299 lines
9.7 KiB
Python
299 lines
9.7 KiB
Python
#!/usr/bin/env python3
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"""
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三体问题求解器演示脚本
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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from three_body_problem import ThreeBodySolver, Particle, ThreeBodyConfig, ThreeBodyVisualizer
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def demo_basic_usage():
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"""演示基本用法"""
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print("=" * 60)
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print("三体问题求解器 - 基本用法演示")
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print("=" * 60)
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# 1. 创建自定义三体系统
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print("\n1. 创建自定义三体系统...")
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particles = [
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Particle(mass=1.0, position=[1.0, 0.0, 0.0], velocity=[0.0, 1.0, 0.0], name="Star A", color="red"),
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Particle(mass=1.0, position=[-1.0, 0.0, 0.0], velocity=[0.0, -1.0, 0.0], name="Star B", color="green"),
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Particle(mass=0.1, position=[0.0, 1.0, 0.0], velocity=[-0.5, 0.0, 0.0], name="Star C", color="blue")
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]
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# 2. 创建求解器
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print("2. 创建求解器...")
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solver = ThreeBodySolver(particles, dt=0.001)
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# 3. 模拟5年
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print("3. 模拟5年运动...")
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solver.simulate(total_time=5.0, progress_interval=1000)
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# 4. 分析结果
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print("\n4. 分析模拟结果...")
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trajectories = solver.get_trajectories()
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print(f" 轨迹点数: {len(trajectories[0])}")
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com = solver.get_center_of_mass()
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print(f" 系统质心: [{com[0]:.3f}, {com[1]:.3f}, {com[2]:.3f}] AU")
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momentum_error, angular_momentum_error, energy_error = solver.get_conservation_errors()
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print(f" 动量误差: {momentum_error:.2e}")
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print(f" 角动量误差: {angular_momentum_error:.2e}")
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print(f" 能量相对误差: {energy_error:.2e}")
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# 5. 可视化
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print("\n5. 生成可视化图形...")
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visualizer = ThreeBodyVisualizer(figsize=(14, 10))
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# 创建3D轨迹图
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visualizer.create_3d_plot()
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visualizer.plot_trajectories(solver, title="自定义三体系统")
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# 保存图形
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visualizer.save_figure("demo_basic_3d.png", dpi=300)
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# 创建2D投影图
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fig, ax = visualizer.plot_2d_projection(solver, projection='xy', title="XY平面投影")
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fig.savefig("demo_basic_2d.png", dpi=300, bbox_inches='tight')
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print("\n图形已保存:")
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print(" - demo_basic_3d.png (3D轨迹)")
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print(" - demo_basic_2d.png (2D投影)")
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# 显示图形
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visualizer.show()
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return solver
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def demo_figure8():
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"""演示8字形轨道"""
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print("\n" + "=" * 60)
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print("8字形轨道演示")
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print("=" * 60)
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# 使用预置配置
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particles = ThreeBodyConfig.create_figure8_config()
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# 打印配置信息
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ThreeBodyConfig.print_config_summary(particles)
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# 创建求解器
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solver = ThreeBodySolver(particles, dt=0.001)
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# 模拟10年
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print("\n模拟10年8字形轨道...")
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solver.simulate(total_time=10.0, progress_interval=2000)
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# 可视化
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visualizer = ThreeBodyVisualizer(figsize=(12, 8))
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visualizer.create_3d_plot()
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visualizer.plot_trajectories(solver, title="8字形三体轨道")
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visualizer.save_figure("demo_figure8.png", dpi=300)
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print("\n图形已保存: demo_figure8.png")
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visualizer.show()
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return solver
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def demo_lagrange_points():
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"""演示拉格朗日点"""
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print("\n" + "=" * 60)
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print("拉格朗日点演示")
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print("=" * 60)
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# 创建L4点配置
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particles = ThreeBodyConfig.create_lagrange_point_config(lagrange_point=4)
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# 打印配置信息
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ThreeBodyConfig.print_config_summary(particles)
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# 创建求解器
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solver = ThreeBodySolver(particles, dt=0.001)
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# 模拟50年
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print("\n模拟50年拉格朗日点L4稳定性...")
