python
import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt
from pydy.codegen.ode_function_generators import generate_ode_function
from sympy import symbols
from sympy.physics.mechanics import ReferenceFrame, Point, inertia, RigidBody
from sympy.physics.mechanics.functions import kinematic_equations
python
g, m, M, l, F = symbols('g m M l F')
x, theta = symbols('x theta', cls=kinematic_equations)
python
N = ReferenceFrame('N')
A = N.orientnew('A', 'Axis', [theta, N.y])
P = Point('P')
P.set_vel(N, x * N.x)
PO = P.locatenew('PO', l * A.x)
PO.v2pt_theory(P, N, A)
PO.a2pt_theory(P, N, A)
python
A.inertia = inertia(A, m, m, m)
cart = RigidBody('cart', P, A, M, (A, PO))
python
F_vec = F * N.x
right_hand_side = generate_ode_function([x, theta], [F], [cart], mass_matrix=True)
python
params = {g: 9.81, M: 1.0, m: 0.1, l: 1.0}
python
y = odeint(right_hand_side, x0, t, args=(params,))
x = y[:, 0]
theta = y[:, 1]
plt.plot(t, x, label='Cart Position')
plt.plot(t, theta, label='Pendulum Angle')
plt.xlabel('Time')
plt.ylabel('Position / Angle')
plt.legend()
plt.show()
