The sufficient conditions for the existence of asymptotically pendulum-like motions of a heavy rigid body with a fixed point

Abstract

The present paper continues the study of the asymptotically pendulum-like motions (APM) of a heavy rigid body begun in /1/, where a specific mass distribution is not assumed here a priori. The first Lyapunov method /2/ is used to obtain new sufficient conditions for the existence of APM, which cannot be described by the well-known particular solutions of the Euler-Poisson equations.