Stability of steady-state motions of systems of symmetric rigid bodies with ball-and-socket joints

Abstract

The paper is developed to the study of stability of steady-state motions of a tree-like system. Heavy symmetric rigid bodies are connected at the ends of their symmetry axes with ball-and-socket joints. One of the bodies is fixed. The steady-state motions are obtained when the symmetry axes and rods move as one rigid body, rotating with a constant angular velocity around the vertical and at the same time the bodies rotate uniformly around their symmetry axes. The sufficient conditions for stability of steady-state motions are derived from Routh's theorem for stability of the reduced system.