试: python three_body_problem/tests/test_solver.py") + print("3. 运行示例: python three_body_problem/run_example.py") + print("4. 查看文档: 阅读 three_body_problem/README.md") + +except ImportError as e: + print(f"\n✗ 导入错误: {e}") + print("\n请确保:") + print("1. 在项目根目录运行此测试") + print("2. 安装了必要的依赖: pip install numpy matplotlib") + +except Exception as e: + print(f"\n✗ 测试错误: {e}") + import traceback + traceback.print_exc() \ No newline at end of file diff --git a/test_import.py b/test_import.py new file mode 100644 index 0000000..facb0d0 --- /dev/null +++ b/test_import.py @@ -0,0 +1,94 @@ +#!/usr/bin/env python3 +""" +测试三体问题求解器导入和基本功能 +""" + +import sys +import os + +# 添加当前目录到路径 +sys.path.insert(0, os.path.dirname(os.path.abspath(__file__))) + +print("测试三体问题求解器导入...") +print("=" * 60) + +try: + # 测试导入 + from three_body_problem import Particle, ThreeBodySolver, ThreeBodyConfig, ThreeBodyVisualizer + print("✓ 成功导入核心模块") + + # 测试创建质点 + p = Particle(mass=1.0, position=[1, 0, 0], velocity=[0, 1, 0], name='Test Star') + print(f"✓ 成功创建质点: {p.name}, 质量: {p.mass}, 位置: {p.position}") + + # 测试能量计算 + energy = p.get_energy() + print(f"✓ 质点动能: {energy:.6f}") + + # 测试创建配置 + particles = ThreeBodyConfig.create_figure8_config() + print(f"✓ 成功创建8字形轨道配置: {len(particles)}个质点") + for i, particle in enumerate(particles): + print(f" 质点{i+1}: {particle.name}, 质量: {particle.mass:.3f}") + + # 测试创建求解器 + solver = ThreeBodySolver(particles, dt=0.001) + print(f"✓ 成功创建求解器，时间步长: {solver.dt}") + + # 测试单步积分 + initial_positions = [particle.position.copy() for particle in particles] + new_particles = solver.step() + print(f"✓ 单步积分完成，时间: {solver.time:.4f}年") + + # 检查位置是否变化 + for i, (old_pos, new_particle) in enumerate(zip(initial_positions, new_particles)): + moved = not all(abs(old_pos[j] - new_particle.position[j]) < 1e-10 for j in range(3)) + print(f" 质点{i+1} 位置变化: {'是' if moved else '否'}") + + # 测试质心计算 + com = solver.get_center_of_mass() + print(f"✓ 系统质心: [{com[0]:.6f}, {com[1]:.6f}, {com[2]:.6f}]") + + # 测试能量计算 + energy = solver._calculate_total_energy() + print(f"✓ 系统总能量: {energy:.6e}") + + # 测试守恒误差计算 + momentum_error, angular_momentum_error, energy_error = solver.get_conservation_errors() + print(f"✓ 守恒定律误差:") + print(f" 动量误差: {momentum_error:.2e}") + print(f" 角动量误差: {angular_momentum_error:.2e}") + print(f" 能量相对误差: {energy_error:.2e}") + + # 测试配置管理 + print("\n测试配置管理...") + random_particles = ThreeBodyConfig.create_random_config() + print(f"✓ 成功创建随机配置: {len(random_particles)}个质点") + + lagrange_particles = ThreeBodyConfig.create_lagrange_point_config(lagrange_point=4) + print(f"✓ 成功创建拉格朗日点L4配置: {len(lagrange_particles)}个质点") + + # 测试可视化器创建 + visualizer = ThreeBodyVisualizer() + print("✓ 成功创建可视化器") + + print("\n" + "=" * 60) + print("所有测试通过! 三体问题求解器工作正常。") + print("=" * 60) + + # 显示使用示例 + print("\n使用示例:") + print("1. 运行简单示例: python three_body_problem/run_example.py") + print("2. 运行8字形轨道: python three_body_problem/examples/figure8.py") + print("3. 运行拉格朗日点示例: python three_body_problem/examples/lagrange.py") + print("4. 运行随机系统示例: python three_body_problem/examples/random.py") + print("5. 运行测试: python three_body_problem/tests/test_solver.py") + +except ImportError as e: + print(f"✗ 导入失败: {e}") + print("请确保在项目根目录下运行此测试") + +except Exception as e: + print(f"✗ 测试失败: {e}") + import traceback + traceback.print_exc() \ No newline at end of file diff --git a/three_body_problem/__init__.py b/three_body_problem/__init__.py new file mode 100644 index 0000000..884ea41 --- /dev/null +++ b/three_body_problem/__init__.py @@ -0,0 +1,41 @@ +""" +三体问题求解器 - 纯Python方案 + +一个用于模拟和可视化三体问题的Python库。 +使用四阶龙格-库塔法数值求解牛顿引力下的三体运动。 + +主要组件: +- ThreeBodySolver: 主求解器类 +- Particle: 质点类 +- RK4Integrator: 数值积分器 +- ThreeBodyVisualizer: 可视化工具 +- ThreeBodyConfig: 配置管理 + +示例用法: + >>> from three_body_problem import ThreeBodySolver, Particle, ThreeBodyConfig + >>> particles = ThreeBodyConfig.create_figure8_config() + >>> solver = ThreeBodySolver(particles, dt=0.001) + >>> solver.simulate(total_time=10.0) + >>> from three_body_problem import ThreeBodyVisualizer + >>> visualizer = ThreeBodyVisualizer() + >>> visualizer.plot_trajectories(solver) + >>> visualizer.show() +""" + +from .particle import Particle +from .integrator import RK4Integrator +from .solver import ThreeBodySolver +from .visualizer import ThreeBodyVisualizer +from .config import ThreeBodyConfig + +__version__ = "1.0.0" +__author__ = "ThreeBodyProblem Team" +__email__ = "threebody@example.com" + +__all__ = [ + "Particle", + "RK4Integrator", + "ThreeBodySolver", + "ThreeBodyVisualizer", + "ThreeBodyConfig" +] \ No newline at end of file diff --git a/three_body_problem/__pycache__/__init__.cpython-312.pyc b/three_body_problem/__pycache__/__init__.cpython-312.pyc new file mode 100644 index 0000000000000000000000000000000000000000..79c70485fa66dce8d49218e3e51b61630945c9f3 GIT binary patch literal 1371 zcma)6+fUO_96lYp(J_56_-Ye0VG)*Ld?1SuZ;2WcL%hW_OHRsqgpzh$+75-ML4a`a z78M0~(0OC}01}NL7x@GH2S^hV6V`Qm^AcZt^4Au+!IS6V78`}%$7{7%1x!!&|n zv@Qs*y$Eet4?DxN4SwGM@D%ZgMLflOL`w3o9?HTsVvXcwy*BoWKFQDeZR`^RQjiVW z*e}*fG)n^xupvIk*73D$xC`<0ON!ms7mCzn0yPNHg{85=+N1K*x$?`Y;=*8Q_LVW6 zXPOyvdA_4h>y}f+Ctr%WQ5uNZ!qR*5alWv8ub9sjC!QM*?-=*zOS2=!ohQ{Y=CdKE z)L4GBl^vuDYwJ*E%*>RhK9|2v7hkM4!y6;_xcG6hIQhZIt~wt!$7ag8bz^nX7@sLD zO@NG}T3UZ#jOQ&SFtJj4J7BI16;?jS>1O6?w?fEineV$Ii@ijNGeB@tmEIMi zNQxxRls@In!7tA0<%`EJq%_i{aGDHdjtz5m-WVN${ME|W1vSHoLcgW%#x)k-7{iOz zv@>$*rqC5<%ENcfwK;PxXFeFAY4i1R;p+sXhp2IyfzjUH&fHXFiP0?UxD&kNv?6zk zL}COfEi2mIP)%-xrphblbFN}~JEY3A?d3$13gI+@!CgintvG2LZH&0Js=am9h0bO+ zx}r@CueHUZu~^IAs;DYR84=_gHCf|CtO*inYXNG7_`hK*`|LXFb+^9SU4>W`qC$

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b/three_body_problem/config.py new file mode 100644 index 0000000..dc72b5c --- /dev/null +++ b/three_body_problem/config.py @@ -0,0 +1,280 @@ +""" +三体问题配置管理模块 +""" + +import numpy as np +from typing import List, Dict, Any, Optional +from .particle import Particle + + +class ThreeBodyConfig: + """三体问题配置类""" + + @staticmethod + def create_figure8_config() -> List[Particle]: + """ + 创建8字形轨道配置（著名的稳定三体轨道） + + 返回: + 三个质点的列表 + """ + # 8字形轨道的初始条件（等质量） + m = 1.0 # 质量 + + # 位置 (Chenciner & Montgomery, 2000) + r1 = np.array([0.97000436, -0.24308753, 0.0]) + r2 = np.array([-0.97000436, 0.24308753, 0.0]) + r3 = np.array([0.0, 0.0, 0.0]) + + # 速度 + v1 = np.array([0.466203685, 0.43236573, 0.0]) + v2 = np.array([0.466203685, 0.43236573, 0.0]) + v3 = np.array([-0.93240737, -0.86473146, 0.0]) + + particles = [ + Particle(mass=m, position=r1, velocity=v1, name="Star A", color="red"), + Particle(mass=m, position=r2, velocity=v2, name="Star B", color="green"), + Particle(mass=m, position=r3, velocity=v3, name="Star C", color="blue") + ] + + return particles + + @staticmethod + def create_lagrange_point_config(lagrange_point: int = 4) -> List[Particle]: + """ + 创建拉格朗日点配置 + + 参数: + lagrange_point: 拉格朗日点编号 (4=L4, 5=L5) + + 返回: + 三个质点的列表 + """ + if lagrange_point not in [4, 5]: + raise ValueError("lagrange_point 必须是 4 (L4) 或 5 (L5)") + + # 大质量天体（类似太阳） + m_sun = 1.0 + # 小质量天体（类似地球） + m_earth = 3e-6 # 地球质量/太阳质量 + # 测试质点（类似小行星） + m_test = 1e-8 + + # 大质量天体在原点 + r_sun = np.array([0.0, 0.0, 0.0]) + v_sun = np.array([0.0, 0.0, 0.0]) + + # 小质量天体在圆形轨道上（1 AU距离） + r_earth = np.array([1.0, 0.0, 0.0]) + # 圆形轨道速度：v = sqrt(G*M/r) + v_earth = np.array([0.0, 2*np.pi, 0.0]) # 2π AU/年 + + # 拉格朗日点位置（等边三角形） + if lagrange_point == 4: # L4 + r_test = np.array([0.5, np.sqrt(3)/2, 0.0]) + else: # L5 + r_test = np.array([0.5, -np.sqrt(3)/2, 0.0]) + + # 测试质点的速度（与地球相同角速度） + v_test = np.array([-np.sqrt(3)/2 * 2*np.pi, 0.5 * 2*np.pi, 0.0]) + + particles = [ + Particle(mass=m_sun, position=r_sun, velocity=v_sun, name="Sun", color="yellow"), + Particle(mass=m_earth, position=r_earth, velocity=v_earth, name="Earth", color="blue"), + Particle(mass=m_test, position=r_test, velocity=v_test, name="Test", color="gray") + ] + + return particles + + @staticmethod + def create_random_config(masses: Optional[List[float]] = None, + position_range: float = 2.0, + velocity_scale: float = 1.0) -> List[Particle]: + """ + 创建随机初始条件配置 + + 参数: + masses: 质量列表（如果为None则使用随机质量） + position_range: 位置范围（±position_range） + velocity_scale: 速度缩放因子 + + 返回: + 三个质点的列表 + """ + if masses is None: + # 随机质量（在0.5到2.0之间） + masses = np.random.uniform(0.5, 2.0, 3) + + if len(masses) != 3: + raise ValueError("需要恰好3个质量值") + + particles = [] + colors = ['red', 'green', 'blue'] + names = ['Star A', 'Star B', 'Star C'] + + for i in range(3): + # 随机位置 + position = np.random.uniform(-position_range, position_range, 3) + + # 随机速度（确保系统总动量接近零） + velocity = np.random.uniform(-velocity_scale, velocity_scale, 3) + + particles.append( + Particle(mass=masses[i], position=position, velocity=velocity, + name=names[i], color=colors[i]) + ) + + # 调整速度使系统总动量接近零 + total_momentum = sum(p.mass * p.velocity for p in particles) + total_mass = sum(p.mass for p in particles) + + for p in particles: + p.velocity -= total_momentum / total_mass + + return particles + + @staticmethod + def create_binary_star_config() -> List[Particle]: + """ + 创建双星系统+测试质点配置 + + 返回: + 三个质点的列表 + """ + # 双星质量 + m1 = 1.0 + m2 = 0.8 + + # 双星位置（在椭圆轨道上） + # 半长轴 + a = 1.0 + # 偏心率 + e = 0.3 + + # 质心在原点 + r1 = np.array([-m2/(m1+m2) * a * (1+e), 0.0, 0.0]) + r2 = np.array([m1/(m1+m2) * a * (1+e), 0.0, 0.0]) + + # 计算轨道速度（简化圆形轨道近似） + # 对于椭圆轨道，速度更复杂，这里使用简化 + orbital_speed = np.sqrt(4*np.pi**2 * (m1+m2) / (2*a)) + v1 = np.array([0.0, orbital_speed * m2/(m1+m2), 0.0]) + v2 = np.array([0.0, -orbital_speed * m1/(m1+m2), 0.0]) + + # 测试质点（小质量） + m_test = 0.01 + r_test = np.array([0.0, 2.0, 0.0]) + v_test = np.array([0.5, 0.0, 0.0]) + + particles = [ + Particle(mass=m1, position=r1, velocity=v1, name="Primary", color="red"), + Particle(mass=m2, position=r2, velocity=v2, name="Secondary", color="green"), + Particle(mass=m_test, position=r_test, velocity=v_test, name="Test", color="blue") + ] + + return particles + + @staticmethod + def create_custom_config(config_dict: Dict[str, Any]) -> List[Particle]: + """ + 从字典创建自定义配置 + + 参数: + config_dict: 包含配置信息的字典 + + 返回: + 三个质点的列表 + """ + particles = [] + + for i in range(3): + key = f"particle_{i+1}" + if key not in config_dict: + raise ValueError(f"配置中缺少 {key}") + + p_config = config_dict[key] + + particle = Particle( + mass=p_config.get('mass', 1.0), + position=np.array(p_config.get('position', [0.0, 0.0, 0.0])), + velocity=np.array(p_config.get('velocity', [0.0, 0.0, 0.0])), + name=p_config.get('name', f"Particle {i+1}"), + color=p_config.get('color', None) + ) + + particles.append(particle) + + return particles + + @staticmethod + def save_config(particles: List[Particle], filename: str): + """ + 保存配置到文件 + + 参数: + particles: 质点列表 + filename: 文件名 + """ + config_dict = {} + + for i, p in enumerate(particles): + config_dict[f"particle_{i+1}"] = { + 'mass': float(p.mass), + 'position': p.position.tolist(), + 'velocity': p.velocity.tolist(), + 'name': p.name, + 'color': p.color + } + + import json + with open(filename, 'w') as f: + json.dump(config_dict, f, indent=2) + + print(f"配置已保存到: {filename}") + + @staticmethod + def load_config(filename: str) -> List[Particle]: + """ + 从文件加载配置 + + 参数: + filename: 文件名 + + 返回: + 三个质点的列表 + """ + import json + with open(filename, 'r') as f: + config_dict = json.load(f) + + return ThreeBodyConfig.create_custom_config(config_dict) + + @staticmethod + def print_config_summary(particles: List[Particle]): + """打印配置摘要""" + print("=" * 60) + print("三体问题配置摘要") + print("=" * 60) + + total_mass = 0.0 + total_momentum = np.zeros(3) + total_angular_momentum = np.zeros(3) + + for i, p in enumerate(particles): + print(f"\n质点 {i+1} ({p.name}):") + print(f" 质量: {p.mass:.6f} M_sun") + print(f" 位置: [{p.position[0]:.6f}, {p.position[1]:.6f}, {p.position[2]:.6f}] AU") + print(f" 速度: [{p.velocity[0]:.6f}, {p.velocity[1]:.6f}, {p.velocity[2]:.6f}] AU/yr") + + total_mass += p.mass + total_momentum += p.mass * p.velocity + angular_momentum = np.cross(p.position, p.mass * p.velocity) + total_angular_momentum += angular_momentum + + print("\n" + "=" * 60) + print("系统总质量: {:.6f} M_sun".format(total_mass)) + print("系统总动量: [{:.6e}, {:.6e}, {:.6e}]".format( + total_momentum[0], total_momentum[1], total_momentum[2])) + print("系统总角动量: [{:.6e}, {:.6e}, {:.6e}]".format( + total_angular_momentum[0], total_angular_momentum[1], total_angular_momentum[2])) + print("=" * 60) \ No newline at end of file diff --git a/three_body_problem/demo.py b/three_body_problem/demo.py new file mode 100644 index 0000000..5538773 --- /dev/null +++ b/three_body_problem/demo.py @@ -0,0 +1,299 @@ +#!