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Lin constraints, Clebsch potentials and variational principles

Cendra, Hernan and Marsden, Jerrold E. (1987) Lin constraints, Clebsch potentials and variational principles. Physica D, 27 (1-2). pp. 63-89. ISSN 0167-2789. doi:10.1016/0167-2789(87)90005-4.

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The Poisson bracket formulation of fluid, plasma and rigid body type systems has undergone considerable recent development using techniques of symmetry group reduction. The relationship between this approach and that using Lin constraints and Clebsch potentials is established. The connection is made in the setting of abstract Clebsch variables as well as that of variational principles on reduced spaces. Variational principles for both the Clebsch and reduced form (such as fluids in spatial representation) are derived from the standard variational principle of Hamilton in material (Lagrangian) representation using reduction theory.

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Additional Information:© 1987 Published by Elsevier Science. Received 1 August 1986. Revised manuscript received 4 November 1986. We thank Darryl Holm, Abeno Ibon, Richard Montgomery, Tudor Ratiu, and Alan Weinstein for their valuable comments on various aspects of this work.
Funding AgencyGrant Number
Department of Energy (DOE)DE·AT-085-ER12097
Issue or Number:1-2
Record Number:CaltechAUTHORS:20100727-072431782
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19191
Deposited By: Ruth Sustaita
Deposited On:27 Jul 2010 23:41
Last Modified:08 Nov 2021 23:50

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