Routhian reduction for quasi-invariant Lagrangians

Details Routhian reduction for quasi-invariant Lagrangians Routhian reduction for quasi-invariant Lagrangians

2009-12-04

arxiv.org/abs/0912.0863v1

J. Math. Phys. 51(2) 2010

Mathematics

Differential Geometry

24 pages, 3 figures

Scientific paper

10.1063/1.3277181

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.

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