Equilibria and stability of an n-pendulum forced by rapid oscillations

Abstract

Recent efforts have focused on developing a theory of open-loop control for a class of velocity-controlled superarticulated mechanical systems by high-frequency periodic forcing. From this work, the averaged potential has emerged as the primary tool in equilibrium and stability analysis. In this paper, we present a study of the equilibria and stability of a periodically-forced cart and n-pendulum on an inclined plane. We present an exact model for the n-degree-of-freedom system, nondimensionalize the model, and compute the averaged potential. Equilibria and their stability are found through a critical point analysis of the averaged potential. The results for the n-DOF system are numerically verified for the vertically forced cart and double pendulum.