Mechanical Systems on an almost K\"ahler model of a Finsler Manifold

TL;DR

This paper develops a new framework for mechanical systems on an almost Kähler model of a Finsler manifold, deriving analogous Euler-Lagrange and Hamilton equations to extend classical mechanics into this geometric setting.

Contribution

It introduces a novel geometric approach to formulating Euler-Lagrange and Hamilton equations on an almost Kähler Finsler manifold, expanding the mathematical tools for Finsler geometry applications.

Findings

Derived new Euler-Lagrange equations for the almost Kähler Finsler setting

Formulated Hamilton equations in the same geometric context

Provided corollaries related to mechanical systems on these manifolds

Abstract

In this study, we present a new analogue of Euler-Lagrange and Hamilton equations on an almost K\"ahler model of a Finsler manifold. Also, we give some corollories about the related mechanical systems and equations.