Variational principles for spin systems and the Kirchhoff rod
arXiv:0904.1428
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.
Submitted to Journal of Geometric Mechanics, 29 pages, no figures