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Semidirect products and reduction in mechanics

Marsden, Jerrold E. and Ratiu, Tudor and Weinstein, Alan J. (1984) Semidirect products and reduction in mechanics. Transactions of the American Mathematical Society, 281 (1). pp. 147-177. ISSN 0002-9947. http://resolver.caltech.edu/CaltechAUTHORS:20100907-154555674

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Abstract

This paper shows how to reduce a Hamiltonian system on the cotangent bundle of a Lie group to a Hamiltonian system in the dual of the Lie algebra of a semidirect product. The procedure simplifies, unifies, and extends work of Greene, Guillemin, Holm, Holmes, Kupershmidt, Marsden, Morrison, Ratiu, Sternberg and others. The heavy top, compressible fluids, magnetohydrodynamics, elasticity, the Maxwell-Vlasov equations and multifluid plasmas are presented as examples. Starting with Lagrangian variables, our method explains in a direct way why semidirect products occur so frequently in examples. It also provides a framework for the systematic introduction of Clebsch, or canonical, variables


Item Type:Article
Related URLs:
URLURL TypeDescription
http://www.ams.org/journals/tran/1984-281-01/S0002-9947-1984-0719663-1/home.htmlPublisherUNSPECIFIED
http://www.cds.caltech.edu/~marsden/bib/1984/01-MaRaWe1984/AuthorUNSPECIFIED
Additional Information:© 1984 American Mathematical Society. Received by the editors September 17, 1982. We would like to thank Darryl Holm, Boris Kupershmidt and Phil Morrison for useful discussions and correspondence. Research partially supported by NSF grants MCS 81-07086, MCS 80-23356, the Miller Institute and DOE contract DE-AT03-82ERI2097. Research partially supported by NSF grant MCS 81-01642.
Funders:
Funding AgencyGrant Number
NSFMCS 81-07086
NSFMCS 80-23356
Miller InstituteUNSPECIFIED
Department of Energy (DOE)DE-AT03-82ERI2097
NSFMCS 81-01642
Classification Code:MSC: Primary 58F05, 58D30, 58G 16, 70H05, 73C50, 76A02; Secondary 22E70, 35L 70, 58B25, 58D05
Record Number:CaltechAUTHORS:20100907-154555674
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100907-154555674
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19814
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:09 Sep 2010 15:41
Last Modified:22 Jul 2013 23:09

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