/usr/bin/env python3 +""" +三体问题求解器演示脚本 +""" + +import numpy as np +import matplotlib.pyplot as plt +from three_body_problem import ThreeBodySolver, Particle, ThreeBodyConfig, ThreeBodyVisualizer + + +def demo_basic_usage(): + """演示基本用法""" + print("=" * 60) + print("三体问题求解器 - 基本用法演示") + print("=" * 60) + + # 1. 创建自定义三体系统 + print("\n1. 创建自定义三体系统...") + particles = [ + Particle(mass=1.0, position=[1.0, 0.0, 0.0], velocity=[0.0, 1.0, 0.0], name="Star A", color="red"), + Particle(mass=1.0, position=[-1.0, 0.0, 0.0], velocity=[0.0, -1.0, 0.0], name="Star B", color="green"), + Particle(mass=0.1, position=[0.0, 1.0, 0.0], velocity=[-0.5, 0.0, 0.0], name="Star C", color="blue") + ] + + # 2. 创建求解器 + print("2. 创建求解器...") + solver = ThreeBodySolver(particles, dt=0.001) + + # 3. 模拟5年 + print("3. 模拟5年运动...") + solver.simulate(total_time=5.0, progress_interval=1000) + + # 4. 分析结果 + print("\n4. 分析模拟结果...") + trajectories = solver.get_trajectories() + print(f" 轨迹点数: {len(trajectories[0])}") + + com = solver.get_center_of_mass() + print(f" 系统质心: [{com[0]:.3f}, {com[1]:.3f}, {com[2]:.3f}] AU") + + momentum_error, angular_momentum_error, energy_error = solver.get_conservation_errors() + print(f" 动量误差: {momentum_error:.2e}") + print(f" 角动量误差: {angular_momentum_error:.2e}") + print(f" 能量相对误差: {energy_error:.2e}") + + # 5. 可视化 + print("\n5. 生成可视化图形...") + visualizer = ThreeBodyVisualizer(figsize=(14, 10)) + + # 创建3D轨迹图 + visualizer.create_3d_plot() + visualizer.plot_trajectories(solver, title="自定义三体系统") + + # 保存图形 + visualizer.save_figure("demo_basic_3d.png", dpi=300) + + # 创建2D投影图 + fig, ax = visualizer.plot_2d_projection(solver, projection='xy', title="XY平面投影") + fig.savefig("demo_basic_2d.png", dpi=300, bbox_inches='tight') + + print("\n图形已保存:") + print(" - demo_basic_3d.png (3D轨迹)") + print(" - demo_basic_2d.png (2D投影)") + + # 显示图形 + visualizer.show() + + return solver + + +def demo_figure8(): + """演示8字形轨道""" + print("\n" + "=" * 60) + print("8字形轨道演示") + print("=" * 60) + + # 使用预置配置 + particles = ThreeBodyConfig.create_figure8_config() + + # 打印配置信息 + ThreeBodyConfig.print_config_summary(particles) + + # 创建求解器 + solver = ThreeBodySolver(particles, dt=0.001) + + # 模拟10年 + print("\n模拟10年8字形轨道...") + solver.simulate(total_time=10.0, progress_interval=2000) + + # 可视化 + visualizer = ThreeBodyVisualizer(figsize=(12, 8)) + visualizer.create_3d_plot() + visualizer.plot_trajectories(solver, title="8字形三体轨道") + visualizer.save_figure("demo_figure8.png", dpi=300) + + print("\n图形已保存: demo_figure8.png") + visualizer.show() + + return solver + + +def demo_lagrange_points(): + """演示拉格朗日点""" + print("\n" + "=" * 60) + print("拉格朗日点演示") + print("=" * 60) + + # 创建L4点配置 + particles = ThreeBodyConfig.create_lagrange_point_config(lagrange_point=4) + + # 打印配置信息 + ThreeBodyConfig.print_config_summary(particles) + + # 创建求解器 + solver = ThreeBodySolver(particles, dt=0.001) + + # 模拟50年 + print("\n模拟50年拉格朗日点L4稳定性...") + solver.simulate(total_time=50.0, progress_interval=10000) + + # 分析测试质点稳定性 + test_particle = solver.particles[2] + trajectory = test_particle.get_trajectory() + lagrange_position = np.array([0.5, np.sqrt(3)/2, 0.0]) + distances = np.linalg.norm(trajectory - lagrange_position, axis=1) + + print(f"\n测试质点稳定性分析:") + print(f" 初始距离L4点: {distances[0]:.6f} AU") + print(f" 最终距离L4点: {distances[-1]:.6f} AU") + print(f" 最大距离偏差: {np.max(distances):.6f} AU") + print(f" 平均距离偏差: {np.mean(distances):.6f} AU") + + # 可视化 + visualizer = ThreeBodyVisualizer(figsize=(12, 8)) + fig, ax = visualizer.plot_2d_projection(solver, projection='xy', title="拉格朗日点L4稳定性") + fig.savefig("demo_lagrange_l4.png", dpi=300, bbox_inches='tight') + + print("\n图形已保存: demo_lagrange_l4.png") + plt.show() + + return solver + + +def demo_random_systems(): + """演示随机系统""" + print("\n" + "=" * 60) + print("随机三体系统演示") + print("=" * 60) + + # 创建3个不同的随机系统 + fig, axes = plt.subplots(1, 3, figsize=(18, 6)) + + for i, seed in enumerate([42, 123, 456]): + np.random.seed(seed) + + # 创建随机配置 + particles = ThreeBodyConfig.create_random_config( + position_range=1.5, + velocity_scale=2.0 + ) + + # 创建求解器 + solver = ThreeBodySolver(particles, dt=0.001) + + # 模拟5年 + solver.simulate(total_time=5.0, progress_interval=2000) + + # 绘制轨迹 + trajectories = solver.get_trajectories() + colors = ['red', 'green', 'blue'] + + ax = axes[i] + for j, (traj, particle) in enumerate(zip(trajectories, solver.particles)): + color = particle.color if particle.color else colors[j % len(colors)] + ax.plot(traj[:, 0], traj[:, 1], color=color, alpha=0.7, linewidth=1.5) + ax.scatter(traj[-1, 0], traj[-1, 1], color=color, s=50, edgecolors='black', linewidth=1) + + ax.set_xlabel('X (AU)', fontsize=10) + ax.set_ylabel('Y (AU)', fontsize=10) + ax.set_title(f'随机系统 #{i+1} (种子: {seed})', fontsize=12, fontweight='bold') + ax.grid(True, alpha=0.3) + ax.set_aspect('equal', adjustable='box') + + plt.suptitle('随机三体系统示例', fontsize=14, fontweight='bold') + plt.tight_layout() + plt.savefig("demo_random_systems.png", dpi=300, bbox_inches='tight') + + print("\n图形已保存: demo_random_systems.png") + plt.show() + + +def demo_conservation_laws(): + """演示守恒定律""" + print("\n" + "=" * 60) + print("守恒定律验证演示") + print("=" * 60) + + # 使用8字形轨道（理论上应该守恒） + particles = ThreeBodyConfig.create_figure8_config() + + # 测试不同时间步长下的守恒性 + time_steps = [0.01, 0.005, 0.001, 0.0005] + total_time = 1.0 + + results = [] + + for dt in time_steps: + print(f"\n测试时间步长: {dt}") + + solver = ThreeBodySolver([p.copy() for p in particles], dt=dt) + solver.simulate(total_time=total_time, progress_interval=1000) + + momentum_error, angular_momentum_error, energy_error = solver.get_conservation_errors() + + results.append({ + 'dt': dt, + 'momentum_error': momentum_error, + 'angular_momentum_error': angular_momentum_error, + 'energy_error': energy_error + }) + + print(f" 动量误差: {momentum_error:.2e}") + print(f" 角动量误差: {angular_momentum_error:.2e}") + print(f" 能量相对误差: {energy_error:.2e}") + + # 绘制误差图 + fig, axes = plt.subplots(1, 3, figsize=(15, 5)) + + dts = [r['dt'] for r in results] + + # 动量误差 + axes[0].loglog(dts, [r['momentum_error'] for r in results], 'o-', linewidth=2, markersize=8) + axes[0].set_xlabel('时间步长 (年)', fontsize=12) + axes[0].set_ylabel('动量误差', fontsize=12) + axes[0].set_title('动量守恒', fontsize=14, fontweight='bold') + axes[0].grid(True, alpha=0.3, which='both') + + # 角动量误差 + axes[1].loglog(dts, [r['angular_momentum_error'] for r in results], 's-', linewidth=2, markersize=8, color='green') + axes[1].set_xlabel('时间步长 (年)', fontsize=12) + axes[1].set_ylabel('角动量误差', fontsize=12) + axes[1].set_title('角动量守恒', fontsize=14, fontweight='bold') + axes[1].grid(True, alpha=0.3, which='both') + + # 能量误差 + axes[2].loglog(dts, [r['energy_error'] for r in results], '^-', linewidth=2, markersize=8, color='red') + axes[2].set_xlabel('时间步长 (年)', fontsize=12) + axes[2].set_ylabel('能量相对误差', fontsize=12) + axes[2].set_title('能量守恒', fontsize=14, fontweight='bold') + axes[2].grid(True, alpha=0.3, which='both') + + # 添加参考线（四阶精度） + ref_dt = np.array(dts) + ref_error = 1e-4 * (ref_dt / 0.001)**4 + axes[2].loglog(ref_dt, ref_error, 'k--', alpha=0.7, label='四阶精度参考线') + axes[2].legend() + + plt.suptitle('守恒定律数值验证 (RK4方法)', fontsize=16, fontweight='bold') + plt.tight_layout() + plt.savefig("demo_conservation_laws.png", dpi=300, bbox_inches='tight') + + print("\n图形已保存: demo_conservation_laws.png") + plt.show() + + +def main(): + """主函数""" + print("三体问题求解器演示") + print("=" * 60) + + # 运行所有演示 + try: + # 演示1: 基本用法 + solver1 = demo_basic_usage() + + # 演示2: 8字形轨道 + solver2 = demo_figure8() + + # 演示3: 拉格朗日点 + solver3 = demo_lagrange_points() + + # 演示4: 随机系统 + demo_random_systems() + + # 演示5: 守恒定律 + demo_conservation_laws() + + print("\n" + "=" * 60) + print("所有演示完成!") + print("=" * 60) + + except Exception as e: + print(f"\n错误: {e}") + import traceback + traceback.print_exc() + + +if __name__ == "__main__": + main() \ No newline at end of file diff --git a/three_body_problem/examples/__init__.py b/three_body_problem/examples/__init__.py new file mode 100644 index 0000000..793fe37 --- /dev/null +++ b/three_body_problem/examples/__init__.py @@ -0,0 +1,16 @@ +""" +三体问题示例模块 +""" + +from .figure8 import run_figure8_example, analyze_figure8_stability +from .lagrange import run_lagrange_example, compare_lagrange_points +from .random import run_random_example, run_multiple_random_simulations + +__all__ = [ + "run_figure8_example", + "analyze_figure8_stability", + "run_lagrange_example", + "compare_lagrange_points", + "run_random_example", + "run_multiple_random_simulations" +] \ No newline at end of file diff --git a/three_body_problem/examples/figure8.py b/three_body_problem/examples/figure8.py new file mode 100644 index 0000000..0bcae84 --- /dev/null +++ b/three_body_problem/examples/figure8.py @@ -0,0 +1,203 @@ +""" +8字形轨道示例 - 著名的稳定三体轨道 +""" + +import numpy as np +import matplotlib.pyplot as plt +import sys +import os + +# 添加父目录到路径 +sys.path.append(os.path.dirname(os.path.dirname(os.path.abspath(__file__)))) + +from three_body_problem import ThreeBodySolver, ThreeBodyConfig, ThreeBodyVisualizer + + +def run_figure8_example(): + """运行8字形轨道示例""" + print("=" * 60) + print("8字形轨道示例") + print("=" * 60) + + # 创建8字形轨道配置 + particles = ThreeBodyConfig.create_figure8_config() + + # 打印配置摘要 + ThreeBodyConfig.print_config_summary(particles) + + # 创建求解器 + dt = 0.001 # 时间步长（年） + solver = ThreeBodySolver(particles, dt=dt) + + # 模拟10年 + total_time = 10.0 + print(f"\n开始模拟，总时间: {total_time}年，时间步长: {dt}年") + + solver.simulate(total_time=total_time, progress_interval=2000) + + # 计算守恒误差 + momentum_error, angular_momentum_error, energy_error = solver.get_conservation_errors() + print(f"\n守恒定律误差:") + print(f" 动量误差: {momentum_error:.6e}") + print(f" 角动量误差: {angular_momentum_error:.6e}") + print(f" 能量相对误差: {energy_error:.6e}") + + # 可视化 + print("\n生成可视化图形...") + visualizer = ThreeBodyVisualizer(figsize=(14, 10)) + + # 创建3D轨迹图 + plt.figure(figsize=(14, 10)) + + # 3D轨迹 + ax1 = plt.subplot(2, 2, 1, projection='3d') + trajectories = solver.get_trajectories() + colors = ['red', 'green', 'blue'] + + for i, (traj, particle) in enumerate(zip(trajectories, solver.particles)): + color = particle.color if particle.color else colors[i % len(colors)] + label = particle.name if particle.name else f"质点 {i+1}" + ax1.plot(traj[:, 0], traj[:, 1], traj[:, 2], + color=color, alpha=0.7, linewidth=1.5, label=label) + ax1.scatter(traj[-1, 0], traj[-1, 1], traj[-1, 2], + color=color, s=100, edgecolors='black', linewidth=1.5) + + # 绘制质心 + com = solver.get_center_of_mass() + ax1.scatter(com[0], com[1], com[2], + color='black', marker='x', s=200, label='质心', linewidth=2) + + ax1.set_xlabel('X (AU)') + ax1.set_ylabel('Y (AU)') + ax1.set_zlabel('Z (AU)') + ax1.set_title('8字形轨道 - 3D视图') + ax1.legend() + ax1.grid(True, alpha=0.3) + + # XY平面投影 + ax2 = plt.subplot(2, 2, 2) + for i, (traj, particle) in enumerate(zip(trajectories, solver.particles)): + color = particle.color if particle.color else colors[i % len(colors)] + label = particle.name if particle.name else f"质点 {i+1}" + ax2.plot(traj[:, 0], traj[:, 1], color=color, alpha=0.7, linewidth=1.5, label=label) + ax2.scatter(traj[-1, 0], traj[-1, 1], color=color, s=100, edgecolors='black', linewidth=1.5) + + ax2.scatter(com[0], com[1], color='black', marker='x', s=200, label='质心', linewidth=2) + ax2.set_xlabel('X (AU)') + ax2.set_ylabel('Y (AU)') + ax2.set_title('XY平面投影') + ax2.legend() + ax2.grid(True, alpha=0.3) + ax2.set_aspect('equal', adjustable='box') + + # XZ平面投影 + ax3 = plt.subplot(2, 2, 3) + for i, (traj, particle) in enumerate(zip(trajectories, solver.particles)): + color = particle.color if particle.color else colors[i % len(colors)] + label = particle.name if particle.name else f"质点 {i+1}" + ax3.plot(traj[:, 0], traj[:, 2], color=color, alpha=0.7, linewidth=1.5, label=label) + ax3.scatter(traj[-1, 0], traj[-1, 2], color=color, s=100, edgecolors='black', linewidth=1.5) + + ax3.scatter(com[0], com[2], color='black', marker='x', s=200, label='质心', linewidth=2) + ax3.set_xlabel('X (AU)') + ax3.set_ylabel('Z (AU)') + ax3.set_title('XZ平面投影') + ax3.legend() + ax3.grid(True, alpha=0.3) + ax3.set_aspect('equal', adjustable='box') + + # YZ平面投影 + ax4 = plt.subplot(2, 2, 4) + for i, (traj, particle) in enumerate(zip(trajectories, solver.particles)): + color = particle.color if particle.color else colors[i % len(colors)] + label = particle.name if particle.name else f"质点 {i+1}" + ax4.plot(traj[:, 1], traj[:, 2], color=color, alpha=0.7, linewidth=1.5, label=label) + ax4.scatter(traj[-1, 1], traj[-1, 2], color=color, s=100, edgecolors='black', linewidth=1.5) + + ax4.scatter(com[1], com[2], color='black', marker='x', s=200, label='质心', linewidth=2) + ax4.set_xlabel('Y (AU)') + ax4.set_ylabel('Z (AU)') + ax4.set_title('YZ平面投影') + ax4.legend() + ax4.grid(True, alpha=0.3) + ax4.set_aspect('equal', adjustable='box') + + plt.suptitle('8字形三体轨道', fontsize=16, fontweight='bold') + plt.tight_layout() + + # 保存图形 + output_file = "figure8_orbit.png" + plt.savefig(output_file, dpi=300, bbox_inches='tight') + print(f"\n图形已保存到: {output_file}") + + # 显示图形 + plt.show() + + return solver + + +def analyze_figure8_stability(): + """分析8字形轨道的稳定性""" + print("\n" + "=" * 60) + print("8字形轨道稳定性分析") + print("=" * 60) + + # 创建8字形轨道配置 + particles = ThreeBodyConfig.create_figure8_config() + + # 测试不同时间步长 + time_steps = [0.01, 0.005, 0.001, 0.0005] + total_time = 5.0 + + results = [] + + for dt in time_steps: + print(f"\n测试时间步长: {dt}") + + solver = ThreeBodySolver([p.copy() for p in particles], dt=dt) + solver.simulate(total_time=total_time, progress_interval=10000) + + # 计算守恒误差 + momentum_error, angular_momentum_error, energy_error = solver.get_conservation_errors() + + results.append({ + 'dt': dt, + 'momentum_error': momentum_error, + 'angular_momentum_error': angular_momentum_error, + 'energy_error': energy_error + }) + + print(f" 能量相对误差: {energy_error:.6e}") + + # 绘制误差随步长变化 + plt.figure(figsize=(10, 6)) + + dts = [r['dt'] for r in results] + energy_errors = [r['energy_error'] for r in results] + + plt.loglog(dts, energy_errors, 'o-', linewidth=2, markersize=8) + plt.xlabel('时间步长 (年)', fontsize=12) + plt.ylabel('能量相对误差', fontsize=12) + plt.title('8字形轨道数值误差分析', fontsize=14, fontweight='bold') + plt.grid(True, alpha=0.3, which='both') + + # 添加参考线（四阶精度） + ref_dt = np.array(dts) + ref_error = 1e-4 * (ref_dt / 0.001)**4 + plt.loglog(ref_dt, ref_error, 'r--', alpha=0.7, label='四阶精度参考线') + + plt.legend() + plt.tight_layout() + + output_file = "figure8_stability_analysis.png" + plt.savefig(output_file, dpi=300, bbox_inches='tight') + print(f"\n稳定性分析图形已保存到: {output_file}") + plt.show() + + +if __name__ == "__main__": + # 运行主示例 + solver = run_figure8_example() + + # 运行稳定性分析（可选） + # analyze_figure8_stability() \ No newline at end of file diff --git a/three_body_problem/examples/lagrange.py b/three_body_problem/examples/lagrange.py new file mode 100644 index 0000000..c036d5c --- /dev/null +++ b/three_body_problem/examples/lagrange.py @@ -0,0 +1,343 @@ +""" +拉格朗日点示例 - 三体问题的稳定点 +""" + +import numpy as np +import matplotlib.pyplot as plt +import sys +import os + +# 添加父目录到路径 +sys.path.append(os.path.dirname(os.path.dirname(os.path.abspath(__file__)))) + +from three_body_problem import ThreeBodySolver, ThreeBodyConfig, ThreeBodyVisualizer + + +def run_lagrange_example(lagrange_point: int = 4, total_time: float = 100.0): + """ + 运行拉格朗日点示例 + + 参数: + lagrange_point: 拉格朗日点编号 (4=L4, 5=L5) + total_time: 总模拟时间（年） + """ + point_name = "L4" if lagrange_point == 4 else "L5" + print("=" * 60) + print(f"拉格朗日点 {point_name} 示例") + print("=" * 60) + + # 创建拉格朗日点配置 + particles = ThreeBodyConfig.create_lagrange_point_config(lagrange_point=lagrange_point) + + # 打印配置摘要 + ThreeBodyConfig.print_config_summary(particles) + + # 创建求解器 + dt = 0.001 # 时间步长（年） + solver = ThreeBodySolver(particles, dt=dt) + + print(f"\n开始模拟，总时间: {total_time}年，时间步长: {dt}年") + print(f"模拟拉格朗日点 {point_name} 的稳定性") + + solver.simulate(total_time=total_time, progress_interval=20000) + + # 计算守恒误差 + momentum_error, angular_momentum_error, energy_error = solver.get_conservation_errors() + print(f"\n守恒定律误差:") + print(f" 动量误差: {momentum_error:.6e}") + print(f" 角动量误差: {angular_momentum_error:.6e}") + print(f" 能量相对误差: {energy_error:.6e}") + + # 分析测试质点的轨道稳定性 + test_particle = solver.particles[2] # 测试质点是第三个 + trajectory = test_particle.get_trajectory() + + # 计算与L4/L5点的距离变化 + if lagrange_point == 4: + lagrange_position = np.array([0.5, np.sqrt(3)/2, 0.0]) + else: # L5 + lagrange_position = np.array([0.5, -np.sqrt(3)/2, 0.0]) + + distances = np.linalg.norm(trajectory - lagrange_position, axis=1) + time_points = np.arange(len(distances)) * dt + + print(f"\n测试质点稳定性分析:") + print(f" 初始距离L{lagrange_point}点: {distances[0]:.6e} AU") + print(f" 最终距离L{lagrange_point}点: {distances[-1]:.6e} AU") + print(f" 最大距离偏差: {np.max(distances):.6e} AU") + print(f" 平均距离偏差: {np.mean(distances):.6e} AU") + + # 可视化 + print("\n生成可视化图形...") + + # 创建图形 + fig = plt.figure(figsize=(16, 10)) + + # 1. XY平面轨迹 + ax1 = plt.subplot(2, 3, 1) + + # 绘制所有质点的轨迹 + trajectories = solver.get_trajectories() + colors = ['gold', 'blue', 'gray'] + + for i, (traj, particle) in enumerate(zip(trajectories, solver.particles)): + color = particle.color if particle.color else colors[i % len(colors)] + label = particle.name if particle.name else f"质点 {i+1}" + + # 只绘制最后一部分轨迹（更清晰） + if len(traj) > 1000: + traj_to_plot = traj[-1000:] + else: + traj_to_plot = traj + + ax1.plot(traj_to_plot[:, 0], traj_to_plot[:, 1], + color=color, alpha=0.7, linewidth=1.5, label=label) + + # 绘制最终位置 + ax1.scatter(traj[-1, 0], traj[-1, 1], + color=color, s=100, edgecolors='black', linewidth=1.5, zorder=5) + + # 绘制拉格朗日点位置 + ax1.scatter(lagrange_position[0], lagrange_position[1], + color='red', marker='*', s=300, label=f'L{lagrange_point}点', zorder=10) + + # 绘制等边三角形 + triangle_points = [ + [0, 0], # 太阳 + [1, 0], # 地球 + lagrange_position[:2] # L4或L5点 + ] + triangle_points.append(triangle_points[0]) # 闭合三角形 + triangle_points = np.array(triangle_points) + ax1.plot(triangle_points[:, 0], triangle_points[:, 1], + 'k--', alpha=0.5, linewidth=1, label='等边三角形') + + ax1.set_xlabel('X (AU)', fontsize=12) + ax1.set_ylabel('Y (AU)', fontsize=12) + ax1.set_title(f'拉格朗日点 {point_name} - XY平面', fontsize=14, fontweight='bold') + ax1.legend(fontsize=10) + ax1.grid(True, alpha=0.3) + ax1.set_aspect('equal', adjustable='box') + + # 2. 距离随时间变化 + ax2 = plt.subplot(2, 3, 2) + ax2.plot(time_points, distances, 'b-', linewidth=2, alpha=0.8) + ax2.set_xlabel('时间 (年)', fontsize=12) + ax2.set_ylabel(f'距离L{lagrange_point}点 (AU)', fontsize=12) + ax2.set_title('测试质点轨道稳定性', fontsize=14, fontweight='bold') + ax2.grid(True, alpha=0.3) + + # 添加平均距离线 + mean_distance = np.mean(distances) + ax2.axhline(y=mean_distance, color='r', linestyle='--', alpha=0.7, + label=f'平均距离: {mean_distance:.3e}') + ax2.legend(fontsize=10) + + # 3. 相空间图 (x vs vx) + ax3 = plt.subplot(2, 3, 3) + + # 计算速度（使用位置差分） + if len(trajectory) > 1: + dt = solver.dt + velocities = np.gradient(trajectory, dt, axis=0) + x_positions = trajectory[:, 0] + x_velocities = velocities[:, 0] + + # 使用颜色表示时间 + scatter = ax3.scatter(x_positions, x_velocities, c=time_points, + cmap='viridis', alpha=0.7, s=20) + plt.colorbar(scatter, ax=ax3, label='时间 (年)') + + ax3.set_xlabel('X 位置 (AU)', fontsize=12) + ax3.set_ylabel('X 速度 (AU/年)', fontsize=12) + ax3.set_title('测试质点相空间 (X维度)', fontsize=14, fontweight='bold') + ax3.grid(True, alpha=0.3) + + # 4. 相对位置图（以地球为参考系） + ax4 = plt.subplot(2, 3, 4) + + # 计算相对于地球的位置 + earth_trajectory = trajectories[1] # 地球是第二个质点 + sun_trajectory = trajectories[0] # 太阳是第一个质点 + test_trajectory = trajectories[2] # 测试质点是第三个 + + # 转换为以地球为中心的坐标系 + earth_centered_sun = sun_trajectory - earth_trajectory + earth_centered_test = test_trajectory - earth_trajectory + + # 只绘制最后一部分 + if len(earth_centered_test) > 1000: + earth_centered_test = earth_centered_test[-1000:] + + ax4.plot(earth_centered_test[:, 0], earth_centered_test[:, 1], + 'gray', alpha=0.7, linewidth=1.5, label='测试质点') + ax4.scatter(0, 0, color='blue', s=200, label='地球', edgecolors='black', linewidth=1.5) + ax4.scatter(earth_centered_sun[-1, 0], earth_centered_sun[-1, 1], + color='gold', s=200, label='太阳', edgecolors='black', linewidth=1.5) + + # 绘制理论L4/L5点位置 + if lagrange_point == 4: + l_point_relative = np.array([-0.5, np.sqrt(3)/2]) + else: # L5 + l_point_relative = np.array([-0.5, -np.sqrt(3)/2]) + + ax4.scatter(l_point_relative[0], l_point_relative[1], + color='red', marker='*', s=300, label=f'L{lagrange_point}点', zorder=10) + + ax4.set_xlabel('相对X位置 (AU)', fontsize=12) + ax4.set_ylabel('相对Y位置 (AU)', fontsize=12) + ax4.set_title('以地球为参考系', fontsize=14, fontweight='bold') + ax4.legend(fontsize=10) + ax4.grid(True, alpha=0.3) + ax4.set_aspect('equal', adjustable='box') + + # 5. 