General null Lagrangians, exact gauge functions and forces in Newtonian mechanics

TL;DR

This paper develops a method to construct null Lagrangians and gauge functions, providing a new perspective on the origin of forces in classical mechanics by linking different Newtonian equations through these functions.

Contribution

It introduces a novel approach to define forces using exact gauge functions, independent of traditional Newtonian dynamics.

Findings

Forces can be derived from gauge functions without Newtonian assumptions

The method converts first Newtonian equations into second ones

Provides new insights into the origin of forces in classical mechanics

Abstract

A method to construct general null Lagrangians and their exact gauge functions is developed. The functions are used to define classical forces independently from Newtonian dynamics. It is shown that the forces generated by the exact gauge functions allow for the conversion of the first Newton equation into the second one. The presented approach gives new insights into the origin of forces in Classical Mechanics.