Stability of the inverse pendulum with the hanging point in multifrequency motion

Abstract

In the present paper, the stability of the upper equilibrium position of the pendulum is examined. It is found that if the hanging point undergoes vertical complicated oscillating motion the different components of the motion law reinforce their actions so that the mentioned equilibrium position becomes more stable. On the contrary, if the hanging point moves in the vertical plane the inverse pendulum is less stable under the influence of the horizontal component of the motion.