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Published June 2001 | public
Journal Article

Variational methods, multisymplectic geometry and continuum mechanics

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.

Additional Information

© 2001 Elsevier Science. Received 11 May 2000. Available online 9 May 2001. 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. The authors would like to thank Sanjay Lall, Tudor Ratiu and Michael Ortiz for their comments and interest in this work.

Additional details

Created:
August 21, 2023
Modified:
October 20, 2023