Variational principles for spin systems and the Kirchhoff rod
Chaotic Dynamics
2009-04-10 v1
Abstract
We obtain the affine Euler-Poincar\'e 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.
Cite
@article{arxiv.0904.1428,
title = {Variational principles for spin systems and the Kirchhoff rod},
author = {F. Gay-Balmaz and D. D. Holm and T. S. Ratiu},
journal= {arXiv preprint arXiv:0904.1428},
year = {2009}
}
Comments
Submitted to Journal of Geometric Mechanics, 29 pages, no figures