first

pc-1

three_body_problem/__init__.py

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+"""
+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"
+]

three_body_problem/config.py

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+"""
+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)

three_body_problem/demo.py

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+#!/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()

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"
+]

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()

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()

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)

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

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
+        )

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

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()

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",
+        ],
+    },
+)

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()

three_body_problem/tests/__init__.py

@@ -0,0 +1,3 @@
+"""
+三体问题测试模块
+"""

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)

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")