Infinitesimal time reparametrisation and its applications

TL;DR

This paper introduces a geometric framework for Sundman infinitesimal time-reparametrisation, highlighting its applications to geodesic motions and mechanical systems, with the Jacobi metric as a key example.

Contribution

It develops a geometric approach to Sundman time-reparametrisation and demonstrates its applications to mechanical systems and geodesic motions.

Findings

Jacobi metric as a special case of Sundman transformation

Application of the theory to geodesic motions

Enhanced understanding of time-reparametrisation in mechanical systems

Abstract

A geometric approach to Sundman infinitesimal time-reparametrisation is given and some of its applications are used to illustrate the general theory. Special emphasis is put on geodesic motions and systems described by mechanical type Lagrangians. The Jacobi metric appears as a particular case of a Sundman transformation.