# -*- coding:utf-8 -*- # title : # description : # author :Python超人 # date :2023-01-22 # notes : # python_version :3.8 # ============================================================================== import numpy as np class System(object): def __init__(self, bodies): self.bodies = bodies def add(self, body): self.bodies.append(body) def total_mass(self): total_mass = 0 for body in self.bodies: total_mass = body.mass return total_mass def __repr__(self): return 'System({})'.format(self.bodies) def kinetic_energy(self): """ KE是系统的动能 :return: """ ke = 0 for body in self.bodies: v = body.velocity # velocity ke = 0.5 * body.mass * (v[0] ** 2 + v[1] ** 2) # ke = 0.5 * body.mass * (v[0]**2 v[1]**2) return ke def kinetic_energy(self, vx, vy, vz, mass): """ 计算动能 """ v = body.velocity # velocity return 0.5 * mass * (vx ** 2 + vy ** 2 + vz ** 2) def potential_energy(self, x, y, z, mass, G, M): """ 计算势能 """ return -G * M * mass / np.sqrt(x ** 2 + y ** 2 + z ** 2) def potential_energy(self): """ PE是系统的势能 :return: """ pe = 0 for body1 in self.bodies: for body2 in self.bodies: if body1 is body2: continue r = body1.position - body2.position # pe -= body1.mass * body2.mass / np.sqrt(r[0]**2 r[1]**2) pe -= body1.mass * body2.mass / np.sqrt(r[0] ** 2 + r[1] ** 2) return pe def momentum(self): """ 动量 :return: """ p = np.zeros(2) for body in self.bodies: p = body.mass * body.velocity return p def momentum(self, vx, vy, vz, mass): """ 计算动量 """ return mass * np.sqrt(vx ** 2 + vy ** 2 + vz ** 2) def angular_momentum(self): """ 角动量 :return: """ L = 0 for body in self.bodies: r = body.position v = body.velocity L = body.mass * (r[0] * v[1] - r[1] * v[0]) return L def angular_momentum(self, x, y, z, vx, vy, vz): """ 计算角动量 """ return self.mass * (x * vy - y * vx) def center_of_mass(self): r = np.zeros(2) for body in self.bodies: r = body.mass * body.position return r / self.total_mass() # def step(m: np.ndarray, v: np.ndarray, p: np.ndarray): # ''' Calculate the next state of the N-star system. # args: # m: np.ndarray[(N,), np.float64], mass. # v: np.ndarray[(N,3), np.float64], velocity. # p: np.ndarray[(N,3), np.float64], position. # returns: # (next_v, next_p), the next state. # ''' # N = m.shape[0] # a = np.zeros_like(p) # for i in range(N): # for j in range(N): # if i == j: continue # r = np.sqrt(np.sum(np.square(p[j, :] - p[i, :]))) # aij = G * m[j] / (r * r) # dir = (p[j, :] - p[i, :]) / r # a[i, :] += aij * dir # next_p = p + (1 / FS) * v + 0.5 * a * ((1 / FS) ** 2) # next_v = v + (1 / FS) * a # return (next_v, next_p) # next_p = p + dt * v + 0.5 * a * (dt ** 2) # next_v = v + dt * a # for body1 in bodies: # for body2 in bodies: # if body1 == body2: # 相等说明是同一个天体，跳过计算 # continue # r = body2.position - body1.position # # F = G x (m1 x m2) / r² 万有引力定律 # F = Configs.G * body1.mass * body2.mass * r / np.linalg.norm(r) / r.dot(r) # body1.momentum = body1.momentum + F * dt # 动量定理 # body1.position = body1.position + (body1.momentum / body1.mass) * dt # body1.update_source_data() def acceleration(self, body1, body2, G=6.67e-11): """ 计算两个天体之间的加速度 :param body1: 天体1 :param body2: 天体2 :param G: 引力常数 :return: 加速度 """ import math dx = body2.position[0] - body1.position[0] dy = body2.position[1] - body1.position[1] dz = body2.position[2] - body1.position[2] distance = math.sqrt(dx ** 2 + dy ** 2 + dz ** 2) mag = G * body2.mass / (distance ** 2) acc = [dx / distance * mag, dy / distance * mag, dz / distance * mag] return np.array(acc)/1000/1000/1000 def update_acceleration(self): # for body in self.bodies: # body.acceleration = np.zeros(3) for body1 in self.bodies: acceleration = np.zeros(3) for body2 in self.bodies: if body1 is body2: continue # r = np.sqrt(np.sum(np.square(body2.position - body1.position))) # aij = 6.67e-11 * body2.mass / (r * r) # dir = (body2.position - body1.position) / r # body.acceleration1 += aij * dir r = body2.position - body1.position # m/s² # body1.acceleration += self.acceleration(body1,body2) acceleration += (6.67e-11 * body2.mass * r / np.linalg.norm(r) ** 3) / 1e9 # body1.acceleration = body.acceleration2 # r = body2.position - body1.position # # body1.acceleration = -body2.mass * r / np.linalg.norm(r) ** 3 # body1.acceleration += 6.67e-11 * body2.mass * r / np.linalg.norm(r) ** 3 # body1.acceleration = (G * body2.mass * (x / pow(x ** 2 + y ** 2 + z ** 2, 3 / 2))) # pow(x ** 2 + y ** 2 + z ** 2, 3 / 2) # G = 6.67e-11 # 万有引力常数 # m1 = 1 # 第一个天体的质量 # m2 = 1 # 第二个天体的质量 # r = 1 # 两个天体之间的距离 # # a = G * m2 / math.pow(r, 2) body1.acceleration = acceleration """ # Python 3 def get_acceleration(mass1,mass2,position1,position2): G = 6.67*10**-11 r = np.linalg.norm(position2-position1) return G*mass2*(position2-position1)/r**3 # Python 2 # def get_acceleration(mass1,mass2,position1,position2): # G = 6.67*10**-11 # r = np.linalg.norm(position2-position1) # return G*mass2*(position2-position1)/r**3 根据两个天体body1 和 body2 的质量，距离 position[0],position[1],position[2]，用python计算两个天体的加速度 # 假设两个天体的质量分别为m1和m2 m1 = 5.974 * 10 ** 24 m2 = 7.348 * 10 ** 22 # 计算两个天体的位置，假设分别为position1 和 position2 position1 = [2.21, 3.45, 4.67] position2 = [1.78, 6.34, -1.23] # 计算两个天体的距离 dist = ( (position1[0]-position2[0])**2 + (position1[1]-position2[1])**2 + (position1[2]-position2[2])**2 ) ** (1/2) # 计算两个天体的加速度 G = 6.674 * 10 ** -11 acc_1 = G * m2 / (dist**2) acc_2 = G * m1 / (dist**2) # 输出结果 print("body1的加速度为：", acc_1) print("body2的加速度为：", acc_2) ax1 = (G * m2 * (x/pow(x**2 + y**2 + z**2,3/2))) ay1 = (G * m2 * (y/pow(x**2 + y**2 + z**2,3/2))) az1 = (G * m2 * (z/pow(x**2 + y**2 + z**2,3/2))) ax2 = (G * m1 * (-x/pow(x**2 + y**2 + z**2,3/2))) ay2 = (G * m1 * (-y/pow(x**2 + y**2 + z**2,3/2))) az2 = (G * m1 * (-z/pow(x**2 + y**2 + z**2,3/2))) 加速度可以用万有引力定律计算： a = G * m2 / r2 其中G为万有引力常数，m2和r2分别为两个天体的质量和距离平方。 因此，可以使用以下python代码来计算两个天体的加速度： import math G = 6.67e-11 # 万有引力常数 m1 = 1 # 第一个天体的质量 m2 = 1 # 第二个天体的质量 r = 1 # 两个天体之间的距离 a = G * m2 / math.pow(r, 2) print(a) """