Variational Methods, Multisymplectic Geometry and Continuum Mechanics
نویسندگان
چکیده
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. Research partially supported by the California Institute of Technology and NSF contract KDI/ATM-9873133. Research partially supported by NSF-KDI/ATM-9873133 and the Alfred P. Sloan Research Fellowship.
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