Asymptotic stability, instability, and stabilization of relative equilibria

Bloch, A. M., P. S. Krishnaprasad, J. E. Marsden and T. S. Ratiu

Proc. of ACC., IEEE, Boston, (1991), 1120-1125

Abstract:

In this paper we analyze 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. We use a modification of the Energy-Casimir and Energy-Momentum methods for Hamiltonian systems to analyze systems with dissipation. Our work couples the modern theory of block diagonalization to the classical work of Chetaev.