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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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.
| Item Type: | Book Section | ||||||||||||||||
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| 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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| Record Number: | CaltechAUTHORS:20101012-083137228 | ||||||||||||||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20101012-083137228 | ||||||||||||||||
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| 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. | ||||||||||||||||
| ID Code: | 20390 | ||||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||||
| Deposited By: | Ruth Sustaita | ||||||||||||||||
| Deposited On: | 23 Nov 2010 20:05 | ||||||||||||||||
| Last Modified: | 26 Dec 2012 12:31 |
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