Variational methods, multisymplectic geometry and continuum mechanics

Jerrold E. Marsden, Sergey Pekarsky, Steve Shkoller, Matthew West

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)253-284
Number of pages32
JournalJournal of Geometry and Physics
Issue number3-4
StatePublished - Jun 2001
Externally publishedYes


  • 53C15
  • 76A02
  • 76M30
  • Classical field theory
  • Continuum mechanics
  • Multisymplectic geometry
  • Variational methods

ASJC Scopus subject areas

  • Mathematical Physics
  • General Physics and Astronomy
  • Geometry and Topology


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