1. The problem statement, all variables and given/known data As a small verification of a larger problem, I'm trying to determine how the dynamics of an inverted pendulum attached to a frictionless cart would behave. The cart has no input force applied, so all horizontal movements would be due purely to the centrifugal+normal force of the pendulum, being driven by gravity. The initial conditions of the system would be that the initial cart speed/position = 0, the initial angular rate of pendulum = 0, and the initial positional angle of the pendulum = 0.01 radians, and just let to fall 2. Relevant equations 3. The attempt at a solution After solving through all the kinematic laws, and trying to simulate the system, what I am seeing is that without friction, the pendulum continues to swing perpetually back and forth, always reaching the initial height at a angle symmetrical to the starting angle. Does this sound feasible?