General solution of equations of motion for a classical particle in 9-dimensional Finslerian space

TL;DR

This paper develops a Lagrangian framework for a classical particle in a 9-dimensional Finslerian space with a cubic metric, deriving the general equations of motion and confirming the Galilean inertia law.

Contribution

It provides the first explicit solution of equations of motion for particles in a 9D Finslerian space with a cubic metric, expanding Finsler geometry applications.

Findings

Derived the general solution of equations of motion.

Confirmed Galilean law of inertia in Finslerian space.

Established a Lagrangian description for particles in 9D Finslerian geometry.

Abstract

A Lagrangian description of a classical particle in a 9-dimensional flat Finslerian space with a cubic metric function is constructed. The general solution of equations of motion for such a particle is obtained. The Galilean law of inertia for the Finslerian space is confirmed.