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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 253-284 |
| Number of pages | 32 |
| Journal | Journal of Geometry and Physics |
| Volume | 38 |
| Issue number | 3-4 |
| DOIs | |
| State | Published - Jun 2001 |
| Externally published | Yes |
Keywords
- 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