Invariant manifolds in the Clebsch–Tisserand–Brun problem

Abstract

A series of new invariant manifolds of various dimensions is obtained in Clebsch–Tisserand–Brun problems using a certain modification of the Routh–Lyapunov procedure, and their stability, including their stability with respect to a part of the variables, is investigated. Cases of asymptotic stability of equilibrium positions on one-dimensional invariant manifolds are presented, and the consequences of this fact for the original system are indicated.