A simple example to demonstrate the issues with having specified positions, velocities, and accelerations.

specified_acceleration_example.py

#!/usr/bin/env python

"""This derives the equations of motion for a point mass pendulum on a
laterally moving base, i.e. the classic inverted pendulum on a moving cart.

  iy
  ^       E
  |        o m
  |     l /      |
  |      /       v g
  |   J / theta
O -----o------> ix
  |-x->|

"""

import sympy as sy
import sympy.physics.mechanics as me

m, l, g = sy.symbols('m, l, g')
theta, omega, x, v, a = me.dynamicsymbols('theta, omega, x, v, a')

inertial_frame = me.ReferenceFrame('I')
pendulum_frame = inertial_frame.orientnew('P', 'Axis', (theta,
                                                        inertial_frame.z))

pendulum_frame.set_ang_vel(inertial_frame, omega * inertial_frame.z)

origin = me.Point('O')

joint = origin.locatenew('J', x * inertial_frame.x)
joint.set_vel(inertial_frame, v * inertial_frame.x)
joint.set_acc(inertial_frame, a * inertial_frame.x)

end = joint.locatenew('E', l * pendulum_frame.x)
end.v2pt_theory(joint, inertial_frame, pendulum_frame)
end.a2pt_theory(joint, inertial_frame, pendulum_frame)

bob = me.Particle('B', end, m)

gravitational_force = -m * g * inertial_frame.y

kane = me.KanesMethod(inertial_frame, (theta,), (omega,),
                      (theta.diff() - omega,))

fr, frstar = kane.kanes_equations([(end, gravitational_force)], [bob])