Gay-Balmaz, FrancoisHolm, Darryl D.Ratiu, Tudor S.2011-12-162011-12-162011-12-16200910.3934/jgm.2009.1.417https://infoscience.epfl.ch/handle/20.500.14299/74600WOS:000207826700002We obtain the affine Euler-Poincare 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.variational principlessymmetryLagrangian reductoncocycleaffine Euler-Poincare equationsspin systemKirchhoff rodtext::journal::journal article::research article