Routhian reduction for quasi-invariant Lagrangians
Differential Geometry
2010-02-02 v1 Mathematical Physics
math.MP
Abstract
In this paper we describe Routhian reduction as a special case of standard symplectic reduction, also called Marsden-Weinstein reduction. We use this correspondence to present a generalization of Routhian reduction for quasi-invariant Lagrangians, i.e. Lagrangians that are invariant up to a total time derivative. We show how functional Routhian reduction can be seen as a particular instance of reduction of a quasi-invariant Lagrangian, and we exhibit a Routhian reduction procedure for the special case of Lagrangians with quasi-cyclic coordinates. As an application we consider the dynamics of a charged particle in a magnetic field.
Keywords
Cite
@article{arxiv.0912.0863,
title = {Routhian reduction for quasi-invariant Lagrangians},
author = {B. Langerock and F. Cantrijn and J. Vankerschaver},
journal= {arXiv preprint arXiv:0912.0863},
year = {2010}
}
Comments
24 pages, 3 figures