Lagrangian reduction of nonholonomic discrete mechanical systems

TL;DR

This paper develops a Lagrangian reduction method for nonholonomic discrete mechanical systems with symmetry, leading to a simplified discrete reduced system and illustrating the approach with specific examples.

Contribution

It introduces a novel reduction and reconstruction process for nonholonomic discrete systems with symmetry, expanding the tools for analyzing such systems.

Findings

Reduction process yields a discrete reduced system

Techniques applied to two types of symmetric systems

Able to derive forced discrete mechanical systems

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.