Variational methods, multisymplectic geometry and continuum mechanics
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Variational methods, multisymplectic geometry and continuum mechanics

  • Author(s): Marsden, Jerrold E.
  • Pekarsky, Sergey
  • Shkoller, Steve
  • West, Matthew
  • et al.

Published Web Location

https://arxiv.org/pdf/math/0005034.pdf
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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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