Invariant Manifolds in the Classic and Generalized Goryachev–Chaplygin Problem

Abstract

AbstractWith the aid of computer algebra methods, we have conducted qualitative analysis of the phase space for the classic and generalized Goryachev–Chaplygin problem. In particular, we have found a series of new invariant manifolds of various dimension which possess some extremal property. Motions on a one-dimensional invariant manifold have been investigated. It was shown that these motions are asymptotically stable on this manifold, and one of equilibrium points on the manifold is a limit point for these motions.Keywordsthe Goryachev–Chaplygin problemcomputer algebrainvariant manifoldsstability