Aspects of reduction and transformation of Lagrangian systems with symmetry

E. García-Toraño Andrés; Bavo Langerock; Frans Cantrijn

doi:10.3934/jgm.2014.6.1

Article Contents

2014, Volume 6, Issue 1: 1-23. Doi: 10.3934/jgm.2014.6.1

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Aspects of reduction and transformation of Lagrangian systems with symmetry

1.
Department of Mathematics, Ghent University, Krijgslaan 281 S22, B9000 Ghent
2.
Belgian Institute for Space Aeronomy, Ringlaan 3, B1180 Brussels

Received: July 2013

Revised: January 2014

Published: March 2014

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Abstract

This paper contains results on geometric Routh reduction and it is a continuation of a previous paper [7] where a new class of transformations is introduced between Lagrangian systems obtained after Routh reduction. In general, these reduced Lagrangian systems have magnetic force terms and are singular in the sense that the Lagrangian does not depend on some velocity components. The main purpose of this paper is to show that the Routh reduction process itself is entirely captured by the application of such a new transformation on the initial Lagrangian system with symmetry.

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Mathematics Subject Classification: 37J05, 37J15, 53D20.

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