[Locally Conformal Higher Order Lagrangian Dynamics

TL;DR

This paper introduces higher order Lagrangian dynamics with a locally conformal structure, deriving specific Euler-Lagrange equations for second- and third-order cases to expand the theoretical framework of advanced dynamical systems.

Contribution

It develops the formulation of locally conformal higher order Euler-Lagrange equations, focusing on second- and third-order cases, advancing the mathematical understanding of conformal Lagrangian dynamics.

Findings

Derived second- and third-order locally conformal Euler-Lagrange equations.

Established a theoretical framework for higher order conformal Lagrangian systems.

Enhanced the mathematical tools for analyzing conformal properties in dynamical systems.

Abstract

This work presents higher order Lagrangian dynamics possessing locally conformal character. More concretely, locally conformal higher order Euler-Lagrange equations are written with particular focus on the second- and the third-order cases.