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Published June 1991 | Published
Book Section - Chapter Open

Asymptotic Stability, Instability and Stabilization of Relative Equilibria

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.

Additional Information

© 1991. Supported in part by NSF Grant DMS-90-02136 and a Seed Grant from Ohio State University. Supported in part by AFOSR-87-0073 and AFOSR-90-0105 and NSF Engineering Resarch Program grant AFOSR-87-0073. Supported in part by DOE Contract DE-FG03-88ER-25064. Supported in part by NSF Grant DMS-8922699.

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