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 http://resolver.caltech.edu/CaltechAUTHORS:20100903-104102896
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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.
|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.|
|Subject Keywords:||Variational methods; Multisymplectic geometry; Continuum mechanics|
|Classification Code:||MSC: 76A02; 76M30; 53C15|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||08 Sep 2010 16:21|
|Last Modified:||26 Dec 2012 12:23|
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