another way that an inverted pendulum may be stabilized, without any feedback or control mechanism, is by oscillating the pivot rapidly up and down. this is called kapitza's pendulum. if the oscillation is sufficiently strong (in terms of its acceleration and amplitude) then the inverted pendulum can recover from perturbations in a strikingly counterintuitive manner. if the driving point moves in simple harmonic motion, the pendulum's motion is described by the mathieu equation.