用python绘制三维倒立摆

由于绘制三维图形需要使用专业的图形库，因此需要先安装相关库，比如matplotlib、numpy和mplot3d等。在安装完成后，可以使用下面的代码来绘制三维倒立摆：

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# 定义参数
g = 9.8 # 重力加速度
l = 1.0 # 摆杆长度
m = 1.0 # 摆杆质量

# 定义初始状态
theta1 = np.pi/4 # 摆1的初始角度
theta2 = np.pi/2 # 摆2的初始角度
omega1 = 0.0 # 摆1的初始角速度
omega2 = 0.0 # 摆2的初始角速度

# 定义时间步长和总时间
dt = 0.01
t = np.arange(0, 10, dt)

# 定义函数
def f(theta1, theta2, omega1, omega2, t):
    dtheta1dt = omega1
    dtheta2dt = omega2
    domega1dt = (-g*(2*m+m)*np.sin(theta1)-m*g*np.sin(theta1-2*theta2)-2*np.sin(theta1-theta2)*m*(omega2**2*l+omega1**2*l*np.cos(theta1-theta2)))/(l*(2*m+m-m*np.cos(2*theta1-2*theta2)))
    domega2dt = (2*np.sin(theta1-theta2)*(omega1**2*l*(m+2*(2*m+m))+g*(m+2*(2*m+m))*np.cos(theta1)+omega2**2*l*m*np.cos(theta1-theta2)))/(l*(2*m+m-m*np.cos(2*theta1-2*theta2)))
    return dtheta1dt, dtheta2dt, domega1dt, domega2dt

# 计算运动轨迹
theta1s = []
theta2s = []
omega1s = []
omega2s = []
for i in range(len(t)):
    theta1s.append(theta1)
    theta2s.append(theta2)
    omega1s.append(omega1)
    omega2s.append(omega2)
    dtheta1dt, dtheta2dt, domega1dt, domega2dt = f(theta1, theta2, omega1, omega2, t[i])
    theta1 += dtheta1dt*dt
    theta2 += dtheta2dt*dt
    omega1 += domega1dt*dt
    omega2 += domega2dt*dt

# 绘制三维图形
fig = plt.figure()
ax = fig.gca(projection='3d')

x = l*np.sin(theta1s) + l*np.sin(theta2s)
y = -l*np.cos(theta1s) - l*np.cos(theta2s)
z = np.zeros(len(t))

ax.plot(x, y, z)
ax.set_xlabel('X Label')
ax.set_ylabel('Y Label')
ax.set_zlabel('Z Label')
ax.set_title('Inverted Pendulum')
plt.show()

代码中首先定义了重力加速度、摆杆长度和摆杆质量等参数，然后定义了初始状态和时间步长等变量。接着定义了一个函数f来计算摆杆的运动状态，最后使用循环计算摆杆的运动轨迹，并绘制出三维图形。