Variational symmetries of Lagrangian systems with higher-order derivatives

TL;DR

This paper presents an elementary derivation of variational symmetries and integrals of motion for higher-order Lagrangian systems, making the concepts accessible and applicable to systems depending on acceleration and higher derivatives.

Contribution

It introduces a simple derivation method for variational symmetries in higher-order Lagrangian systems, expanding the toolkit for analyzing such systems.

Findings

Derivation technique for variational symmetries in higher-order systems

Examples illustrating the method's application

Applicable to systems with derivatives beyond acceleration

Abstract

We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of readers with interest in higher-order Lagrangians and symmetries. The discussed technique is also applicable to the Lagrangian systems with higher-order derivatives.