Hybrid Routhian reduction for simple hybrid forced Lagrangian systems

TL;DR

This paper extends Routh reduction techniques to simple hybrid forced mechanical systems, providing conditions for symmetry reduction with external forces and demonstrating its application through an example and simulations.

Contribution

It introduces a general framework for symmetry reduction in hybrid Lagrangian systems with external forces, focusing on cyclic coordinates and illustrating practical applicability.

Findings

Established conditions for symmetry reduction in hybrid forced systems

Demonstrated reduction procedure with an example

Validated results through numerical simulations

Abstract

This paper discusses Routh reduction for simple hybrid forced mechanical systems. We give general conditions on whether it is possible to perform symmetry reduction for a simple hybrid Lagrangian system subject to non-conservative external forces, emphasizing the case of case of cyclic coordinates. We illustrate the applicability of the symmetry reduction procedure with an example and numerical simulations.