American Institute of Mathematical Sciences

December  2009, 1(4): 417-444. doi: 10.3934/jgm.2009.1.417

Variational principles for spin systems and the Kirchhoff rod

 1 Control and Dynamical Systems, California Institute of Technology, Pasadena, CA 911125, United States 2 Department of Mathematics and Institute for Mathematical Sciences, Imperial College, London, SW7 2AZ, United Kingdom 3 Section de Mathématiques and Bernoulli Center, Ecole Polytechnique Fédérale de Lausanne, Lausanne, CH-1015, Switzerland

Received  April 2009 Revised  July 2009 Published  January 2010

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.
Citation: François Gay-Balma, Darryl D. Holm, Tudor S. Ratiu. Variational principles for spin systems and the Kirchhoff rod. Journal of Geometric Mechanics, 2009, 1 (4) : 417-444. doi: 10.3934/jgm.2009.1.417
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