Lagrangian reduction of nonholonomic discrete mechanical systems

Pages: 69 - 111, Volume 2, Issue 1, March 2010

doi:10.3934/jgm.2010.2.69       Abstract        Full Text (524.8K)       Related Articles

Javier Fernández - Instituto Balseiro, Universidad Nacional de Cuyo – C.N.E.A., Av. Bustillo 9500, San Carlos de Bariloche, R8402AGP, Argentina (email)
Cora Tori - Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 50 y 115, La Plata, Buenos Aires, 1900, Argentina (email)
Marcela Zuccalli - Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 50 y 115, La Plata, Buenos Aires, 1900, Argentina (email)

Abstract: In this paper we propose a process of lagrangian reduction and reconstruction for nonholonomic discrete mechanical systems where the action of a continuous symmetry group makes the configuration space a principal bundle. The result of the reduction process is a discrete dynamical system that we call the discrete reduced system. We illustrate the techniques by analyzing two types of discrete symmetric systems where it is possible to go further and obtain (forced) discrete mechanical systems that determine the dynamics of the discrete reduced system.

Keywords:  Geometric mechanics, discrete mechanical systems, reduction, nonholonomic mechanics.
Mathematics Subject Classification:  Primary: 37J15, 37J60; Secondary: 70G75.

Received: November 2009;      Revised: April 2010;      Published: April 2010.