Department of Mathematics
Variational methods, multisymplectic geometry and continuum mechanics
- Author(s): Marsden, Jerrold E.
- Pekarsky, Sergey
- Shkoller, Steve
- West, Matthew
- et al.
Published Web Locationhttps://arxiv.org/pdf/math/0005034.pdf
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.