On the global version of Euler-Lagrange equations

TL;DR

This paper explores how the torsion tensor of a covariant derivative on velocity phase space influences the formulation of global Euler-Lagrange equations, emphasizing the geometric structure involved.

Contribution

It introduces the role of torsion in the covariant derivative for a global expression of Euler-Lagrange equations, advancing the geometric understanding.

Findings

Torsion tensor is involved in the global Euler-Lagrange equations.

Covariant derivative with torsion provides a consistent global formulation.

Highlights the geometric significance of torsion in variational calculus.

Abstract

The introduction of a covariant derivative on the velocity phase space is needed for a global expression of Euler-Lagrange equations. The aim of this paper is to show how its torsion tensor turns out to be involved in such a version.