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solver.simulate(total_time=50.0, progress_interval=10000)
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# 分析测试质点稳定性
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test_particle = solver.particles[2]
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trajectory = test_particle.get_trajectory()
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lagrange_position = np.array([0.5, np.sqrt(3)/2, 0.0])
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distances = np.linalg.norm(trajectory - lagrange_position, axis=1)
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print(f"\n测试质点稳定性分析:")
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print(f" 初始距离L4点: {distances[0]:.6f} AU")
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print(f" 最终距离L4点: {distances[-1]:.6f} AU")
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print(f" 最大距离偏差: {np.max(distances):.6f} AU")
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print(f" 平均距离偏差: {np.mean(distances):.6f} AU")
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# 可视化
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visualizer = ThreeBodyVisualizer(figsize=(12, 8))
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fig, ax = visualizer.plot_2d_projection(solver, projection='xy', title="拉格朗日点L4稳定性")
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fig.savefig("demo_lagrange_l4.png", dpi=300, bbox_inches='tight')
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print("\n图形已保存: demo_lagrange_l4.png")
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plt.show()
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return solver
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def demo_random_systems():
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"""演示随机系统"""
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print("\n" + "=" * 60)
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print("随机三体系统演示")
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print("=" * 60)
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# 创建3个不同的随机系统
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fig, axes = plt.subplots(1, 3, figsize=(18, 6))
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for i, seed in enumerate([42, 123, 456]):
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np.random.seed(seed)
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# 创建随机配置
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particles = ThreeBodyConfig.create_random_config(
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position_range=1.5,
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velocity_scale=2.0
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)
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# 创建求解器
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solver = ThreeBodySolver(particles, dt=0.001)
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# 模拟5年
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solver.simulate(total_time=5.0, progress_interval=2000)
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# 绘制轨迹
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trajectories = solver.get_trajectories()
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colors = ['red', 'green', 'blue']
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ax = axes[i]
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for j, (traj, particle) in enumerate(zip(trajectories, solver.particles)):
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color = particle.color if particle.color else colors[j % len(colors)]
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ax.plot(traj[:, 0], traj[:, 1], color=color, alpha=0.7, linewidth=1.5)
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ax.scatter(traj[-1, 0], traj[-1, 1], color=color, s=50, edgecolors='black', linewidth=1)
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ax.set_xlabel('X (AU)', fontsize=10)
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ax.set_ylabel('Y (AU)', fontsize=10)
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ax.set_title(f'随机系统 #{i+1} (种子: {seed})', fontsize=12, fontweight='bold')
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ax.grid(True, alpha=0.3)
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ax.set_aspect('equal', adjustable='box')
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plt.suptitle('随机三体系统示例', fontsize=14, fontweight='bold')
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plt.tight_layout()
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plt.savefig("demo_random_systems.png", dpi=300, bbox_inches='tight')
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print("\n图形已保存: demo_random_systems.png")
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plt.show()
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def demo_conservation_laws():
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"""演示守恒定律"""
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print("\n" + "=" * 60)
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print("守恒定律验证演示")
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print("=" * 60)
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# 使用8字形轨道（理论上应该守恒）
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particles = ThreeBodyConfig.create_figure8_config()
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# 测试不同时间步长下的守恒性
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time_steps = [0.01, 0.005, 0.001, 0.0005]
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total_time = 1.0
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results = []
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for dt in time_steps:
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print(f"\n测试时间步长: {dt}")
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solver = ThreeBodySolver([p.copy() for p in particles], dt=dt)
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solver.simulate(total_time=total_time, progress_interval=1000)
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momentum_error, angular_momentum_error, energy_error = solver.get_conservation_errors()
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results.append({
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'dt': dt,
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'momentum_error': momentum_error,
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'angular_momentum_error': angular_momentum_error,
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'energy_error': energy_error
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})
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print(f" 动量误差: {momentum_error:.2e}")
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print(f" 角动量误差: {angular_momentum_error:.2e}")
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print(f" 能量相对误差: {energy_error:.2e}")
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# 绘制误差图
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fig, axes = plt.subplots(1, 3, figsize=(15, 5))
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dts = [r['dt'] for r in results]
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# 动量误差
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axes[0].loglog(dts, [r['momentum_error'] for r in results], 'o-', linewidth=2, markersize=8)
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axes[0].set_xlabel('时间步长 (年)', fontsize=12)
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axes[0].set_ylabel('动量误差', fontsize=12)
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axes[0].set_title('动量守恒', fontsize=14, fontweight='bold')
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axes[0].grid(True, alpha=0.3, which='both')
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# 角动量误差
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axes[1].loglog(dts, [r['angular_momentum_error'] for r in results], 's-', linewidth=2, markersize=8, color='green')
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axes[1].set_xlabel('时间步长 (年)', fontsize=12)
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axes[1].set_ylabel('角动量误差', fontsize=12)
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axes[1].set_title('角动量守恒', fontsize=14, fontweight='bold')
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axes[1].grid(True, alpha=0.3, which='both')
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# 能量误差
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axes[2].loglog(dts, [r['energy_error'] for r in results], '^-', linewidth=2, markersize=8, color='red')
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axes[2].set_xlabel('时间步长 (年)', fontsize=12)
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axes[2].set_ylabel('能量相对误差', fontsize=12)
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axes[2].set_title('能量守恒', fontsize=14, fontweight='bold')
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axes[2].grid(True, alpha=0.3, which='both')
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# 添加参考线（四阶精度）
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ref_dt = np.array(dts)
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ref_error = 1e-4 * (ref_dt / 0.001)**4
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axes[2].loglog(ref_dt, ref_error, 'k--', alpha=0.7, label='四阶精度参考线')
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axes[2].legend()
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plt.suptitle('守恒定律数值验证 (RK4方法)', fontsize=16, fontweight='bold')
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plt.tight_layout()
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plt.savefig("demo_conservation_laws.png", dpi=300, bbox_inches='tight')
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print("\n图形已保存: demo_conservation_laws.png")
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plt.show()
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def main():
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"""主函数"""
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print("三体问题求解器演示")
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print("=" * 60)
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# 运行所有演示
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try:
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# 演示1: 基本用法
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solver1 = demo_basic_usage()
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# 演示2: 8字形轨道
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solver2 = demo_figure8()
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# 演示3: 拉格朗日点
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solver3 = demo_lagrange_points()
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# 演示4: 随机系统
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demo_random_systems()
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# 演示5: 守恒定律
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demo_conservation_laws()
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print("\n" + "=" * 60)
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print("所有演示完成!")
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print("=" * 60)
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except Exception as e:
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print(f"\n错误: {e}")
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import traceback
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traceback.print_exc()
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if __name__ == "__main__":
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main() |