Variational Methods, Multisymplectic Geometry and Continuum Mechanics
By Jerrold E. Marsden, S. Pekarsky, Steve Shkoller, Matthew West. 2000
143 citations recorded by the source corpus.
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.
Subfields: Computational Mechanics, Numerical Analysis, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/7649d600535e9f018ba4a6df5c77a7e564263946
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In Computational Mechanics
- Jerrold E. Marsden
- Magdalena Ortiz
- Adrian J. Lew
- Matthew West
- Sina Ober-Blöbaum
- Sanjay Lall
- Oliver Junge
- Uri M. Ascher
In Numerical Analysis
- Jerrold E. Marsden
- Magdalena Ortiz
- Adrian J. Lew
- Matthew West
- Sina Ober-Blöbaum
- Sanjay Lall
- Sigrid Leyendecker
- Oliver Junge
In Statistical and Nonlinear Physics
- Jerrold E. Marsden
- Magdalena Ortiz
- Matthew West
- Adrian J. Lew
- Sanjay Lall
- Sina Ober-Blöbaum
- Petr Krysl
- Uri M. Ascher
Citations in the corpus
- Asynchronous Variational Integrators (2003, background): “The discrete version of Hamilton’s principle states that the discrete trajectory having prescribed initial and final end points renders the discrete action sum stationary with respect to admissible variations of the coordinate set (seeMarsden &West [2001] andMarsden, Patrick & Shkoller [1998]).”