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Lagrange–Poincaré field equations

Lagrange-Poincaré field equations
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Nov 2011Embargo end date: 01 Jan 2009 United States, France English Publisher:Elsevier BVJournal:Journal of Geometry and Physics, volume 61, pages 2,120-2,146 (issn: 0393-0440, Copyright policy )Funded by:EC | FCCA
Authors: Ellis, David C. P.; Gay-Balmaz, François; Holm, Darryl D.; Ratiu, Tudor S.;

doi: 10.1016/j.geomphys.2011.06.007 , 10.48550/arxiv.0910.0874

arXiv: 0910.0874

Lagrange–Poincaré field equations

Abstract

The Lagrange-Poincare equations of classical mechanics are cast into a field theoretic context together with their associated constrained variational principle. An integrability/reconstruction condition is established that relates solutions of the original problem with those of the reduced problem. The Kelvin-Noether theorem is formulated in this context. Applications to the isoperimetric problem, the Skyrme model for meson interaction, metamorphosis image dynamics, and molecular strands illustrate various aspects of the theory.

Submitted to Journal of Geometry and Physics, 45 pages, 1 figure

Countries
United States, France
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Keywords

FOS: Physical sciences, 530, Skyrme model, 510, Field theories, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Euler–Lagrange equations, [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], Mathematical Physics, Conservation laws, covariant reduction, [PHYS.MECA]Physics [physics]/Mechanics [physics], Mathematical Physics (math-ph), 540, Nonlinear Sciences - Chaotic Dynamics, variational problem, Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems, Covariant reduction, Symmetries and conservation laws in mechanics of particles and systems, Euler-Lagrange equations, [PHYS.MECA] Physics [physics]/Mechanics [physics], Chaotic Dynamics (nlin.CD), Symmetries, principle bundle reduction

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
28
Top 10%
Top 10%
Top 10%
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