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.
Highlights
The elimination of degrees of freedom of a symmetric mechanical system, the basic goal of reduction theory, is an old subject that dates back to the mid-nineteen century
The work of Routh in the context of abelian symmetries of classical mechanical systems was extended by many others in an effort to explore different aspects of the reduction process
One important feature whose discrete analogue has been exposed only partially in the literature is the reduction of symmetries
Summary
The elimination of degrees of freedom of a symmetric mechanical system, the basic goal of reduction theory, is an old subject that dates back to the mid-nineteen century. The purpose of the present work is to describe a reduction and reconstruction process for discrete time mechanical systems with nonholonomic constraints, in the lagrangian setting. The statement of this result is written in terms that are not obviously defined on the reduced system; the purpose of Section 6 is to give an intrinsic version of that result, which we achieve with Corollary 6.5. We wish to thank Hernan Cendra for his interest and valuable comments on this work
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