基于python和牛顿力学的物理模拟装置.zip

import turtle class Phy: ''' 逻辑：创建点→以下循环→计算力→计算加速度→计算速度→计算位置 ''' def __init__(self, m, v, p, r=None, color="black", e=0): ''' 创建一个点 :param m: float 质量大小，取正数 :param v: list[x,y,z] x,y,z为float 速度，矢量 :param p: list[x,y,z] x,y,z为float 位置 :param color: str or tuple(r,g,b) 点的颜色 :param r: float 点的半径 :param e: float 电荷 a: list[x,y,z] 加速度，矢量 ''' self.m = m self.v = v self.p = p self.a = [0, 0, 0] if r is None: r = m ** 0.3 self.r = r self.axianshi = self.a self.color = color self.e=e Phy.biao.append(self) biao = [] # 这个表里记录了所有被创建的点，计算时会遍历它 def __str__(self): return f"m={self.m},v={self.v},p={self.p},a={self.axianshi}" def force(self, li): ''' 对某点施力 :param li: list[x,y,z] x,y,z为float 力，矢量 :return: None 直接修改a，无返回 ''' self.a[0] += li[0] / self.m self.a[1] += li[1] / self.m self.a[2] += li[2] / self.m def force2(self, lisize, p): ''' 对某点施力，不同的是，这里只需要提供力的大小和对象位置 :param lisize: float 力的大小 :param p: list[x,y,z] 力的方向 :return: None 直接修改a，无返回 ''' mdx = [p[0] - self.p[0], p[1] - self.p[1], p[2] - self.p[2]] odx = ((p[0] - self.p[0]) ** 2 + (p[1] - self.p[1]) ** 2 + (p[2] - self.p[2]) ** 2) ** 0.5 li = [lisize * mdx[0] / odx, lisize * mdx[1] / odx, lisize * mdx[2] / odx] self.force(li) def resilience(self, x=None, k=100, other=None, string=False): ''' 对某两个点施以弹力 :param x: float 弹簧原长 None 默认当前长度为原长 :param k: float 劲度系数 :param other: Phy 弹簧的另一个点 :param string: bool 弹力模型为线型（True）或杆型（False） :return: None 直接修改a，无返回 ''' if x is None and (not ((self, other) in Phy.rbook.keys())): Phy.rbook[(self, other)] = ((other.p[0] - self.p[0]) ** 2 + (other.p[1] - self.p[1]) ** 2 + ( other.p[2] - self.p[2]) ** 2) ** 0.5 x = Phy.rbook[(self, other)] elif x is None: x = Phy.rbook[(self, other)] dx = ((other.p[0] - self.p[0]) ** 2 + (other.p[1] - self.p[1]) ** 2 + (other.p[2] - self.p[2]) ** 2) ** 0.5 - x if dx<0 and string is True: lisize=0 else: lisize = dx * k self.force2(lisize, other.p) other.force2(lisize, self.p) if not((self, other) in Phy.rbiao): Phy.rbiao.append((self, other)) rbook = {} # 用来储存弹簧的长度，向x填入None时用 rbiao = [] # 用来储存需要连成弹簧的点，显示用，显示后要清空！ @classmethod def rread(cls,biao): ''' 将弹力列表中的内容转为弹力 :param biao: [{"self":Phy, "other":Phy, "x":float, "k":float, "string":bool},...] :return: None ''' for i in biao: i["self"].resilience(i["x"],i["k"],i["other"],i["string"]) def bounce(self, k, other="*"): ''' 对指定点施以弹力（撞击时） :param k: float 劲度系数 :param other: "*" 或 Phy 施力的另一个物体，当为"*"时指对所有点 :return: None 直接修改a，无返回 ''' if other == "*": for i in Phy.biao: if i == self: continue elif (((i.p[0] - self.p[0]) ** 2 + (i.p[1] - self.p[1]) ** 2 + ( i.p[2] - self.p[2]) ** 2) ** 0.5) - self.r - i.r <= 0: self.resilience(self.r + i.r, k / 2, i) else: if (((other.p[0] - self.p[0]) ** 2 + (other.p[1] - self.p[1]) ** 2 + ( other.p[2] - self.p[2]) ** 2) ** 0.5) - self.r - other.r <= 0: self.resilience(self.r + other.r, k, other) @classmethod def gravity(cls, g): ''' 对全部点施以引力 :param g: float 引力常数 :return: None 直接修改a，无返回 ''' for oout in Phy.biao: for oin in Phy.biao: if oout == oin: continue r = ((oout.p[0] - oin.p[0]) ** 2 + (oout.p[1] - oin.p[1]) ** 2 + (oout.p[2] - oin.p[2]) ** 2) ** 0.5 G = g * oout.m * oin.m / (r ** 2) oout.force2(G, oin.p) @classmethod def coulomb(cls,k): ''' 对全部点施以静电力 :param k: 静电力常量 :return: None 直接修改a，无返回 ''' for oout in Phy.biao: for oin in Phy.biao: if oout == oin: continue r = ((oout.p[0] - oin.p[0]) ** 2 + (oout.p[1] - oin.p[1]) ** 2 + (oout.p[2] - oin.p[2]) ** 2) ** 0.5 f = -k * oout.e * oin.e / (r ** 2) oout.force2(f, oin.p) def electrostatic(self,k): ''' 对某点施以静电力 :param k: 静电力常量 :return: None 直接修改a，无返回 ''' for i in Phy.biao: if i==self: continue r = ((self.p[0]-i.p[0])**2+(self.p[1]-i.p[1])**2+(self.p[2]-i.p[2])**2)**0.5 if r==0: r=10e-9 f = -k*self.e*i.e/r**2 self.force2(f,i.p) @classmethod def momentum(cls): ''' 计算全局动量和 :return: list[x,y,z] 矢量 ''' dongliang = [0, 0, 0] for i in Phy.biao: dongliang[0] += i.v[0] * i.m dongliang[1] += i.v[1] * i.m dongliang[2] += i.v[2] * i.m return dongliang @classmethod def run(cls, t): ''' 运行当前模型（力的应该在run之前运算） :param t: float 运行一帧的时间 :return: None 直接修改每个点的v、p、a，无返回 ''' for dian in Phy.biao: dian.v[0] = dian.v[0] + dian.a[0] * t dian.v[1] = dian.v[1] + dian.a[1] * t dian.v[2] = dian.v[2] + dian.a[2] * t dian.p[0] = dian.p[0] + dian.v[0] * t dian.p[1] = dian.p[1] + dian.v[1] * t dian.p[2] = dian.p[2] + dian.v[2] * t dian.axianshi = dian.a[:] dian.a = [0, 0, 0] @classmethod def hprun(cls,t): ''' 以更高精度运行当前模型（建议在恒力模型中使用，力的应该在run之前运算） :param t: float 运行一帧的时间 :return: None 直接修改每个点的v、p、a，无返回 ''' for dian in Phy.biao: dian.p[0] = dian.p[0] + dian.v[0] * t + 0.5 * dian.a[0] * t ** 2 dian.p[1] = dian.p[1] + dian.v[1] * t + 0.5 * dian.a[1] * t ** 2 dian.p[2] = dian.p[2] + dian.v[2] * t + 0.5 * dian.a[2] * t ** 2 dian.v[0] = dian.v[0] + dian.a[0] * t dian.v[1] = dian.v[1] + dian.a[1] * t dian.v[2] = dian.v[2] + dian.a[2] * t dian.axianshi = dian.a[:] dian.a = [0, 0, 0] @classmethod def tready(cls): ''' 在使用显示模块前需要调用这个函数 :return: None ''' import turtle turtle.tracer(0) turtle.penup() turtle.hideturtle()