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March  2010, 2(1): 69-111. doi: 10.3934/jgm.2010.2.69

Lagrangian reduction of nonholonomic discrete mechanical systems

Javier Fernández 1, , Cora Tori 2, and  Marcela Zuccalli 2,

1. 

Instituto Balseiro, Universidad Nacional de Cuyo – C.N.E.A., Av. Bustillo 9500, San Carlos de Bariloche, R8402AGP, Argentina
2. 

Departamento de Matemática, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 50 y 115, La Plata, Buenos Aires, 1900, Argentina, Argentina

Received  November 2009 Revised  April 2010 Published  April 2010

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: nonholonomic mechanics., Geometric mechanics, reduction, discrete mechanical systems.
Mathematics Subject Classification: Primary: 37J15, 37J60; Secondary: 70G7.
Citation: Javier Fernández, Cora Tori, Marcela Zuccalli. Lagrangian reduction of nonholonomic discrete mechanical systems. Journal of Geometric Mechanics, 2010, 2 (1) : 69-111. doi: 10.3934/jgm.2010.2.69
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