Variational Methods, Multisymplectic Geometry and Continuum Mechanics

Marsden, J. E., S. Pekarsky, S. Shkoller and M. West

J. Geometry and Physics, 38, 253-284


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.