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Variational methods, multisymplectic geometry and continuum mechanics

Marsden, Jerrold E. and Pekarsky, Sergey and Shkoller, Steve and West, Matthew (2001) Variational methods, multisymplectic geometry and continuum mechanics. Journal of Geometry and Physics, 38 (3-4). pp. 253-284. ISSN 0393-0440. doi:10.1016/S0393-0440(00)00066-8.

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This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order multisymplectic field theories with constraints, such as the incompressibility constraint. The results obtained in this paper set the stage for multisymplectic reduction and for the further development of Veselov-type multisymplectic discretizations and numerical algorithms. The latter will be the subject of a companion paper.

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Additional Information:© 2001 Elsevier Science. Received 11 May 2000. Available online 9 May 2001. Research partially supported by the California Institute of Technology and NSF contract KDI/ATM-9873133. Research partially supported by NSF-KDI/ATM-9873133 and the Alfred P. Sloan Research Fellowship. The authors would like to thank Sanjay Lall, Tudor Ratiu and Michael Ortiz for their comments and interest in this work.
Funding AgencyGrant Number
California Institute of TechnologyUNSPECIFIED
Alfred P. Sloan Research FellowshipUNSPECIFIED
Subject Keywords:Variational methods; Multisymplectic geometry; Continuum mechanics
Issue or Number:3-4
Classification Code:MSC: 76A02; 76M30; 53C15
Record Number:CaltechAUTHORS:20100903-104102896
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19778
Deposited By: Ruth Sustaita
Deposited On:08 Sep 2010 16:21
Last Modified:08 Nov 2021 23:55

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