Lagrangian Reduction on Homogeneous Spaces with Advected Parameters - Vizman, C. (Symmetry, Integrability and Geometry: Methods and Applications, 2015)
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-Poincaré equations with advected parameters.