Lagrangian reduction of symmetric discrete mechanical systems: a survey

TL;DR

This paper surveys the authors' work on Lagrangian reduction methods for symmetric discrete mechanical systems, including systems with constraints and external forces, inspired by foundational works in the field.

Contribution

It provides an overview of their results on reduction techniques for discrete-time systems with various complexities, extending existing theories.

Findings

Developed reduction methods for nonholonomic discrete systems

Extended reduction theory to systems with external forcing

Presented a staged reduction approach for complex systems

Abstract

In this note we survey some of our results on the Lagrangian reduction of discrete-time mechanical systems (DMSs). It is intended as an introduction to the general ideas that we used in the reduction of DMSs with nonholonomic constraints, DMSs with external forcing, as well as a theory of reduction by stages for such systems. This line of work was inspired by the paper and the monograph written by H. Cendra, J. Marsden and T. Ratiu in 2001.