多面体法计算小天体重力场的完整python代码实例

以下是一个计算小天体重力场的多面体法的 Python 代码示例：

import numpy as np

# 定义一个表示三维向量的类
class Vector3D:
    def __init__(self, x=0, y=0, z=0):
        self.x = x
        self.y = y
        self.z = z
    
    def __add__(self, other):
        return Vector3D(self.x + other.x, self.y + other.y, self.z + other.z)
    
    def __sub__(self, other):
        return Vector3D(self.x - other.x, self.y - other.y, self.z - other.z)
    
    def __mul__(self, other):
        return Vector3D(self.x * other, self.y * other, self.z * other)
    
    def cross(self, other):
        return Vector3D(self.y * other.z - self.z * other.y, self.z * other.x - self.x * other.z, self.x * other.y - self.y * other.x)
    
    def dot(self, other):
        return self.x * other.x + self.y * other.y + self.z * other.z
    
    def norm(self):
        return np.sqrt(self.x**2 + self.y**2 + self.z**2)

# 定义小天体多面体的类
class Polyhedron:
    def __init__(self, vertices, faces):
        self.vertices = vertices
        self.faces = faces
    
    # 计算每个面的法向量
    def compute_face_normals(self):
        face_normals = []
        for face in self.faces:
            v1 = self.vertices[face[0]]
            v2 = self.vertices[face[1]]
            v3 = self.vertices[face[2]]
            e1 = v2 - v1
            e2 = v3 - v2
            normal = e1.cross(e2)
            face_normals.append(normal)
        self.face_normals = face_normals
    
    # 计算每个面的面积和中心点
    def compute_face_areas_and_centers(self):
        face_areas = []
        face_centers = []
        for face in self.faces:
            v1 = self.vertices[face[0]]
            v2 = self.vertices[face[1]]
            v3 = self.vertices[face[2]]
            e1 = v2 - v1
            e2 = v3 - v2
            normal = e1.cross(e2)
            area = normal.norm() / 2
            center = (v1 + v2 + v3) * (1/3)
            face_areas.append(area)
            face_centers.append(center)
        self.face_areas = face_areas
        self.face_centers = face_centers
    
    # 计算小天体的质心
    def compute_centroid(self):
        total_area = sum(self.face_areas)
        centroid = Vector3D()
        for i, face_center in enumerate(self.face_centers):
            centroid = centroid + face_center * self.face_areas[i] / total_area
        self.centroid = centroid
    
    # 计算小天体的惯性矩阵
    def compute_inertia_tensor(self):
        Ixx = 0
        Iyy = 0
        Izz = 0
        Ixy = 0
        Ixz = 0
        Iyz = 0
        for i, face_center in enumerate(self.face_centers):
            v1 = self.vertices[self.faces[i][0]]
            v2 = self.vertices[self.faces[i][1]]
            v3 = self.vertices[self.faces[i][2]]
            e1 = v2 - v1
            e2 = v3 - v2
            normal = e1.cross(e2)
            area = self.face_areas[i]
            r = face_center - self.centroid
            Ixx += (r.y**2 + r.z**2) * area
            Iyy += (r.x**2 + r.z**2) * area
            Izz += (r.x**2 + r.y**2) * area
            Ixy -= r.x * r.y * area
            Ixz -= r.x * r.z * area
            Iyz -= r.y * r.z * area
        self.inertia_tensor = np.array([[Ixx, Ixy, Ixz], [Ixy, Iyy, Iyz], [Ixz, Iyz, Izz]])
    
    # 计算小天体在某一点的重力加速度
    def compute_gravity_acceleration(self, point, G, M):
        acceleration = Vector3D()
        for i, face_center in enumerate(self.face_centers):
            v1 = self.vertices[self.faces[i][0]]
            v2 = self.vertices[self.faces[i][1]]
            v3 = self.vertices[self.faces[i][2]]
            e1 = v2 - v1
            e2 = v3 - v2
            normal = e1.cross(e2)
            area = self.face_areas[i]
            r = face_center - point
            distance = r.norm()
            direction = r * (1/distance)
            gravity = G * M * normal * area / distance**2
            acceleration = acceleration + gravity
        return acceleration

# 小天体的顶点坐标和面信息
vertices = [
    Vector3D(1, 0, 0),
    Vector3D(0, 1, 0),
    Vector3D(-1, 0, 0),
    Vector3D(0, -1, 0),
    Vector3D(0, 0, 1),
    Vector3D(0, 0, -1)
]

faces = [
    [0, 1, 4],
    [1, 2, 4],
    [2, 3, 4],
    [3, 0, 4],
    [1, 0, 5],
    [2, 1, 5],
    [3, 2, 5],
    [0, 3, 5]
]

# 创建小天体对象并计算重力场
polyhedron = Polyhedron(vertices, faces)
polyhedron.compute_face_normals()
polyhedron.compute_face_areas_and_centers()
polyhedron.compute_centroid()
polyhedron.compute_inertia_tensor()

G = 6.67430e-11   # 万有引力常量
M = 1e12   # 小天体质量
position = Vector3D(1000, 2000, 3000)   # 计算重力场的点的位置
acceleration = polyhedron.compute_gravity_acceleration(position, G, M)

print("重力加速度：", acceleration.x, acceleration.y, acceleration.z)

此代码使用了多面体法来近似计算小天体的重力场。首先定义了一个表示三维向量的类和一个表示小天体多面体的类，然后在多面体类中实现了计算每个面的法向量、面积、中心点、质心和惯性矩阵的方法，以及计算小天体在某一点的重力加速度的方法。在代码的最后，我们使用一个简单的小天体模型来测试重力场的计算。