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Reduction and Hamiltonian structures on duals of semidirect product Lie algebras

Marsden, Jerrold E. and Ratiu, Tudor and Weinstein, Alan J. (1984) Reduction and Hamiltonian structures on duals of semidirect product Lie algebras. In: Fluids and Plasmas : Geometry and Dynamics. Contemporary mathematics . No.28. American Mathematical Society , Providence, R.I., pp. 55-100. ISBN 0821850288 http://resolver.caltech.edu/CaltechAUTHORS:20100908-070424350

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Abstract

With the heavy top and compressible flow as guiding examples, this paper discusses the Hamiltonian structure of systems on duals of semidirect product Lie algebras by reduction from Lagrangian to Eulerian coordinates. Special emphasis is placed on the left-right duality which brings out the dual role of the spatial and body (i.e. Eulerian and convective) descriptions. For example, the heavy top in spatial coordinates has a Lie-Poisson structure on the dual of a semidirect product Lie algebra in which the moment of inertia is a dynamic variable. For compressible fluids in the convective picture, the metric tensor similarly becomes a dynamic variable. Relationships to the existing literature are given.


Item Type:Book Section
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http://www.cds.caltech.edu/~marsden/bib/1984/08-MaRaWe1984/AuthorUNSPECIFIED
Additional Information:© 1984 American Mathematical Society. Research partially supported by DOE contract DE-AT03-82ER12097. Research partially supported by an NSF postdoctoral fellowship.
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Funding AgencyGrant Number
Department of EnergyDE-AT03-82ER12097
NSF postdoctoral fellowshipUNSPECIFIED
Record Number:CaltechAUTHORS:20100908-070424350
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100908-070424350
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ID Code:19817
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:15 Sep 2010 21:15
Last Modified:22 Jul 2013 23:08

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