first

pc-1

three_body_problem/examples/__init__.py

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+"""
+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

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+"""
+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

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+"""
+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)