""" 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)