On subharmonic motions of a pendulum in a movable platform

The motion of a pendulum on a rotating platform is investigated in the presence of disturbances caused by its vertical harmonic oscillations of small amplitude. The parameters of the unperturbed system are considered close to the values, upon passing through which the number of relative equilibria of the pendulum and the nature of their stability change. The non-linear problem of the existence and stability of periodic motions of the pendulum relative to the platform with a period multiple to the period of its vertical oscillations is solved. The question of the splitting of separatrices of the unperturbed system is also considered.