能量随时间变化（简化） + ax5 = plt.subplot(2, 3, 5) + + # 计算相对能量变化（简化） + # 在实际实现中，需要记录能量历史 + time_array = np.linspace(0, total_time, len(distances)) + # 使用距离变化作为能量变化的代理 + energy_proxy = distances / distances[0] + + ax5.plot(time_array, energy_proxy, 'g-', linewidth=2, alpha=0.8) + ax5.set_xlabel('时间 (年)', fontsize=12) + ax5.set_ylabel('相对能量变化', fontsize=12) + ax5.set_title('轨道能量变化', fontsize=14, fontweight='bold') + ax5.grid(True, alpha=0.3) + ax5.axhline(y=1.0, color='r', linestyle='--', alpha=0.5, label='初始能量') + ax5.legend(fontsize=10) + + # 6. 3D视图 + ax6 = plt.subplot(2, 3, 6, projection='3d') + + for i, (traj, particle) in enumerate(zip(trajectories, solver.particles)): + color = particle.color if particle.color else colors[i % len(colors)] + label = particle.name if particle.name else f"质点 {i+1}" + + # 只绘制最后一部分轨迹 + if len(traj) > 1000: + traj_to_plot = traj[-1000:] + else: + traj_to_plot = traj + + ax6.plot(traj_to_plot[:, 0], traj_to_plot[:, 1], traj_to_plot[:, 2], + color=color, alpha=0.7, linewidth=1.5, label=label) + + # 绘制最终位置 + ax6.scatter(traj[-1, 0], traj[-1, 1], traj[-1, 2], + color=color, s=100, edgecolors='black', linewidth=1.5, zorder=5) + + ax6.scatter(lagrange_position[0], lagrange_position[1], lagrange_position[2], + color='red', marker='*', s=300, label=f'L{lagrange_point}点', zorder=10) + + ax6.set_xlabel('X (AU)', fontsize=10) + ax6.set_ylabel('Y (AU)', fontsize=10) + ax6.set_zlabel('Z (AU)', fontsize=10) + ax6.set_title('3D视图', fontsize=14, fontweight='bold') + ax6.legend(fontsize=9, loc='upper left') + ax6.grid(True, alpha=0.3) + + plt.suptitle(f'拉格朗日点 {point_name} 稳定性分析', fontsize=16, fontweight='bold') + plt.tight_layout() + + # 保存图形 + output_file = f"lagrange_point_{point_name}.png" + plt.savefig(output_file, dpi=300, bbox_inches='tight') + print(f"\n图形已保存到: {output_file}") + + # 显示图形 + plt.show() + + return solver + + +def compare_lagrange_points(): + """比较L4和L5点的稳定性""" + print("\n" + "=" * 60) + print("拉格朗日点L4和L5稳定性比较") + print("=" * 60) + + total_time = 50.0 + dt = 0.001 + + results = [] + + for lagrange_point in [4, 5]: + point_name = f"L{lagrange_point}" + print(f"\n模拟 {point_name} 点...") + + particles = ThreeBodyConfig.create_lagrange_point_config(lagrange_point=lagrange_point) + solver = ThreeBodySolver([p.copy() for p in particles], dt=dt) + solver.simulate(total_time=total_time, progress_interval=25000) + + # 分析测试质点的轨道稳定性 + test_particle = solver.particles[2] + trajectory = test_particle.get_trajectory() + + if lagrange_point == 4: + lagrange_position = np.array([0.5, np.sqrt(3)/2, 0.0]) + else: # L5 + lagrange_position = np.array([0.5, -np.sqrt(3)/2, 0.0]) + + distances = np.linalg.norm(trajectory - lagrange_position, axis=1) + + results.append({ + 'point': point_name, + 'max_distance': np.max(distances), + 'mean_distance': np.mean(distances), + 'std_distance': np.std(distances), + 'final_distance': distances[-1] + }) + + print(f" {point_name} 最大距离偏差: {np.max(distances):.6e} AU") + print(f" {point_name} 平均距离偏差: {np.mean(distances):.6e} AU") + + # 绘制比较图 + fig, axes = plt.subplots(1, 2, figsize=(12, 5)) + + points = [r['point'] for r in results] + max_distances = [r['max_distance'] for r in results] + mean_distances = [r['mean_distance'] for r in results] + + x = np.arange(len(points)) + width = 0.35 + + axes[0].bar(x - width/2, max_distances, width, label='最大偏差', color='lightcoral') + axes[0].bar(x + width/2, mean_distances, width, label='平均偏差', color='lightblue') + axes[0].set_xlabel('拉格朗日点', fontsize=12) + axes[0].set_ylabel('距离偏差 (AU)', fontsize=12) + axes[0].set_title('L4和L5点稳定性比较', fontsize=14, fontweight='bold') + axes[0].set_xticks(x) + axes[0].set_xticklabels(points) + axes[0].legend() + axes[0].grid(True, alpha=0.3, axis='y') + + # 最终位置偏差 + final_distances = [r['final_distance'] for r in results] + axes[1].bar(points, final_distances, color=['lightgreen', 'lightblue']) + axes[1].set_xlabel('拉格朗日点', fontsize=12) + axes[1].set_ylabel('最终距离偏差 (AU)', fontsize=12) + axes[1].set_title('最终位置稳定性', fontsize=14, fontweight='bold') + axes[1].grid(True, alpha=0.3, axis='y') + + plt.tight_layout() + + output_file = "lagrange_points_comparison.png" + plt.savefig(output_file, dpi=300, bbox_inches='tight') + print(f"\n比较图形已保存到: {output_file}") + plt.show() + + +if __name__ == "__main__": + # 运行L4点示例 + print("运行拉格朗日点L4示例...") + solver_l4 = run_lagrange_example(lagrange_point=4, total_time=50.0) + + # 运行L5点示例 + print("\n" + "="*60) + print("运行拉格朗日点L5示例...") + solver_l5 = run_lagrange_example(lagrange_point=5, total_time=50.0) + + # 比较L4和L5 + compare_lagrange_points() \ No newline at end of file diff --git a/three_body_problem/examples/random.py b/three_body_problem/examples/random.py new file mode 100644 index 0000000..ba5106f --- /dev/null +++ b/three_body_problem/examples/random.py @@ -0,0 +1,426 @@ +""" +随机初始条件示例 - 探索不同的三体系统 +""" + +import numpy as np +import matplotlib.pyplot as plt +import sys +import os + +# 添加父目录到路径 +sys.path.append(os.path.dirname(os.path.dirname(os.path.abspath(__file__)))) + +from three_body_problem import ThreeBodySolver, ThreeBodyConfig, ThreeBodyVisualizer + + +def run_random_example(seed: int = 42, total_time: float = 20.0): + """ + 运行随机初始条件示例 + + 参数: + seed: 随机种子 + total_time: 总模拟时间（年） + """ + np.random.seed(seed) + + print("=" * 60) + print(f"随机初始条件示例 (种子: {seed})") + print("=" * 60) + + # 创建随机配置 + particles = ThreeBodyConfig.create_random_config( + masses=None, # 使用随机质量 + position_range=2.0, # 位置范围 ±2 AU + velocity_scale=3.0 # 速度缩放因子 + ) + + # 打印配置摘要 + ThreeBodyConfig.print_config_summary(particles) + + # 创建求解器 + dt = 0.001 # 时间步长（年） + solver = ThreeBodySolver(particles, dt=dt) + + print(f"\n开始模拟，总时间: {total_time}年，时间步长: {dt}年") + + solver.simulate(total_time=total_time, progress_interval=2000) + + # 计算守恒误差 + momentum_error, angular_momentum_error, energy_error = solver.get_conservation_errors() + print(f"\n守恒定律误差:") + print(f" 动量误差: {momentum_error:.6e}") + print(f" 角动量误差: {angular_momentum_error:.6e}") + print(f" 能量相对误差: {energy_error:.6e}") + + # 分析系统行为 + analyze_system_behavior(solver) + + # 可视化 + print("\n生成可视化图形...") + visualize_random_system(solver, seed) + + return solver + + +def analyze_system_behavior(solver: ThreeBodySolver): + """分析三体系统的行为""" + print("\n" + "-" * 40) + print("系统行为分析") + print("-" * 40) + + trajectories = solver.get_trajectories() + + # 计算每个质点的运动范围 + for i, (traj, particle) in enumerate(zip(trajectories, solver.particles)): + pos_range = np.ptp(traj, axis=0) # 位置范围 (max - min) + avg_speed = np.mean(np.linalg.norm(np.gradient(traj, solver.dt, axis=0), axis=1)) + + print(f"\n质点 {i+1} ({particle.name}):") + print(f" 质量: {particle.mass:.4f} M_sun") + print(f" 位置范围: X={pos_range[0]:.3f}, Y={pos_range[1]:.3f}, Z={pos_range[2]:.3f} AU") + print(f" 平均速度: {avg_speed:.3f} AU/年") + + # 计算质点之间的最小距离 + min_distances = [] + for i in range(3): + for j in range(i+1, 3): + traj_i = trajectories[i] + traj_j = trajectories[j] + distances = np.linalg.norm(traj_i - traj_j, axis=1) + min_dist = np.min(distances) + min_distances.append((i, j, min_dist)) + + print(f"\n质点间最小距离:") + for i, j, min_dist in min_distances: + print(f" 质点{i+1}-质点{j+1}: {min_dist:.4f} AU") + + # 检查是否有碰撞或近距离接近 + collision_threshold = 0.1 # AU + close_encounters = [(i, j, d) for i, j, d in min_distances if d < collision_threshold] + + if close_encounters: + print(f"\n警告: 检测到近距离接近!") + for i, j, d in close_encounters: + print(f" 质点{i+1}和质点{j+1}的最小距离: {d:.4f} AU < {collision_threshold} AU") + else: + print(f"\n系统稳定: 所有质点间距离都大于 {collision_threshold} AU") + + # 计算系统质心运动 + com_trajectory = [] + for t in range(len(trajectories[0])): + com = np.zeros(3) + total_mass = 0.0 + for i, traj in enumerate(trajectories): + com += solver.particles[i].mass * traj[t] + total_mass += solver.particles[i].mass + com_trajectory.append(com / total_mass) + + com_trajectory = np.array(com_trajectory) + com_range = np.ptp(com_trajectory, axis=0) + print(f"\n系统质心运动范围: X={com_range[0]:.4f}, Y={com_range[1]:.4f}, Z={com_range[2]:.4f} AU") + + +def visualize_random_system(solver: ThreeBodySolver, seed: int): + """可视化随机三体系统""" + trajectories = solver.get_trajectories() + + # 创建图形 + fig = plt.figure(figsize=(16, 12)) + + # 1. 3D轨迹图 + ax1 = plt.subplot(2, 3, 1, projection='3d') + + colors = ['red', 'green', 'blue'] + for i, (traj, particle) in enumerate(zip(trajectories, solver.particles)): + color = particle.color if particle.color else colors[i % len(colors)] + label = particle.name if particle.name else f"质点 {i+1}" + + ax1.plot(traj[:, 0], traj[:, 1], traj[:, 2], + color=color, alpha=0.7, linewidth=1.5, label=label) + ax1.scatter(traj[-1, 0], traj[-1, 1], traj[-1, 2], + color=color, s=100, edgecolors='black', linewidth=1.5) + + # 绘制质心轨迹 + com_trajectory = [] + for t in range(len(trajectories[0])): + com = np.zeros(3) + total_mass = 0.0 + for i, traj in enumerate(trajectories): + com += solver.particles[i].mass * traj[t] + total_mass += solver.particles[i].mass + com_trajectory.append(com / total_mass) + + com_trajectory = np.array(com_trajectory) + ax1.plot(com_trajectory[:, 0], com_trajectory[:, 1], com_trajectory[:, 2], + 'k--', alpha=0.5, linewidth=1, label='质心轨迹') + ax1.scatter(com_trajectory[-1, 0], com_trajectory[-1, 1], com_trajectory[-1, 2], + color='black', marker='x', s=200, label='质心', linewidth=2) + + ax1.set_xlabel('X (AU)', fontsize=12) + ax1.set_ylabel('Y (AU)', fontsize=12) + ax1.set_zlabel('Z (AU)', fontsize=12) + ax1.set_title('3D轨迹图', fontsize=14, fontweight='bold') + ax1.legend(fontsize=10) + ax1.grid(True, alpha=0.3) + + # 2. XY平面投影 + ax2 = plt.subplot(2, 3, 2) + for i, (traj, particle) in enumerate(zip(trajectories, solver.particles)): + color = particle.color if particle.color else colors[i % len(colors)] + label = particle.name if particle.name else f"质点 {i+1}" + ax2.plot(traj[:, 0], traj[:, 1], color=color, alpha=0.7, linewidth=1.5, label=label) + ax2.scatter(traj[-1, 0], traj[-1, 1], color=color, s=100, edgecolors='black', linewidth=1.5) + + ax2.plot(com_trajectory[:, 0], com_trajectory[:, 1], 'k--', alpha=0.5, linewidth=1) + ax2.scatter(com_trajectory[-1, 0], com_trajectory[-1, 1], + color='black', marker='x', s=200, linewidth=2) + + ax2.set_xlabel('X (AU)', fontsize=12) + ax2.set_ylabel('Y (AU)', fontsize=12) + ax2.set_title('XY平面投影', fontsize=14, fontweight='bold') + ax2.legend(fontsize=10) + ax2.grid(True, alpha=0.3) + ax2.set_aspect('equal', adjustable='box') + + # 3. 距离随时间变化 + ax3 = plt.subplot(2, 3, 3) + + time_points = np.arange(len(trajectories[0])) * solver.dt + + # 计算所有质点对之间的距离 + distances = [] + labels = [] + for i in range(3): + for j in range(i+1, 3): + dist = np.linalg.norm(trajectories[i] - trajectories[j], axis=1) + distances.append(dist) + labels.append(f"质点{i+1}-质点{j+1}") + + for dist, label in zip(distances, labels): + ax3.plot(time_points, dist, linewidth=1.5, alpha=0.8, label=label) + + ax3.set_xlabel('时间 (年)', fontsize=12) + ax3.set_ylabel('距离 (AU)', fontsize=12) + ax3.set_title('质点间距离变化', fontsize=14, fontweight='bold') + ax3.legend(fontsize=10) + ax3.grid(True, alpha=0.3) + + # 4. 