Variational methods, multisymplectic geometry and continuum mechanics
Differential Geometry
2008-11-26 v1 Symplectic Geometry
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.
Cite
@article{arxiv.math/0005034,
title = {Variational methods, multisymplectic geometry and continuum mechanics},
author = {Jerrold E. Marsden and Sergey Pekarsky and Steve Shkoller and Matthew West},
journal= {arXiv preprint arXiv:math/0005034},
year = {2008}
}