Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids
Mathematical Physics
2009-03-26 v1 Differential Geometry
math.MP
Abstract
The Lagrangian and Hamiltonian structures for an ideal gauge-charged fluid are determined. Using a Kaluza-Klein point of view, the equations of motion are obtained by Lagrangian and Poisson reductions associated to the automorphism group of a principal bundle. As a consequence of the Lagrangian approach, a Kelvin-Noether theorem is obtained. The Hamiltonian formulation determines a non-canonical Poisson bracket associated to these equations.
Keywords
Cite
@article{arxiv.0903.4287,
title = {Reduced Lagrangian and Hamiltonian formulations of Euler-Yang-Mills fluids},
author = {François Gay-Balmaz and Tudor S. Ratiu},
journal= {arXiv preprint arXiv:0903.4287},
year = {2009}
}