Subharmonic Motions of a Pendulum on a Movable Platform

Abstract

The motion of a pendulum on a rotating platform is studied under the presence of perturbations caused by vertical harmonic oscillations of small amplitude. The parameters of the unperturbed system are considered close to the values at the transition through which the number of the pendulum’s relative equilibria and the character of their stability change. The nonlinear problem about the existence and stability of the motions of a periodic pendulum with respect to the platform with the period aliquot to the period of its vertical oscillations is solved. The question about the splitting of separatrices of the unperturbed system is also considered.