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Asymptotic Stability, Instability and Stabilization of Relative Equilibria

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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http://www.cds.caltech.edu/~marsden/bib/1991/07-BlKrMaRa1991/AuthorUNSPECIFIED
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4791550&isnumber=4791300PublisherUNSPECIFIED
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.
Funders:
Funding AgencyGrant Number
NSFDMS-90-02136
Seed Grant from Ohio State UniversityUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)AFOSR-87-0073
Air Force Office of Scientific Research (AFOSR) AFOSR-90-0105
NSF Engineering Research ProgramUNSPECIFIED
DOEDE-FG03-88ER-25064
NSFDMS-8922699
Record Number:CaltechAUTHORS:20101012-083137228
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20101012-083137228
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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