Asymptotic stability, instability and stabilization of relative equilibria

Abstract

An analysis is made of asymptotic stability, instability, and stabilization for the relative equilibria, i.e., equilibria modulo a group action, of natural mechanical systems. The practical applications of these results are to rotating mechanical systems where the group is the rotation group. A modification of the energy-Casimir and energy-momentum methods is used for Hamiltonian systems to analyze systems with dissipation. This work couples the modern theory of block diagonalization to the classical work of N. G. Chetaev (1961).