Finsler geodesics of Lagrangian systems through Routh reduction

TL;DR

This paper demonstrates that solutions to Euler-Lagrange equations of certain convex Lagrangians can be viewed as geodesics of a related Finsler metric using Routh reduction, linking variational mechanics and Finsler geometry.

Contribution

It introduces a novel approach connecting Routh reduction with Finsler geodesics for convex Lagrangian systems, providing new geometric insights.

Findings

Solutions correspond to Finsler geodesics on specific energy levels

Routh reduction simplifies the analysis of Lagrangian systems

Establishes a geometric interpretation of Lagrangian solutions

Abstract

We make use of a symmetry reduction technique called Routh reduction to show that the solutions of the Euler-Lagrange equations of a strongly convex autonomous Lagrangian which lie on a specific energy level can be thought of as geodesics of an associated Finsler function.