On the stability of permanent rotations of a chain of two Lagrange gyrostats in a central gravitational field

Abstract

In this paper we study the problem of the motion of a two-gyrostat chain about a fixed point in a central gravitational field. We assume that the mass distribution of each gyrostat is analo-gous to the one of a Lagrange top, the gyrostatic moment of each gyrostat is constant relative to its carrier, and the center of a spherical joint connecting the gyrostats belongs to their dynamic symmetry axes. We establish and analyze sufficient conditions for stability of the chain's permanent rotations about a vertical axis. Our findings extend corresponding results in the dynamics of a single gyrostat to a case of the two-gyrostat chain as well as generalize some of the known properties of permanent rotations in the many-body dynamics.