#include #include #include #include #include #include using namespace std; // 常量定义 const double G = 6.67430e-11; // 引力常数 (m^3 kg^-1 s^-2) const double DT = 0.01; // 时间步长 const int TMAX = 100; // 总时间步数 // 三维向量结构体 struct Vec3 { double x, y, z; Vec3() : x(0), y(0), z(0) {} Vec3(double x, double y, double z) : x(x), y(y), z(z) {} Vec3 operator+(const Vec3& other) const { return Vec3(x + other.x, y + other.y, z + other.z); } Vec3 operator-(const Vec3& other) const { return Vec3(x - other.x, y - other.y, z - other.z); } Vec3 operator*(double scalar) const { return Vec3(x * scalar, y * scalar, z * scalar); } Vec3 operator/(double scalar) const { return Vec3(x / scalar, y / scalar, z / scalar); } double magnitude() const { return sqrt(x*x + y*y + z*z); } }; // 天体结构体 struct Body { double mass; // 质量 Vec3 position; // 位置 Vec3 velocity; // 速度 Vec3 force; // 受力 }; // 计算第i个物体所受的引力 Vec3 compute_force(int i, const vector& bodies) { Vec3 total_force(0, 0, 0); for (size_t j = 0; j < bodies.size(); j++) { if (i == j) continue; // 跳过自己 // 计算从物体i指向物体j的向量 Vec3 r_vec = bodies[j].position - bodies[i].position; double distance = r_vec.magnitude(); // 避免除以零（物体重合的情况） if (distance < 1e-10) continue; // 计算引力大小: F = G * m_i * m_j / r^2 double force_magnitude = G * bodies[i].mass * bodies[j].mass / (distance * distance); // 计算力的方向（单位向量） Vec3 force_direction = r_vec / distance; // 累加力（考虑方向） total_force = total_force + force_direction * force_magnitude; } return total_force; } int main(int argc, char** argv) { // 可以从命令行参数获取天体数量 int n = 4; // 默认4个天体 bool verbose = false; if (argc > 1) { n = atoi(argv[1]); } if (argc > 2) { verbose = (strcmp(argv[2], "--verbose") == 0 || strcmp(argv[2], "-v") == 0); } cout << "N体问题串行模拟" << endl; cout << "天体数量: " << n << endl; cout << "时间步长: " << DT << " s" << endl; cout << "总步数: " << TMAX << endl; cout << "----------------------------------------" << endl; // 初始化天体系统 vector bodies(n); vector bodies_new(n); // 初始化天体数据（简化版：模拟太阳系内行星） // 使用简化的单位系统以便观察效果 double mass_scale = 1e24; // 质量缩放因子 double dist_scale = 1e8; // 距离缩放因子 double vel_scale = 1e3; // 速度缩放因子 // 中心天体（类似太阳） bodies[0].mass = 1000 * mass_scale; bodies[0].position = Vec3(0, 0, 0); bodies[0].velocity = Vec3(0, 0, 0); // 其他天体（类似行星） for (int i = 1; i < n; i++) { bodies[i].mass = (1.0 + i * 0.5) * mass_scale; double angle = 2.0 * M_PI * i / n; double radius = (1.0 + i * 0.5) * dist_scale; bodies[i].position = Vec3( radius * cos(angle), radius * sin(angle), 0.0 ); // 给予切向速度以形成轨道 double orbital_speed = sqrt(G * bodies[0].mass / radius); bodies[i].velocity = Vec3( -orbital_speed * sin(angle), orbital_speed * cos(angle), 0.0 ); } // 输出初始状态 cout << fixed << setprecision(6); if(verbose){ cout << "\n初始状态:" << endl; for (int i = 0; i < n; i++) { cout << "天体 " << i << ": 质量=" << bodies[i].mass/mass_scale << "e24 kg, " << "位置=(" << bodies[i].position.x/dist_scale << ", " << bodies[i].position.y/dist_scale << ", " << bodies[i].position.z/dist_scale << ")e8 m" << endl; } } // 主循环：N体模拟 cout << "\n开始模拟..." << endl; time_t start_time = clock(); for (int t = 0; t < TMAX; t++) { // 第一步：计算所有物体新的速度和位置 for (int i = 0; i < n; i++) { // 计算第i个物体所受的力 Vec3 F = compute_force(i, bodies); // 计算新速度: v^(t+1) = v^t + F * dt / m Vec3 v_new = bodies[i].velocity + F * DT / bodies[i].mass; // 计算新位置: x^(t+1) = x^t + v^(t+1) * dt Vec3 x_new = bodies[i].position + v_new * DT; // 保存到临时数组 bodies_new[i].mass = bodies[i].mass; bodies_new[i].position = x_new; bodies_new[i].velocity = v_new; } // 第二步：更新所有物体的速度和位置 for (int i = 0; i < n; i++) { bodies[i].position = bodies_new[i].position; bodies[i].velocity = bodies_new[i].velocity; } // 每10步输出一次状态 if (verbose && (t + 1) % 10 == 0) { cout << "时间步 " << t + 1 << ":" << endl; for (int i = 0; i < n; i++) { cout << " 天体 " << i << ": " << "位置=(" << bodies[i].position.x/dist_scale << ", " << bodies[i].position.y/dist_scale << ", " << bodies[i].position.z/dist_scale << ")e8 m, " << "速度=(" << bodies[i].velocity.x/vel_scale << ", " << bodies[i].velocity.y/vel_scale << ", " << bodies[i].velocity.z/vel_scale << ")e3 m/s" << endl; } } } time_t end_time = clock(); double elapsed_secs = double(end_time - start_time) / CLOCKS_PER_SEC; cout << "\n模拟用时: " << elapsed_secs << " 秒" << endl; cout << "\n模拟完成!" << endl; return 0; }