Variational principles for spin systems and the Kirchhoff rod

Creators: Gay-Balma, François; Holm, Darryl D.; Ratiu, Tudor S.

Abstract

We obtain the affine Euler-Poincaré equations by standard Lagrangian reduction and deduce the associated Clebsch-constrained variational principle. These results are illustrated in deriving the equations of motion for continuum spin systems and Kirchhoff's rod, where they provide a unified geometric interpretation.

Additional Information

© 2009 American Institute of Mathematical Sciences. Received April 2009; revised July 2009. Communicated by Juan-Pablo Ortega. The first author was partially supported by Swiss NSF grant 200020-117511 and a Swiss NSF Postdoctoral Fellowship. The second author was partially supported by a Royal Society of London Wolfson Award. The third author was partially supported by Swiss NSF grant 200020-126630.

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Resource type: Journal Article
Publisher: American Institute of Mathematical Sciences
Published in: Journal of Geometric Mechanics, 1(4), 417-444, ISSN: 1941-4889.

Created:: August 19, 2023
Modified:: October 20, 2023