Variational methods, multisymplectic geometry and continuum mechanics

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 inco...

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Bibliographic Details
Published inJournal of geometry and physics Vol. 38; no. 3; pp. 253 - 284
Main Authors Marsden, Jerrold E., Pekarsky, Sergey, Shkoller, Steve, West, Matthew
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2001
Subjects
Continuum mechanics
Multisymplectic geometry
Variational methods
Classical field theory
76A02
Variational methods
53C15
Multisymplectic geometry
Continuum mechanics
76M30
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Summary: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.
ISSN:0393-0440
1879-1662
DOI:10.1016/S0393-0440(00)00066-8