Variational principles for spin systems and the Kirchhoff rod

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Gay-Balmaz, F.
Holm, D. D.
Ratiu, T. S.
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Abstract
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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.
Comment: Submitted to Journal of Geometric Mechanics, 29 pages, no figures
Keywords
Nonlinear Sciences - Chaotic Dynamics
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