### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 009, 10 pages      arXiv:1408.3019      https://doi.org/10.3842/SIGMA.2015.009

### Lagrangian Reduction on Homogeneous Spaces with Advected Parameters

Cornelia Vizman
Department of Mathematics, West University of Timişoara, Romania

Received August 14, 2014, in final form January 22, 2015; Published online January 29, 2015

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.

Key words: Lagrangian; homogeneous space; Euler-Poincaré equation.

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