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-Poincaré equations with advected parameters.

References in corpus (3)

• Geodesic Equations on Diffeomorphism Groups
• Geometry of diffeomorphism groups, complete integrability and optimal transport
• Variational principles for spin systems and the Kirchhoff rod