Cendra, Hernán and Holm, Darryl D. and Marsden, Jerrold E. and Ratiu, Tudor S. (1998) Lagrangian Reduction, the EulerPoincaré Equations, and Semidirect Products. American Mathematical Society Translations, 186 (1). pp. 125. ISSN 00659290. http://resolver.caltech.edu/CaltechAUTHORS:20100907110819892

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Abstract
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 LiePoisson 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 KelvinNoether 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 9633161 and DOE contract DEFG0395ER25251. Research partially supported by NSF Grant DMS9503273 and DOE contract DEFG03 95ER25245A000.  
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Record Number:  CaltechAUTHORS:20100907110819892  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20100907110819892  
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ID Code:  19800  
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Deposited By:  Ruth Sustaita  
Deposited On:  09 Sep 2010 15:48  
Last Modified:  26 Dec 2012 12:23 
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