Lagrangian Reduction on Homogeneous Spaces with Advected Parameters
Abstract
We study the Euler-Lagrange equations for a parameter dependent G-invariant Lagrangian on a homogeneous G-space. We consider the pullback of the parameter dependent Lagrangian to the Lie group G, emphasizing the special invariance properties of the associated Euler-Poincar\'e equations with advected parameters.
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