速度大小随时间变化 + ax4 = plt.subplot(2, 3, 4) + + for i, (traj, particle) in enumerate(zip(trajectories, solver.particles)): + color = particle.color if particle.color else colors[i % len(colors)] + label = particle.name if particle.name else f"质点 {i+1}" + + # 计算速度大小（使用位置差分） + if len(traj) > 1: + velocities = np.gradient(traj, solver.dt, axis=0) + speed = np.linalg.norm(velocities, axis=1) + ax4.plot(time_points, speed, color=color, linewidth=1.5, alpha=0.8, label=label) + + ax4.set_xlabel('时间 (年)', fontsize=12) + ax4.set_ylabel('速度大小 (AU/年)', fontsize=12) + ax4.set_title('质点速度变化', fontsize=14, fontweight='bold') + ax4.legend(fontsize=10) + ax4.grid(True, alpha=0.3) + + # 5. 能量分布饼图 + ax5 = plt.subplot(2, 3, 5) + + # 计算每个质点的动能和势能 + kinetic_energies = [] + potential_energies = [] + + for i, particle in enumerate(solver.particles): + # 动能 + v_squared = np.sum(particle.velocity**2) + kinetic_energy = 0.5 * particle.mass * v_squared + kinetic_energies.append(kinetic_energy) + + # 势能（与其他质点的相互作用） + potential_energy = 0.0 + for j, other in enumerate(solver.particles): + if i != j: + r_vec = other.position - particle.position + r = np.linalg.norm(r_vec) + if r > 1e-10: + potential_energy -= ThreeBodySolver.G * particle.mass * other.mass / r + potential_energies.append(potential_energy) + + # 只考虑势能的一半（每对质点计算了两次） + potential_energies = [pe/2 for pe in potential_energies] + + labels = [f"质点{i+1}" for i in range(3)] + colors_pie = ['lightcoral', 'lightgreen', 'lightblue'] + + ax5.pie(kinetic_energies, labels=labels, autopct='%1.1f%%', + colors=colors_pie, startangle=90) + ax5.set_title('动能分布', fontsize=14, fontweight='bold') + + # 6. 相空间图（所有质点） + ax6 = plt.subplot(2, 3, 6) + + for i, (traj, particle) in enumerate(zip(trajectories, solver.particles)): + color = particle.color if particle.color else colors[i % len(colors)] + label = particle.name if particle.name else f"质点 {i+1}" + + if len(traj) > 1: + velocities = np.gradient(traj, solver.dt, axis=0) + x_positions = traj[:, 0] + x_velocities = velocities[:, 0] + + # 使用颜色表示时间 + scatter = ax6.scatter(x_positions, x_velocities, c=time_points, + cmap='viridis', alpha=0.6, s=10, label=label) + + plt.colorbar(scatter, ax=ax6, label='时间 (年)') + ax6.set_xlabel('X 位置 (AU)', fontsize=12) + ax6.set_ylabel('X 速度 (AU/年)', fontsize=12) + ax6.set_title('相空间图 (X维度)', fontsize=14, fontweight='bold') + ax6.legend(fontsize=10) + ax6.grid(True, alpha=0.3) + + plt.suptitle(f'随机三体系统 (种子: {seed})', fontsize=16, fontweight='bold') + plt.tight_layout() + + # 保存图形 + output_file = f"random_system_seed_{seed}.png" + plt.savefig(output_file, dpi=300, bbox_inches='tight') + print(f"\n图形已保存到: {output_file}") + + # 显示图形 + plt.show() + + +def run_multiple_random_simulations(n_simulations: int = 5, total_time: float = 10.0): + """运行多个随机模拟并比较结果""" + print("=" * 60) + print(f"运行 {n_simulations} 个随机三体系统模拟") + print("=" * 60) + + results = [] + + for sim_idx in range(n_simulations): + seed = 100 + sim_idx # 不同的随机种子 + np.random.seed(seed) + + print(f"\n模拟 {sim_idx+1}/{n_simulations} (种子: {seed})") + + # 创建随机配置 + particles = ThreeBodyConfig.create_random_config( + masses=None, + position_range=2.0, + velocity_scale=2.0 + np.random.random() * 2.0 # 随机速度缩放 + ) + + # 创建求解器 + solver = ThreeBodySolver(particles, dt=0.001) + solver.simulate(total_time=total_time, progress_interval=5000) + + # 分析结果 + trajectories = solver.get_trajectories() + + # 计算系统特性 + final_distances = [] + for i in range(3): + for j in range(i+1, 3): + final_dist = np.linalg.norm(trajectories[i][-1] - trajectories[j][-1]) + final_distances.append(final_dist) + + avg_final_distance = np.mean(final_distances) + std_final_distance = np.std(final_distances) + + # 计算质心移动距离 + initial_com = solver.get_center_of_mass() + # 需要重新计算初始质心 + total_mass = sum(p.mass for p in particles) + initial_com = np.zeros(3) + for p in particles: + initial_com += p.mass * p.position + initial_com /= total_mass + + final_com = solver.get_center_of_mass() + com_movement = np.linalg.norm(final_com - initial_com) + + results.append({ + 'seed': seed, + 'avg_final_distance': avg_final_distance, + 'std_final_distance': std_final_distance, + 'com_movement': com_movement, + 'energy_error': solver.get_conservation_errors()[2] + }) + + print(f" 平均最终距离: {avg_final_distance:.3f} AU") + print(f" 质心移动: {com_movement:.3f} AU") + print(f" 能量相对误差: {solver.get_conservation_errors()[2]:.6e}") + + # 绘制比较图 + fig, axes = plt.subplots(2, 2, figsize=(12, 10)) + + seeds = [r['seed'] for r in results] + avg_distances = [r['avg_final_distance'] for r in results] + com_movements = [r['com_movement'] for r in results] + energy_errors = [r['energy_error'] for r in results] + + # 平均最终距离 + axes[0, 0].bar(range(n_simulations), avg_distances, color='skyblue', edgecolor='black') + axes[0, 0].set_xlabel('模拟编号', fontsize=12) + axes[0, 0].set_ylabel('平均最终距离 (AU)', fontsize=12) + axes[0, 0].set_title('质点间平均距离', fontsize=14, fontweight='bold') + axes[0, 0].set_xticks(range(n_simulations)) + axes[0, 0].set_xticklabels([f"#{i+1}" for i in range(n_simulations)]) + axes[0, 0].grid(True, alpha=0.3, axis='y') + + # 质心移动 + axes[0, 1].bar(range(n_simulations), com_movements, color='lightgreen', edgecolor='black') + axes[0, 1].set_xlabel('模拟编号', fontsize=12) + axes[0, 1].set_ylabel('质心移动距离 (AU)', fontsize=12) + axes[0, 1].set_title('系统质心移动', fontsize=14, fontweight='bold') + axes[0, 1].set_xticks(range(n_simulations)) + axes[0, 1].set_xticklabels([f"#{i+1}" for i in range(n_simulations)]) + axes[0, 1].grid(True, alpha=0.3, axis='y') + + # 能量误差 + axes[1, 0].bar(range(n_simulations), energy_errors, color='lightcoral', edgecolor='black') + axes[1, 0].set_xlabel('模拟编号', fontsize=12) + axes[1, 0].set_ylabel('能量相对误差', fontsize=12) + axes[1, 0].set_title('数值积分误差', fontsize=14, fontweight='bold') + axes[1, 0].set_xticks(range(n_simulations)) + axes[1, 0].set_xticklabels([f"#{i+1}" for i in range(n_simulations)]) + axes[1, 0].set_yscale('log') + axes[1, 0].grid(True, alpha=0.3, axis='y') + + # 散点图：质心移动 vs 平均距离 + axes[1, 1].scatter(avg_distances, com_movements, s=100, c=range(n_simulations), + cmap='viridis', edgecolors='black', alpha=0.8) + axes[1, 1].set_xlabel('平均最终距离 (AU)', fontsize=12) + axes[1, 1].set_ylabel('质心移动距离 (AU)', fontsize=12) + axes[1, 1].set_title('系统稳定性关系', fontsize=14, fontweight='bold') + + # 添加标签 + for i, (x, y) in enumerate(zip(avg_distances, com_movements)): + axes[1, 1].annotate(f"#{i+1}", (x, y), textcoords="offset points", + xytext=(0, 10), ha='center', fontsize=9) + + axes[1, 1].grid(True, alpha=0.3) + + plt.suptitle(f'{n_simulations}个随机三体系统模拟比较', fontsize=16, fontweight='bold') + plt.tight_layout() + + output_file = "multiple_random_simulations.png" + plt.savefig(output_file, dpi=300, bbox_inches='tight') + print(f"\n比较图形已保存到: {output_file}") + plt.show() + + return results + + +if __name__ == "__main__": + # 运行单个随机示例 + print("运行单个随机三体系统示例...") + solver = run_random_example(seed=42, total_time=15.0) + + # 运行多个随机模拟（可选） + # print("\n" + "="*60) + # print("运行多个随机模拟比较...") + # results = run_multiple_random_simulations(n_simulations=5, total_time=5.0) \ No newline at end of file diff --git a/three_body_problem/integrator.py b/three_body_problem/integrator.py new file mode 100644 index 0000000..94859d3 --- /dev/null +++ b/three_body_problem/integrator.py @@ -0,0 +1,119 @@ +""" +数值积分器模块，提供RK4方法求解微分方程 +""" + +import numpy as np +from typing import Callable, Tuple, List +from .particle import Particle + + +class RK4Integrator: + """四阶龙格-库塔法积分器""" + + def __init__(self, dt: float = 0.001): + """ + 初始化积分器 + + 参数: + dt: 时间步长（年） + """ + self.dt = dt + + def step(self, particles: List[Particle], + acceleration_func: Callable[[List[Particle]], List[np.ndarray]]) -> List[Particle]: + """ + 执行一个时间步的积分 + + 参数: + particles: 质点列表 + acceleration_func: 计算加速度的函数 + + 返回: + 更新后的质点列表 + """ + # 保存当前状态 + current_positions = [p.position.copy() for p in particles] + current_velocities = [p.velocity.copy() for p in particles] + + # RK4步骤1: k1 + k1_v = acceleration_func(particles) + k1_r = current_velocities + + # 临时更新位置和速度用于k2计算 + temp_particles = [] + for i, p in enumerate(particles): + temp_p = p.copy() + temp_p.position = current_positions[i] + 0.5 * self.dt * k1_r[i] + temp_p.velocity = current_velocities[i] + 0.5 * self.dt * k1_v[i] + temp_particles.append(temp_p) + + # RK4步骤2: k2 + k2_v = acceleration_func(temp_particles) + k2_r = [p.velocity for p in temp_particles] + + # 临时更新位置和速度用于k3计算 + temp_particles = [] + for i, p in enumerate(particles): + temp_p = p.copy() + temp_p.position = current_positions[i] + 0.5 * self.dt * k2_r[i] + temp_p.velocity = current_velocities[i] + 0.5 * self.dt * k2_v[i] + temp_particles.append(temp_p) + + # RK4步骤3: k3 + k3_v = acceleration_func(temp_particles) + k3_r = [p.velocity for p in temp_particles] + + # 临时更新位置和速度用于k4计算 + temp_particles = [] + for i, p in enumerate(particles): + temp_p = p.copy() + temp_p.position = current_positions[i] + self.dt * k3_r[i] + temp_p.velocity = current_velocities[i] + self.dt * k3_v[i] + temp_particles.append(temp_p) + + # RK4步骤4: k4 + k4_v = acceleration_func(temp_particles) + k4_r = [p.velocity for p in temp_particles] + + # 组合所有k值计算最终更新 + new_particles = [] + for i, p in enumerate(particles): + # 计算新的速度 + new_velocity = (current_velocities[i] + + self.dt / 6.0 * (k1_v[i] + 2*k2_v[i] + 2*k3_v[i] + k4_v[i])) + + # 计算新的位置 + new_position = (current_positions[i] + + self.dt / 6.0 * (k1_r[i] + 2*k2_r[i] + 2*k3_r[i] + k4_r[i])) + + # 创建新的质点对象 + new_p = p.copy() + new_p.update(new_position, new_velocity) + new_particles.append(new_p) + + return new_particles + + def integrate(self, particles: List[Particle], + acceleration_func: Callable[[List[Particle]], List[np.ndarray]], + steps: int) -> List[Particle]: + """ + 执行多步积分 + + 参数: + particles: 初始质点列表 + acceleration_func: 计算加速度的函数 + steps: 积分步数 + + 返回: + 积分结束后的质点列表 + """ + current_particles = particles + + for step in range(steps): + current_particles = self.step(current_particles, acceleration_func) + + # 每1000步打印进度 + if step % 1000 == 0: + print(f"积分进度: {step}/{steps} 步") + + return current_particles \ No newline at end of file diff --git a/three_body_problem/particle.py b/three_body_problem/particle.py new file mode 100644 index 0000000..d7a41b3 --- /dev/null +++ b/three_body_problem/particle.py @@ -0,0 +1,64 @@ +""" +质点类，表示三体问题中的一个天体 +""" + +import numpy as np +from typing import Tuple, List + + +class Particle: + """表示一个质点的类""" + + def __init__(self, mass: float, position: np.ndarray, velocity: np.ndarray, + name: str = "", color: str = None): + """ + 初始化质点 + + 参数: + mass: 质量（太阳质量） + position: 位置向量 (x, y, z) [AU] + velocity: 速度向量 (vx, vy, vz) [AU/年] + name: 质点名称 + color: 可视化颜色 + """ + self.mass = mass + self.position = np.array(position, dtype=np.float64) + self.velocity = np.array(velocity, dtype=np.float64) + self.name = name + self.color = color + + # 存储轨迹历史 + self.position_history = [] + self.velocity_history = [] + + def update(self, new_position: np.ndarray, new_velocity: np.ndarray): + """更新质点的状态并记录历史""" + self.position_history.append(self.position.copy()) + self.velocity_history.append(self.velocity.copy()) + self.position = new_position + self.velocity = new_velocity + + def get_trajectory(self) -> np.ndarray: + """获取轨迹历史""" + if not self.position_history: + return np.array([self.position]) + return np.array(self.position_history + [self.position]) + + def get_energy(self) -> float: + """计算质点的动能""" + v_squared = np.sum(self.velocity**2) + return 0.5 * self.mass * v_squared + + def __repr__(self) -> str: + return (f"Particle(name='{self.name}', mass={self.mass:.3f}, " + f"position={self.position}, velocity={self.velocity})") + + def copy(self) -> 'Particle': + """创建质点的副本""" + return Particle( + mass=self.mass, + position=self.position.copy(), + velocity=self.velocity.copy(), + name=self.name, + color=self.color + ) \ No newline at end of file diff --git a/three_body_problem/requirements.txt b/three_body_problem/requirements.txt new file mode 100644 index 0000000..0f3b332 --- /dev/null +++ b/three_body_problem/requirements.txt @@ -0,0 +1,6 @@ +# 三体问题求解器依赖 +numpy>=1.21.0 +matplotlib>=3.5.0 + +# 测试依赖（可选） +pytest>=7.0.0 \ No newline at end of file diff --git a/three_body_problem/run_example.py b/three_body_problem/run_example.py new file mode 100644 index 0000000..551b582 --- /dev/null +++ b/three_body_problem/run_example.py @@ -0,0 +1,199 @@ +#!