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 (6)

• Lagrangian Reduction, the Euler--Poincaré Equations, and Semidirect Products
• Reduction theory for symmetry breaking with applications to nematic systems
• Geodesic Equations on Diffeomorphism Groups
• Generalized Euler-Poincaré equations on Lie groups and homogeneous spaces, orbit invariants and applications
• Geometry of diffeomorphism groups, complete integrability and optimal transport
• Variational principles for spin systems and the Kirchhoff rod

Cited by in corpus (1)

• $G$-Strands on symmetric spaces