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Variational methods, multisymplectic geometry and continuum mechanics

Jerrold E. Marsden·Sergey Pekarsky·Steve Shkoller·Matthew West
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Abstract

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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Jerrold E. Marsden, Sergey Pekarsky, Steve Shkoller, Matthew West. 2000-05-03. Variational methods, multisymplectic geometry and continuum mechanics. https://doi.org/10.1016/s0393-0440(00)00066-8

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