Nonstandard Null Lagrangians and gauge Functions for Newtonian Law of Inertia

TL;DR

This paper introduces new nonstandard null Lagrangians and gauge functions for Newton's law of inertia, highlighting their invariance properties and physical implications.

Contribution

It derives the first exact nonstandard null Lagrangian and gauge function specific to the law of inertia, expanding the theoretical framework.

Findings

New nonstandard null Lagrangians and gauge functions derived

Invariance of action used to make Lagrangians exact

Physical implications of these Lagrangians discussed

Abstract

New null Lagrangians and gauge functions are derived and they are called nonstandard because their forms are different than those previously found. The invariance of the action is used to make the Lagrangians and gauge functions exact. The first exact nonstandard null Lagrangian and its gauge function for the law of inertia are obtained, and their physical implications are discussed.