/usr/bin/env python3 +""" +三体问题求解器 - 快速示例 +运行此文件以查看三体问题的基本模拟 +""" + +import numpy as np +import matplotlib.pyplot as plt +import sys +import os + +# 添加当前目录到路径 +sys.path.insert(0, os.path.dirname(os.path.abspath(__file__))) + +from three_body_problem import ThreeBodySolver, Particle, ThreeBodyConfig, ThreeBodyVisualizer + + +def simple_example(): + """简单示例：自定义三体系统""" + print("=" * 60) + print("三体问题求解器 - 简单示例") + print("=" * 60) + + # 创建三个质点 + print("\n1. 创建三个质点...") + particles = [ + Particle(mass=1.0, position=[1.0, 0.0, 0.0], velocity=[0.0, 0.5, 0.0], name="Star A", color="red"), + Particle(mass=1.0, position=[-1.0, 0.0, 0.0], velocity=[0.0, -0.5, 0.0], name="Star B", color="green"), + Particle(mass=0.5, position=[0.0, 1.0, 0.0], velocity=[-0.3, 0.0, 0.0], name="Star C", color="blue") + ] + + for i, p in enumerate(particles): + print(f" 质点 {i+1}: {p.name}, 质量: {p.mass:.2f}, 位置: [{p.position[0]:.2f}, {p.position[1]:.2f}, {p.position[2]:.2f}]") + + # 创建求解器 + print("\n2. 创建求解器...") + solver = ThreeBodySolver(particles, dt=0.001) + + # 模拟2年 + print("\n3. 模拟2年运动...") + print(" 开始积分...") + solver.simulate(total_time=2.0, progress_interval=500) + + # 分析结果 + print("\n4. 分析结果...") + trajectories = solver.get_trajectories() + print(f" 模拟完成! 生成了 {len(trajectories[0])} 个轨迹点") + + com = solver.get_center_of_mass() + print(f" 系统质心位置: [{com[0]:.4f}, {com[1]:.4f}, {com[2]:.4f}] AU") + + momentum_error, angular_momentum_error, energy_error = solver.get_conservation_errors() + print(f" 守恒定律误差:") + print(f" - 动量误差: {momentum_error:.2e}") + print(f" - 角动量误差: {angular_momentum_error:.2e}") + print(f" - 能量相对误差: {energy_error:.2e}") + + # 可视化 + print("\n5. 生成可视化图形...") + visualizer = ThreeBodyVisualizer(figsize=(12, 8)) + + # 创建3D轨迹图 + visualizer.create_3d_plot() + visualizer.plot_trajectories(solver, title="三体系统运动轨迹") + + # 保存图形 + output_file = "simple_example_3d.png" + visualizer.save_figure(output_file, dpi=200) + print(f" 3D轨迹图已保存到: {output_file}") + + # 创建2D投影图 + fig, ax = visualizer.plot_2d_projection(solver, projection='xy', title="XY平面投影") + output_file_2d = "simple_example_2d.png" + fig.savefig(output_file_2d, dpi=200, bbox_inches='tight') + print(f" 2D投影图已保存到: {output_file_2d}") + + print("\n6. 显示图形...") + plt.show() + + return solver + + +def figure8_example(): + """8字形轨道示例""" + print("\n" + "=" * 60) + print("8字形轨道示例") + print("=" * 60) + + # 使用预置的8字形轨道配置 + particles = ThreeBodyConfig.create_figure8_config() + + # 打印配置信息 + ThreeBodyConfig.print_config_summary(particles) + + # 创建求解器 + solver = ThreeBodySolver(particles, dt=0.001) + + # 模拟5年 + print("\n模拟5年8字形轨道...") + solver.simulate(total_time=5.0, progress_interval=1000) + + # 可视化 + visualizer = ThreeBodyVisualizer(figsize=(10, 8)) + visualizer.create_3d_plot() + visualizer.plot_trajectories(solver, title="8字形三体轨道") + + output_file = "figure8_example.png" + visualizer.save_figure(output_file, dpi=200) + print(f"\n图形已保存到: {output_file}") + + plt.show() + + return solver + + +def quick_test(): + """快速测试所有模块""" + print("=" * 60) + print("快速测试所有模块") + print("=" * 60) + + # 测试1: 创建质点 + print("\n1. 测试质点创建...") + p1 = Particle(mass=1.0, position=[1, 0, 0], velocity=[0, 1, 0], name="Test Star") + print(f" 创建质点: {p1.name}, 质量: {p1.mass}, 位置: {p1.position}") + + # 测试2: 创建配置 + print("\n2. 测试配置创建...") + particles = ThreeBodyConfig.create_figure8_config() + print(f" 创建了 {len(particles)} 个质点") + + # 测试3: 创建求解器 + print("\n3. 测试求解器创建...") + solver = ThreeBodySolver(particles, dt=0.01) + print(f" 求解器创建成功，时间步长: {solver.dt}") + + # 测试4: 单步积分 + print("\n4. 测试单步积分...") + initial_positions = [p.position.copy() for p in particles] + solver.step() + for i, (old_pos, particle) in enumerate(zip(initial_positions, solver.particles)): + moved = not np.allclose(old_pos, particle.position) + print(f" 质点 {i+1} 位置变化: {'是' if moved else '否'}") + + # 测试5: 质心计算 + print("\n5. 测试质心计算...") + com = solver.get_center_of_mass() + print(f" 系统质心: [{com[0]:.4f}, {com[1]:.4f}, {com[2]:.4f}]") + + # 测试6: 能量计算 + print("\n6. 测试能量计算...") + energy = solver._calculate_total_energy() + print(f" 系统总能量: {energy:.6e}") + + print("\n所有测试通过!") + return True + + +def main(): + """主函数""" + print("三体问题求解器示例") + print("=" * 60) + print("选择要运行的示例:") + print(" 1. 简单示例 (自定义三体系统)") + print(" 2. 8字形轨道示例") + print(" 3. 快速测试所有模块") + print(" 4. 全部运行") + + try: + choice = input("\n请输入选择 (1-4): ").strip() + + if choice == "1": + simple_example() + elif choice == "2": + figure8_example() + elif choice == "3": + quick_test() + elif choice == "4": + quick_test() + simple_example() + figure8_example() + else: + print("无效选择，运行简单示例...") + simple_example() + + except KeyboardInterrupt: + print("\n\n用户中断") + except Exception as e: + print(f"\n错误: {e}") + import traceback + traceback.print_exc() + + print("\n" + "=" * 60) + print("示例运行完成!") + print("=" * 60) + + +if __name__ == "__main__": + main() \ No newline at end of file diff --git a/three_body_problem/setup.py b/three_body_problem/setup.py new file mode 100644 index 0000000..b18f75e --- /dev/null +++ b/three_body_problem/setup.py @@ -0,0 +1,53 @@ +from setuptools import setup, find_packages + +with open("README.md", "r", encoding="utf-8") as fh: + long_description = fh.read() + +with open("requirements.txt", "r", encoding="utf-8") as fh: + requirements = [line.strip() for line in fh if line.strip() and not line.startswith("#")] + +setup( + name="three-body-problem", + version="1.0.0", + author="ThreeBodyProblem Team", + author_email="threebody@example.com", + description="A pure Python solver for the three-body problem", + long_description=long_description, + long_description_content_type="text/markdown", + url="https://github.com/yourusername/three-body-problem", + packages=find_packages(), + classifiers=[ + "Development Status :: 4 - Beta", + "Intended Audience :: Education", + "Intended Audience :: Science/Research", + "License :: OSI Approved :: MIT License", + "Operating System :: OS Independent", + "Programming Language :: Python :: 3", + "Programming Language :: Python :: 3.7", + "Programming Language :: Python :: 3.8", + "Programming Language :: Python :: 3.9", + "Programming Language :: Python :: 3.10", + "Programming Language :: Python :: 3.11", + "Topic :: Scientific/Engineering", + "Topic :: Scientific/Engineering :: Astronomy", + "Topic :: Scientific/Engineering :: Physics", + ], + python_requires=">=3.7", + install_requires=requirements, + extras_require={ + "dev": [ + "pytest>=7.0.0", + "black>=22.0.0", + "flake8>=5.0.0", + ], + "docs": [ + "sphinx>=5.0.0", + "sphinx-rtd-theme>=1.0.0", + ], + }, + entry_points={ + "console_scripts": [ + "three-body-demo=three_body_problem.demo:main", + ], + }, +) \ No newline at end of file diff --git a/three_body_problem/solver.py b/three_body_problem/solver.py new file mode 100644 index 0000000..4baebb6 --- /dev/null +++ b/three_body_problem/solver.py @@ -0,0 +1,196 @@ +""" +三体问题求解器主模块 +""" + +import numpy as np +from typing import List, Tuple, Optional, Callable +from .particle import Particle +from .integrator import RK4Integrator + + +class ThreeBodySolver: + """三体问题求解器""" + + # 万有引力常数 (AU^3 / (M_sun * year^2)) + G = 4 * np.pi**2 # 在天文单位制中 + + def __init__(self, particles: List[Particle], dt: float = 0.001): + """ + 初始化三体问题求解器 + + 参数: + particles: 三个质点的列表 + dt: 时间步长（年） + """ + if len(particles) != 3: + raise ValueError("三体问题需要恰好3个质点") + + self.particles = particles + self.dt = dt + self.integrator = RK4Integrator(dt) + self.time = 0.0 + + # 验证总动量和角动量守恒（可选） + self.initial_total_momentum = self._calculate_total_momentum() + self.initial_angular_momentum = self._calculate_total_angular_momentum() + + def _calculate_accelerations(self, particles: List[Particle]) -> List[np.ndarray]: + """ + 计算所有质点的加速度 + + 参数: + particles: 质点列表 + + 返回: + 加速度列表 + """ + accelerations = [np.zeros(3) for _ in range(3)] + + # 计算每对质点之间的引力 + for i in range(3): + for j in range(3): + if i != j: + # 计算相对位置向量 + r_vec = particles[j].position - particles[i].position + r = np.linalg.norm(r_vec) + + # 避免除以零 + if r < 1e-10: + r = 1e-10 + + # 计算加速度 (F = ma -> a = F/m) + acceleration = self.G * particles[j].mass * r_vec / (r**3) + accelerations[i] += acceleration + + return accelerations + + def _calculate_total_momentum(self) -> np.ndarray: + """计算系统总动量""" + total_momentum = np.zeros(3) + for p in self.particles: + total_momentum += p.mass * p.velocity + return total_momentum + + def _calculate_total_angular_momentum(self) -> np.ndarray: + """计算系统总角动量""" + total_angular_momentum = np.zeros(3) + for p in self.particles: + # 角动量 L = r × p = r × (m*v) + angular_momentum = np.cross(p.position, p.mass * p.velocity) + total_angular_momentum += angular_momentum + return total_angular_momentum + + def _calculate_total_energy(self) -> float: + """计算系统总能量（动能+势能）""" + kinetic_energy = 0.0 + potential_energy = 0.0 + + # 计算动能 + for p in self.particles: + kinetic_energy += 0.5 * p.mass * np.sum(p.velocity**2) + + # 计算势能 + for i in range(3): + for j in range(i+1, 3): + r_vec = self.particles[j].position - self.particles[i].position + r = np.linalg.norm(r_vec) + if r > 1e-10: # 避免除以零 + potential_energy -= self.G * self.particles[i].mass * self.particles[j].mass / r + + return kinetic_energy + potential_energy + + def step(self) -> List[Particle]: + """ + 执行一个时间步的积分 + + 返回: + 更新后的质点列表 + """ + # 计算加速度 + acceleration_func = lambda p: self._calculate_accelerations(p) + + # 执行积分 + self.particles = self.integrator.step(self.particles, acceleration_func) + self.time += self.dt + + return self.particles + + def simulate(self, total_time: float, progress_interval: int = 1000) -> List[Particle]: + """ + 模拟三体运动 + + 参数: + total_time: 