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The Journal of Geometric Mechanics (JGM)
 

Aspects of reduction and transformation of Lagrangian systems with symmetry

Pages: 1 - 23, Volume 6, Issue 1, March 2014      doi:10.3934/jgm.2014.6.1

 
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E. García-Toraño Andrés - Department of Mathematics, Ghent University, Krijgslaan 281 S22, B9000 Ghent, Belgium (email)
Bavo Langerock - Belgian Institute for Space Aeronomy, Ringlaan 3, B1180 Brussels, Belgium (email)
Frans Cantrijn - Department of Mathematics, Ghent University, Krijgslaan 281 S22, B9000 Ghent, Belgium (email)

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.

Keywords:  Symplectic reduction, Routh reduction, Lagrangian reduction.
Mathematics Subject Classification:  37J05, 37J15, 53D20.

Received: July 2013;      Revised: January 2014;      Available Online: April 2014.

 References