AV-differential geometry and Newtonian mechanics

TL;DR

This paper introduces a frame-independent formulation of Newtonian mechanics using affine differential geometry, enabling the construction of Lagrangian and Hamiltonian objects independent of inertial frames.

Contribution

It develops a novel affine differential geometric framework for analytical mechanics that is invariant under changes of inertial reference frames.

Findings

Frame-independent Lagrangian and Hamiltonian formulations are constructed.

Affine differential geometry replaces traditional vector bundle methods.

Legendre transformation is shown to be inertial frame independent.

Abstract

A frame independent formulation of analytical mechanics in the Newtonian space-time is presented The differential geometry of affine values i.e., the differential geometry in which affine bundles replace vector bundles and sections of one dimensional affine bundles replace functions on manifolds, is uded. Lagragian and hamiltonian generating objects, together with the Legendre transformation independent on inertial frame are constructed.