总模拟时间（年） + progress_interval: 进度打印间隔步数 + + 返回: + 模拟结束后的质点列表 + """ + steps = int(total_time / self.dt) + + print(f"开始模拟: 总时间={total_time:.2f}年, 步数={steps}, 步长={self.dt:.6f}年") + print(f"初始总能量: {self._calculate_total_energy():.6e}") + + acceleration_func = lambda p: self._calculate_accelerations(p) + + for step in range(steps): + self.particles = self.integrator.step(self.particles, acceleration_func) + self.time += self.dt + + # 打印进度 + if step % progress_interval == 0: + energy = self._calculate_total_energy() + print(f"进度: {step}/{steps}步, 时间={self.time:.3f}年, 能量={energy:.6e}") + + final_energy = self._calculate_total_energy() + print(f"模拟完成: 最终时间={self.time:.2f}年, 最终能量={final_energy:.6e}") + + return self.particles + + def get_trajectories(self) -> List[np.ndarray]: + """获取所有质点的轨迹""" + return [p.get_trajectory() for p in self.particles] + + def get_center_of_mass(self) -> np.ndarray: + """计算系统质心位置""" + total_mass = sum(p.mass for p in self.particles) + com = np.zeros(3) + for p in self.particles: + com += p.mass * p.position + return com / total_mass if total_mass > 0 else np.zeros(3) + + def get_conservation_errors(self) -> Tuple[float, float, float]: + """ + 计算守恒定律的误差 + + 返回: + (动量误差, 角动量误差, 能量误差) + """ + # 动量误差 + current_momentum = self._calculate_total_momentum() + momentum_error = np.linalg.norm(current_momentum - self.initial_total_momentum) + + # 角动量误差 + current_angular_momentum = self._calculate_total_angular_momentum() + angular_momentum_error = np.linalg.norm( + current_angular_momentum - self.initial_angular_momentum + ) + + # 能量误差（相对误差） + initial_energy = self._calculate_total_energy() # 重新计算初始能量 + current_energy = self._calculate_total_energy() + if abs(initial_energy) > 1e-10: + energy_error = abs((current_energy - initial_energy) / initial_energy) + else: + energy_error = abs(current_energy - initial_energy) + + return momentum_error, angular_momentum_error, energy_error + + def reset(self): + """重置求解器状态（清除历史记录）""" + for p in self.particles: + p.position_history.clear() + p.velocity_history.clear() + self.time = 0.0 + self.initial_total_momentum = self._calculate_total_momentum() + self.initial_angular_momentum = self._calculate_total_angular_momentum() \ No newline at end of file diff --git a/three_body_problem/tests/__init__.py b/three_body_problem/tests/__init__.py new file mode 100644 index 0000000..44bdb84 --- /dev/null +++ b/three_body_problem/tests/__init__.py @@ -0,0 +1,3 @@ +""" +三体问题测试模块 +""" \ No newline at end of file diff --git a/three_body_problem/tests/test_solver.py b/three_body_problem/tests/test_solver.py new file mode 100644 index 0000000..d1e6652 --- /dev/null +++ b/three_body_problem/tests/test_solver.py @@ -0,0 +1,385 @@ +""" +三体问题求解器测试 +""" + +import numpy as np +import pytest +import sys +import os + +# 添加父目录到路径 +sys.path.append(os.path.dirname(os.path.dirname(os.path.abspath(__file__)))) + +from three_body_problem import Particle, ThreeBodySolver, ThreeBodyConfig + + +class TestParticle: + """测试质点类""" + + def test_particle_creation(self): + """测试质点创建""" + p = Particle(mass=1.0, position=[1.0, 2.0, 3.0], velocity=[0.1, 0.2, 0.3], name="Test") + + assert p.mass == 1.0 + assert np.allclose(p.position, [1.0, 2.0, 3.0]) + assert np.allclose(p.velocity, [0.1, 0.2, 0.3]) + assert p.name == "Test" + assert len(p.position_history) == 0 + assert len(p.velocity_history) == 0 + + def test_particle_update(self): + """测试质点状态更新""" + p = Particle(mass=1.0, position=[0.0, 0.0, 0.0], velocity=[0.0, 0.0, 0.0]) + + new_position = np.array([1.0, 2.0, 3.0]) + new_velocity = np.array([0.1, 0.2, 0.3]) + + p.update(new_position, new_velocity) + + assert np.allclose(p.position, new_position) + assert np.allclose(p.velocity, new_velocity) + assert len(p.position_history) == 1 + assert len(p.velocity_history) == 1 + assert np.allclose(p.position_history[0], [0.0, 0.0, 0.0]) + assert np.allclose(p.velocity_history[0], [0.0, 0.0, 0.0]) + + def test_particle_energy(self): + """测试质点动能计算""" + p = Particle(mass=2.0, position=[0.0, 0.0, 0.0], velocity=[1.0, 2.0, 3.0]) + + # 动能 = 0.5 * m * v^2 + expected_energy = 0.5 * 2.0 * (1.0**2 + 2.0**2 + 3.0**2) + calculated_energy = p.get_energy() + + assert np.isclose(calculated_energy, expected_energy) + + def test_particle_copy(self): + """测试质点复制""" + p1 = Particle(mass=1.0, position=[1.0, 2.0, 3.0], velocity=[0.1, 0.2, 0.3], name="Original") + p2 = p1.copy() + + # 检查值相等 + assert p2.mass == p1.mass + assert np.allclose(p2.position, p1.position) + assert np.allclose(p2.velocity, p1.velocity) + assert p2.name == p1.name + + # 检查是深拷贝 + p2.position[0] = 100.0 + assert p1.position[0] == 1.0 # 原始对象不应改变 + + +class TestThreeBodySolver: + """测试三体问题求解器""" + + def test_solver_creation(self): + """测试求解器创建""" + particles = [ + Particle(mass=1.0, position=[1.0, 0.0, 0.0], velocity=[0.0, 1.0, 0.0]), + Particle(mass=1.0, position=[-1.0, 0.0, 0.0], velocity=[0.0, -1.0, 0.0]), + Particle(mass=0.001, position=[0.0, 1.0, 0.0], velocity=[-1.0, 0.0, 0.0]) + ] + + solver = ThreeBodySolver(particles, dt=0.001) + + assert len(solver.particles) == 3 + assert solver.dt == 0.001 + assert solver.time == 0.0 + + def test_solver_wrong_number_of_particles(self): + """测试错误数量的质点""" + particles = [ + Particle(mass=1.0, position=[0.0, 0.0, 0.0], velocity=[0.0, 0.0, 0.0]), + Particle(mass=1.0, position=[1.0, 0.0, 0.0], velocity=[0.0, 0.0, 0.0]) + ] + + with pytest.raises(ValueError, match="三体问题需要恰好3个质点"): + ThreeBodySolver(particles, dt=0.001) + + def test_acceleration_calculation(self): + """测试加速度计算""" + # 创建简单的测试配置：三个质点在等边三角形顶点 + particles = [ + Particle(mass=1.0, position=[0.0, 0.0, 0.0], velocity=[0.0, 0.0, 0.0]), + Particle(mass=1.0, position=[1.0, 0.0, 0.0], velocity=[0.0, 0.0, 0.0]), + Particle(mass=1.0, position=[0.5, np.sqrt(3)/2, 0.0], velocity=[0.0, 0.0, 0.0]) + ] + + solver = ThreeBodySolver(particles, dt=0.001) + + # 计算加速度 + accelerations = solver._calculate_accelerations(particles) + + # 检查加速度形状 + assert len(accelerations) == 3 + for acc in accelerations: + assert acc.shape == (3,) + + # 由于对称性，第一个质点的加速度应该指向其他两个质点的方向 + # 这里只检查计算是否成功，不检查具体值 + + def test_center_of_mass(self): + """测试质心计算""" + particles = [ + Particle(mass=1.0, position=[1.0, 0.0, 0.0], velocity=[0.0, 0.0, 0.0]), + Particle(mass=2.0, position=[-1.0, 0.0, 0.0], velocity=[0.0, 0.0, 0.0]), + Particle(mass=3.0, position=[0.0, 1.0, 0.0], velocity=[0.0, 0.0, 0.0]) + ] + + solver = ThreeBodySolver(particles, dt=0.001) + com = solver.get_center_of_mass() + + # 计算期望的质心 + total_mass = 1.0 + 2.0 + 3.0 + expected_com = np.array([ + (1.0*1.0 + 2.0*(-1.0) + 3.0*0.0) / total_mass, + (1.0*0.0 + 2.0*0.0 + 3.0*1.0) / total_mass, + (1.0*0.0 + 2.0*0.0 + 3.0*0.0) / total_mass + ]) + + assert np.allclose(com, expected_com) + + def test_energy_calculation(self): + """测试能量计算""" + particles = [ + Particle(mass=1.0, position=[1.0, 0.0, 0.0], velocity=[0.0, 1.0, 0.0]), + Particle(mass=1.0, position=[-1.0, 0.0, 0.0], velocity=[0.0, -1.0, 0.0]), + Particle(mass=1.0, position=[0.0, 0.0, 1.0], velocity=[0.0, 0.0, 0.0]) + ] + + solver = ThreeBodySolver(particles, dt=0.001) + energy = solver._calculate_total_energy() + + # 能量应该是有限的实数 + assert np.isfinite(energy) + assert isinstance(energy, float) + + def test_single_step(self): + """测试单步积分""" + particles = [ + Particle(mass=1.0, position=[1.0, 0.0, 0.0], velocity=[0.0, 0.5, 0.0]), + Particle(mass=1.0, position=[-1.0, 0.0, 0.0], velocity=[0.0, -0.5, 0.0]), + Particle(mass=0.001, position=[0.0, 1.0, 0.0], velocity=[-0.5, 0.0, 0.0]) + ] + + solver = ThreeBodySolver(particles, dt=0.001) + + # 保存初始位置 + initial_positions = [p.position.copy() for p in particles] + + # 执行单步积分 + new_particles = solver.step() + + # 检查位置是否改变 + for i, (old_pos, new_particle) in enumerate(zip(initial_positions, new_particles)): + assert not np.allclose(old_pos, new_particle.position) + + # 检查时间是否增加 + assert solver.time == 0.001 + + def test_conservation_laws(self): + """测试守恒定律（动量、角动量、能量）""" + # 使用8字形轨道配置（应该是稳定的） + particles = ThreeBodyConfig.create_figure8_config() + + solver = ThreeBodySolver(particles, dt=0.0001) + + # 模拟很短时间 + solver.simulate(total_time=0.1, progress_interval=100) + + # 计算守恒误差 + momentum_error, angular_momentum_error, energy_error = solver.get_conservation_errors() + + # 误差应该很小 + assert momentum_error < 1e-10 + assert angular_momentum_error < 1e-10 + assert energy_error < 1e-5 # 能量守恒要求较低，因为数值误差 + + +class TestThreeBodyConfig: + """测试配置管理""" + + def test_figure8_config(self): + """测试8字形轨道配置""" + particles = ThreeBodyConfig.create_figure8_config() + + assert len(particles) == 3 + assert all(p.mass == 1.0 for p in particles) + + # 检查总动量接近零（8字形轨道应该满足） + total_momentum = np.zeros(3) + for p in particles: + total_momentum += p.mass * p.velocity + + assert np.linalg.norm(total_momentum) < 1e-10 + + def test_lagrange_config(self): + """测试拉格朗日点配置""" + # 测试L4点 + particles_l4 = ThreeBodyConfig.create_lagrange_point_config(lagrange_point=4) + assert len(particles_l4) == 3 + + # 检查质量 + assert particles_l4[0].mass == 1.0 # 太阳 + assert particles_l4[1].mass == 3e-6 # 地球 + assert particles_l4[2].mass == 1e-8 # 测试质点 + + # 测试L5点 + particles_l5 = ThreeBodyConfig.create_lagrange_point_config(lagrange_point=5) + assert len(particles_l5) == 3 + + # 检查位置（L4和L5应该在等边三角形顶点） + r_l4 = particles_l4[2].position + r_l5 = particles_l5[2].position + + assert np.allclose(r_l4, [0.5, np.sqrt(3)/2, 0.0]) + assert np.allclose(r_l5, [0.5, -np.sqrt(3)/2, 0.0]) + + def test_random_config(self): + """测试随机配置""" + particles = ThreeBodyConfig.create_random_config() + + assert len(particles) == 3 + assert all(0.5 <= p.mass <= 2.0 for p in particles) + + # 检查总动量接近零（随机配置会调整速度使总动量为零） + total_momentum = np.zeros(3) + for p in particles: + total_momentum += p.mass * p.velocity + + assert np.linalg.norm(total_momentum) < 1e-10 + + def test_custom_config(self): + """测试自定义配置""" + config_dict = { + 'particle_1': { + 'mass': 1.0, + 'position': [1.0, 0.0, 0.0], + 'velocity': [0.0, 1.0, 0.0], + 'name': 'Star A', + 'color': 'red' + }, + 'particle_2': { + 'mass': 2.0, + 'position': [-1.0, 0.0, 0.0], + 'velocity': [0.0, -0.5, 0.0], + 'name': 'Star B', + 'color': 'green' + }, + 'particle_3': { + 'mass': 0.5, + 'position': [0.0, 1.0, 0.0], + 'velocity': [0.5, 0.0, 0.0], + 'name': 'Star C', + 'color': 'blue' + } + } + + particles = ThreeBodyConfig.create_custom_config(config_dict) + + assert len(particles) == 3 + assert particles[0].name == 'Star A' + assert particles[1].mass == 2.0 + assert np.allclose(particles[2].position, [0.0, 1.0, 0.0]) + + +def test_integration_accuracy(): + """测试数值积分精度""" + # 使用简单的二体问题测试（第三个体质量很小） + particles = [ + Particle(mass=1.0, position=[1.0, 0.0, 0.0], velocity=[0.0, 2*np.pi, 0.0]), + Particle(mass=1.0, position=[-1.0, 0.0, 0.0], velocity=[0.0, -2*np.pi, 0.0]), + Particle(mass=1e-6, position=[0.0, 0.0, 0.0], velocity=[0.0, 0.0, 0.0]) # 很小的测试质点 + ] + + # 测试不同时间步长 + dts = [0.01, 0.005, 0.001, 0.0005] + energy_errors = [] + + for dt in dts: + solver = ThreeBodySolver([p.copy() for p in particles], dt=dt) + solver.simulate(total_time=1.0, progress_interval=10000) + + _, _, energy_error = solver.get_conservation_errors() + energy_errors.append(energy_error) + + # 检查误差随步长减小而减小（四阶方法） + for i in range(len(energy_errors)-1): + # 误差应该大致按 dt^4 减小 + error_ratio = energy_errors[i] / energy_errors[i+1] + dt_ratio = (dts[i] / dts[i+1])**4 + # 允许一定的误差范围 + assert 0.1 < error_ratio / dt_ratio < 10.0 + + +if __name__ == "__main__": + # 运行所有测试 + print("运行三体问题求解器测试...") + + # 创建测试实例 + test_particle = TestParticle() + test_solver = TestThreeBodySolver() + test_config = TestThreeBodyConfig() + + # 运行粒子测试 + print("\n1. 