Variational Methods, Multisymplectic Geometry
and Continuum Mechanics
Marsden, J. E., S. Pekarsky, S. Shkoller and M. West
J. Geometry and Physics, 38, 253-284
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.