Bloch, A. M. and Krishnaprasad, P. S. and Marsden, J. E. and Ratiu, T. S. (1991) Asymptotic Stability, Instability and Stabilization of Relative Equilibria. In: Proceedings of the 1991 American Control Conference. IEEE , Piscataway, NJ, pp. 1120-1125. ISBN 0879425652 http://resolver.caltech.edu/CaltechAUTHORS:20101012-083137228
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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.
|Item Type:||Book Section|
|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.|
|Official Citation:||Bloch, A. M.; Krishnaprasad, P. S.; Marsden, J. E.; Ratiu, T. S.; , "Asymptotic Stability, Instability and Stabilization of Relative Equilibria," American Control Conference, 1991 , vol., no., pp.1120-1125, 26-28 June 1991|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||23 Nov 2010 20:05|
|Last Modified:||26 Dec 2012 12:31|
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