测试质点类:") + test_particle.test_particle_creation() + print(" ✓ test_particle_creation 通过") + + test_particle.test_particle_update() + print(" ✓ test_particle_update 通过") + + test_particle.test_particle_energy() + print(" ✓ test_particle_energy 通过") + + test_particle.test_particle_copy() + print(" ✓ test_particle_copy 通过") + + # 运行求解器测试 + print("\n2. 测试求解器类:") + test_solver.test_solver_creation() + print(" ✓ test_solver_creation 通过") + + try: + test_solver.test_solver_wrong_number_of_particles() + print(" ✗ test_solver_wrong_number_of_particles 应该抛出异常") + except ValueError: + print(" ✓ test_solver_wrong_number_of_particles 通过") + + test_solver.test_acceleration_calculation() + print(" ✓ test_acceleration_calculation 通过") + + test_solver.test_center_of_mass() + print(" ✓ test_center_of_mass 通过") + + test_solver.test_energy_calculation() + print(" ✓ test_energy_calculation 通过") + + test_solver.test_single_step() + print(" ✓ test_single_step 通过") + + test_solver.test_conservation_laws() + print(" ✓ test_conservation_laws 通过") + + # 运行配置测试 + print("\n3. 测试配置管理:") + test_config.test_figure8_config() + print(" ✓ test_figure8_config 通过") + + test_config.test_lagrange_config() + print(" ✓ test_lagrange_config 通过") + + test_config.test_random_config() + print(" ✓ test_random_config 通过") + + test_config.test_custom_config() + print(" ✓ test_custom_config 通过") + + # 运行积分精度测试 + print("\n4. 测试数值积分精度:") + test_integration_accuracy() + print(" ✓ test_integration_accuracy 通过") + + print("\n" + "="*60) + print("所有测试通过!") + print("="*60) \ No newline at end of file diff --git a/three_body_problem/visualizer.py b/three_body_problem/visualizer.py new file mode 100644 index 0000000..fc97b25 --- /dev/null +++ b/three_body_problem/visualizer.py @@ -0,0 +1,321 @@ +""" +三体问题可视化模块 +""" + +import numpy as np +import matplotlib.pyplot as plt +from mpl_toolkits.mplot3d import Axes3D +from typing import List, Optional, Tuple +from .particle import Particle +from .solver import ThreeBodySolver + + +class ThreeBodyVisualizer: + """三体问题可视化类""" + + def __init__(self, figsize: Tuple[int, int] = (12, 10)): + """ + 初始化可视化器 + + 参数: + figsize: 图形大小 + """ + self.figsize = figsize + self.fig = None + self.ax = None + + def create_3d_plot(self): + """创建3D图形""" + self.fig = plt.figure(figsize=self.figsize) + self.ax = self.fig.add_subplot(111, projection='3d') + + def plot_trajectories(self, solver: ThreeBodySolver, + show_current_positions: bool = True, + show_com: bool = True, + title: str = "三体问题轨迹"): + """ + 绘制三体运动轨迹 + + 参数: + solver: 三体问题求解器 + show_current_positions: 是否显示当前位置 + show_com: 是否显示质心 + title: 图形标题 + """ + if self.ax is None: + self.create_3d_plot() + + trajectories = solver.get_trajectories() + + # 绘制每个质点的轨迹 + colors = ['red', 'green', 'blue'] + for i, (traj, particle) in enumerate(zip(trajectories, solver.particles)): + color = particle.color if particle.color else colors[i % len(colors)] + label = particle.name if particle.name else f"质点 {i+1}" + + # 绘制轨迹线 + self.ax.plot(traj[:, 0], traj[:, 1], traj[:, 2], + color=color, alpha=0.7, linewidth=1.5, label=label) + + # 绘制当前位置 + if show_current_positions and len(traj) > 0: + current_pos = traj[-1] + self.ax.scatter(current_pos[0], current_pos[1], current_pos[2], + color=color, s=100, edgecolors='black', linewidth=1.5) + + # 绘制质心 + if show_com: + com = solver.get_center_of_mass() + self.ax.scatter(com[0], com[1], com[2], + color='black', marker='x', s=200, label='质心', linewidth=2) + + # 设置图形属性 + self.ax.set_xlabel('X (AU)', fontsize=12) + self.ax.set_ylabel('Y (AU)', fontsize=12) + self.ax.set_zlabel('Z (AU)', fontsize=12) + self.ax.set_title(title, fontsize=14, fontweight='bold') + self.ax.legend(fontsize=10) + self.ax.grid(True, alpha=0.3) + + # 设置等比例坐标轴 + self.ax.set_aspect('auto') + + def plot_2d_projection(self, solver: ThreeBodySolver, + projection: str = 'xy', + show_current_positions: bool = True, + show_com: bool = True, + title: str = "三体问题轨迹 (2D投影)"): + """ + 绘制2D投影 + + 参数: + solver: 三体问题求解器 + projection: 投影平面 ('xy', 'xz', 'yz') + show_current_positions: 是否显示当前位置 + show_com: 是否显示质心 + title: 图形标题 + """ + if projection not in ['xy', 'xz', 'yz']: + raise ValueError("projection 必须是 'xy', 'xz' 或 'yz'") + + fig, ax = plt.subplots(figsize=(10, 8)) + trajectories = solver.get_trajectories() + + # 确定坐标轴索引 + if projection == 'xy': + x_idx, y_idx = 0, 1 + x_label, y_label = 'X (AU)', 'Y (AU)' + elif projection == 'xz': + x_idx, y_idx = 0, 2 + x_label, y_label = 'X (AU)', 'Z (AU)' + else: # 'yz' + x_idx, y_idx = 1, 2 + x_label, y_label = 'Y (AU)', 'Z (AU)' + + # 绘制每个质点的轨迹 + colors = ['red', 'green', 'blue'] + for i, (traj, particle) in enumerate(zip(trajectories, solver.particles)): + color = particle.color if particle.color else colors[i % len(colors)] + label = particle.name if particle.name else f"质点 {i+1}" + + # 绘制轨迹线 + ax.plot(traj[:, x_idx], traj[:, y_idx], + color=color, alpha=0.7, linewidth=1.5, label=label) + + # 绘制当前位置 + if show_current_positions and len(traj) > 0: + current_pos = traj[-1] + ax.scatter(current_pos[x_idx], current_pos[y_idx], + color=color, s=100, edgecolors='black', linewidth=1.5) + + # 绘制质心 + if show_com: + com = solver.get_center_of_mass() + ax.scatter(com[x_idx], com[y_idx], + color='black', marker='x', s=200, label='质心', linewidth=2) + + # 设置图形属性 + ax.set_xlabel(x_label, fontsize=12) + ax.set_ylabel(y_label, fontsize=12) + ax.set_title(title, fontsize=14, fontweight='bold') + ax.legend(fontsize=10) + ax.grid(True, alpha=0.3) + ax.set_aspect('equal', adjustable='box') + + return fig, ax + + def plot_energy_conservation(self, solver: ThreeBodySolver, + time_points: Optional[np.ndarray] = None): + """ + 绘制能量守恒图 + + 参数: + solver: 三体问题求解器 + time_points: 时间点数组（如果为None，则使用模拟时间） + """ + # 从历史记录中提取能量信息 + # 注意：这里需要修改求解器以记录能量历史 + # 暂时返回一个简单的图形 + fig, ax = plt.subplots(figsize=(10, 6)) + + # 这里可以添加能量历史记录功能 + ax.set_xlabel('时间 (年)', fontsize=12) + ax.set_ylabel('总能量', fontsize=12) + ax.set_title('能量守恒', fontsize=14, fontweight='bold') + ax.grid(True, alpha=0.3) + + return fig, ax + + def plot_phase_space(self, solver: ThreeBodySolver, + particle_index: int = 0, + dimension: str = 'x'): + """ + 绘制相空间图（位置 vs 速度） + + 参数: + solver: 三体问题求解器 + particle_index: 质点索引 (0, 1, 2) + dimension: 维度 ('x', 'y', 'z') + """ + if particle_index not in [0, 1, 2]: + raise ValueError("particle_index 必须是 0, 1, 或 2") + + if dimension not in ['x', 'y', 'z']: + raise ValueError("dimension 必须是 'x', 'y', 或 'z'") + + particle = solver.particles[particle_index] + trajectories = particle.get_trajectory() + + if len(trajectories) < 2: + print("警告：轨迹数据不足，无法绘制相空间图") + return None, None + + # 获取位置和速度历史 + positions = trajectories[:, {'x': 0, 'y': 1, 'z': 2}[dimension]] + + # 注意：速度历史需要从求解器中获取 + # 暂时使用位置差分近似速度 + if len(positions) > 1: + dt = solver.dt + velocities = np.gradient(positions, dt) + else: + velocities = np.zeros_like(positions) + + fig, ax = plt.subplots(figsize=(10, 6)) + + # 绘制相空间轨迹 + scatter = ax.scatter(positions, velocities, c=np.arange(len(positions)), + cmap='viridis', alpha=0.7, s=20) + + # 添加颜色条表示时间 + plt.colorbar(scatter, ax=ax, label='时间步') + + ax.set_xlabel(f'{dimension.upper()} 位置 (AU)', fontsize=12) + ax.set_ylabel(f'{dimension.upper()} 速度 (AU/年)', fontsize=12) + ax.set_title(f'质点 {particle_index+1} 的相空间图 ({dimension.upper()}维度)', + fontsize=14, fontweight='bold') + ax.grid(True, alpha=0.3) + + return fig, ax + + def animate_trajectories(self, solver: ThreeBodySolver, + save_path: Optional[str] = None, + fps: int = 30, + dpi: int = 100): + """ + 创建轨迹动画（需要额外安装 matplotlib.animation） + + 参数: + solver: 三体问题求解器 + save_path: 保存路径（如果为None则显示动画） + fps: 帧率 + dpi: 分辨率 + """ + try: + from matplotlib.animation import FuncAnimation + except ImportError: + print("错误：需要安装 matplotlib.animation 模块") + return + + trajectories = solver.get_trajectories() + if any(len(traj) < 2 for traj in trajectories): + print("错误：轨迹数据不足，无法创建动画") + return + + fig = plt.figure(figsize=(10, 8)) + ax = fig.add_subplot(111, projection='3d') + + # 初始化图形元素 + lines = [] + points = [] + colors = ['red', 'green', 'blue'] + + for i, (traj, particle) in enumerate(zip(trajectories, solver.particles)): + color = particle.color if particle.color else colors[i % len(colors)] + label = particle.name if particle.name else f"质点 {i+1}" + + # 创建轨迹线 + line, = ax.plot([], [], [], color=color, alpha=0.7, linewidth=1.5, label=label) + lines.append(line) + + # 创建当前位置点 + point, = ax.plot([], [], [], 'o', color=color, markersize=8, + markeredgecolor='black', markeredgewidth=1) + points.append(point) + + # 设置坐标轴范围 + all_points = np.vstack(trajectories) + max_range = np.max([all_points[:, i].max() - all_points[:, i].min() for i in range(3)]) + mid_x = (all_points[:, 0].max() + all_points[:, 0].min()) * 0.5 + mid_y = (all_points[:, 1].max() + all_points[:, 1].min()) * 0.5 + mid_z = (all_points[:, 2].max() + all_points[:, 2].min()) * 0.5 + + ax.set_xlim(mid_x - max_range/2, mid_x + max_range/2) + ax.set_ylim(mid_y - max_range/2, mid_y + max_range/2) + ax.set_zlim(mid_z - max_range/2, mid_z + max_range/2) + + ax.set_xlabel('X (AU)', fontsize=12) + ax.set_ylabel('Y (AU)', fontsize=12) + ax.set_zlabel('Z (AU)', fontsize=12) + ax.set_title('三体问题动画', fontsize=14, fontweight='bold') + ax.legend(fontsize=10) + ax.grid(True, alpha=0.3) + + # 动画更新函数 + def update(frame): + for i, (traj, line, point) in enumerate(zip(trajectories, lines, points)): + # 更新轨迹线（显示到当前帧） + line.set_data(traj[:frame+1, 0], traj[:frame+1, 1]) + line.set_3d_properties(traj[:frame+1, 2]) + + # 更新当前位置点 + if frame < len(traj): + point.set_data([traj[frame, 0]], [traj[frame, 1]]) + point.set_3d_properties([traj[frame, 2]]) + + return lines + points + + # 创建动画 + anim = FuncAnimation(fig, update, frames=min(len(traj) for traj in trajectories), + interval=1000/fps, blit=True) + + if save_path: + anim.save(save_path, writer='ffmpeg', fps=fps, dpi=dpi) + print(f"动画已保存到: {save_path}") + else: + plt.show() + + return anim + + def show(self): + """显示所有图形""" + plt.tight_layout() + plt.show() + + def save_figure(self, filename: str, dpi: int = 300): + """保存当前图形""" + if self.fig is not None: + self.fig.savefig(filename, dpi=dpi, bbox_inches='tight') + print(f"图形已保存到: {filename}") + else: + print("警告：没有活动的图形可以保存") \ No newline at end of file diff --git a/tips.md b/tips.md new file mode 100644 index 0000000..e720129 --- /dev/null +++ b/tips.md @@ -0,0 +1,3 @@ +2026-03-11 15:58:59.004 [info] Python 解释器路径: .\.venv\Scripts\python.exe + +a:\Users\bjsde\Documents\GitHub\02 \.venv\Scripts\python.exe \ No newline at end of file