y0=[r0,0,theta0,np.sqrt(2*G*M/r0**3)] res=odeint(f,y0,t,args=(G,M))

这段代码使用了odeint函数来求解常微分方程组。其中，f是一个函数，它描述了常微分方程组的形式；y0是常微分方程组的初始值；t是时间范围；args是其他需要传入f函数的参数。具体来说，y0是一个四元组，分别表示粒子的初始位置、速度大小和方向；G和M分别表示引力常数和中心天体的质量。

需要注意的是，f函数的输入参数为y和t，分别表示当前的状态和时间。该函数的输出值是一个四元组，分别表示位置和速度。在使用odeint函数时，需要将f函数和其他参数传递给它，并指定时间范围和初始值。函数的返回值是一个数组，表示在指定时间范围内粒子的位置和速度的变化情况。

相关问题

以下代码哪里出错了：import numpy as np from scipy.integrate import odeint from matplotlib import animation import matplotlib.pyplot as plt def f(y,t,G,M): return np.array([y[1], y[0]*y[3]**2-G*M/y[0]**2, y[3], -2*y[1]*y[3]/y[0]]) #初始条件 v0=0 #解微分方程 G,M=6.67e-11,2e30 theta0=0 t= np.linspace(0,20,200) r0=1.5e11 y0=[r0,0,theta0,np.sqrt(2*G*M/r0**3)] res=odeint(f,y0,t,args=(G,M)) x=res[:,0]*np.sin(res[:,2]) y=res[:,0]*np.cos(res[:,2]) #画图 fig=plt.figure() plt.axis([-5*r0,5*r0,-5*r0,5*r0]) myline,=plt.plot([],[],'b',lw=2) mypoint,=plt.plot([],[],'ro',ms=20) def animate(i): mypoint.set_data([x[i],y[i]]) myline.set_data(x[:i],y[:i]) return mypoint,myline anim=animation.FuncAnimation(fig,animate,frames=len(t),interval=100) plt.show()

代码中缺少空格，应该在第一行的 import numpy as np 和 from scipy.integrate import odeint 之间加一个空格。正确代码如下：

import numpy as np 
from scipy.integrate import odeint 
from matplotlib import animation 
import matplotlib.pyplot as plt 

def f(y,t,G,M):
    return np.array([y[1],
                     y[0]*y[3]**2-G*M/y[0]**2,
                     y[3],
                     -2*y[1]*y[3]/y[0]])

#初始条件 v0=0
#解微分方程
G,M=6.67e-11,2e30 
theta0=0 
t= np.linspace(0,20,200) 
r0=1.5e11 
y0=[r0,0,theta0,np.sqrt(2*G*M/r0**3)] 
res=odeint(f,y0,t,args=(G,M))

x=res[:,0]*np.sin(res[:,2])
y=res[:,0]*np.cos(res[:,2])

#画图
fig=plt.figure()
plt.axis([-5*r0,5*r0,-5*r0,5*r0])
myline,=plt.plot([],[],'b',lw=2)
mypoint,=plt.plot([],[],'ro',ms=20)

def animate(i):
    mypoint.set_data([x[i],y[i]])
    myline.set_data(x[:i],y[:i])
    return mypoint,myline

anim=animation.FuncAnimation(fig,animate,frames=len(t),interval=100)
plt.show()

import numpy as np from math import * def Pnm(Phi, Degree): P = np.zeros([Degree + 2, Degree + 2]) # 跨阶次正规化勒让德系数 P[1][1] = 1 P[2][1] = sin(Phi) * 3 ** 0.5 P[2][2] = sqrt(3 * (1 - sin(Phi) ** 2)) for j in range(1, 3): for i in range(3, Degree + 2): l = i - 1 m = j - 1 a = sqrt((4 * l ** 2 - 1) / (l ** 2 - m ** 2)) b = sqrt((2 * l + 1) / (2 * l - 3)) * sqrt(((l - 1) ** 2 - m ** 2) / (l ** 2 - m ** 2)) P[i][j] = a * sin(Phi) * P[i - 1][j] - b * P[i - 2][j] for j in range(3, Degree + 1): for i in range(j, j + 2): l = i - 1 m = j - 1 if (m == 2): beta = sqrt(2 * (2 * l + 1) * (l + m - 2) * (l + m - 3) / (2 * l - 3) / (l + m) / (l + m - 1)) gama = sqrt(2 * (l - m + 1) * (l - m + 2) / (l + m) / (l + m - 1)) else: beta = sqrt((2 * l + 1) * (l + m - 2) * (l + m - 3) / (2 * l - 3) / (l + m) / (l + m - 1)) gama = sqrt((l - m + 1) * (l - m + 2) / (l + m) / (l + m - 1)) P[i][j] = beta * P[i - 2][j - 2] - gama * P[i][j - 2] if ((j + 2) < Degree + 2): for i in range(j + 2, Degree + 2): l = i - 1 m = j - 1 alpha = sqrt((2 * l + 1) * (l - m) * (l - m - 1) / (2 * l - 3) / (l + m) / (l + m - 1)) if (m == 2): beta = sqrt(2 * (2 * l + 1) * (l + m - 2) * (l + m - 3) / (2 * l - 3) / (l + m) / (l + m - 1)) gama = sqrt(2 * (l - m + 1) * (l - m + 2) / (l + m) / (l + m - 1)) else: beta = sqrt((2 * l + 1) * (l + m - 2) * (l + m - 3) / (2 * l - 3) / (l + m) / (l + m - 1)) gama = sqrt((l - m + 1) * (l - m + 2) / (l + m) / (l + m - 1)) P[i][j] = alpha * P[i - 2][j] + beta * P[i - 2][j - 2] - gama * P[i][j - 2] l = Degree m = Degree beta = sqrt((2 * l + 1) * (l + m - 2) * (l + m - 3) / (2 * l - 3) / (l + m) / (l + m - 1)) gama = sqrt((l - m + 1) * (l - m + 2) / (l + m) / (l + m - 1)) P[l + 1][m + 1] = beta * P[l + 1 - 2][m + 1 - 2] - gama * P[l + 1][m + 1 - 2] return P def P_final(theta, n, m, Degree=360): Phi = pi / 2 - theta res = Pnm(Phi, Degree) return res a = P_final(radians(58), 360, 360) print(a)

for n in range(Degree): for m in range(n, Degree): if n == m: P[n, m] = sqrt((2 - 1) / 2 * factorial(n) / (4 * pi * factorial(n))) * cos(m * Phi) else: P[n, m] = sqrt((2 * n + 1) / (2 * n * (n + 1)) *