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Lagrangian Reduction, the Euler-Poincaré Equations, and Semidirect Products

Cendra, Hernán and Holm, Darryl D. and Marsden, Jerrold E. and Ratiu, Tudor S. (1998) Lagrangian Reduction, the Euler-Poincaré Equations, and Semidirect Products. American Mathematical Society Translations, 186 (1). pp. 1-25. ISSN 0065-9290.

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There is a well developed and useful theory of Hamiltonian reduction for semidirect products, which applies to examples such as the heavy top, compressible uids and MHD, which are governed by Lie-Poisson type equations. In this paper we study the Lagrangian analogue of this process and link it with the general theory of Lagrangian reduction; that is the reduction of variational principles. These reduced variational principles are interesting in their own right since they involve constraints on the allowed variations, analogous to what one nds in the theory of nonholonomic systems with the Lagrange d'Alembert principle. In addition, the abstract theorems about circulation, what we call the Kelvin-Noether theorem, are given.

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Additional Information:© 1998 American Mathematical Society. Received February 1997; this version, October 8, 1997. Research partially supported by NSF grant DMS 96-33161 and DOE contract DE-FG0395-ER25251. Research partially supported by NSF Grant DMS-9503273 and DOE contract DE-FG03- 95ER25245-A000.
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NSFDMS 96-33161
Department of Energy (DOE)DE-FG0395-ER25251
Department of Energy (DOE)DE-FG03-95ER25245-A000
Record Number:CaltechAUTHORS:20100907-110819892
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19800
Deposited By: Ruth Sustaita
Deposited On:09 Sep 2010 15:48
Last Modified:26 Dec 2012 12:23

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