Lagrangian reduction of forced discrete mechanical systems

TL;DR

This paper develops a method for reducing and reconstructing symmetric forced discrete mechanical systems using Lagrangian techniques, analyzing momentum maps and Poisson structures to simplify complex systems with external forces.

Contribution

It introduces a novel Lagrangian reduction and reconstruction framework specifically for symmetric forced discrete mechanical systems, extending existing theories to include external forces.

Findings

Established conditions for momentum map evolution.

Analyzed Poisson structure behavior under reduction.

Provided a systematic approach for system simplification.

Abstract

In this paper we propose a process of Lagrangian reduction and reconstruction for symmetric discrete-time mechanical systems acted on by external forces, where the symmetry group action on the configuration manifold turns it into a principal bundle. We analyze the evolution of momentum maps and Poisson structures under different conditions.