Routhian reduction for quasi-invariant Lagrangians

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 in a quasi-invariant Lagrangian, and we exhibit a Routhian reduction procedure for the special case of Lagrangians with quasicyclic coordinates. As an application, we consider the dynamics of a charged particle in a magnetic field. © 2010 American Institute of Physics.