Phase flows and vectorial lagrangians in $J^3(\pi)$

TL;DR

This paper generalizes Nambu mechanics to three-dimensional phase space using Liouville's theorem, introducing the concepts of vector Hamiltonian and vector Lagrangian to extend classical mechanics frameworks.

Contribution

It introduces the concepts of vector Hamiltonian and vector Lagrangian within the generalized Nambu mechanics framework for 3D phase space.

Findings

Extension of Nambu mechanics to three dimensions.

Introduction of vector Hamiltonian and Lagrangian concepts.

Based on Liouville's theorem for phase space volume conservation.

Abstract

On the basis of Liouville theorem the generalization of the Nambu mechanics is considered. For three-dimensional phase space the concept of vector hamiltonian and vector lagrangian is entered.