Galilean Classification of Curves

TL;DR

This paper classifies space-time curves under Galilean transformations using Cartan's method, identifying invariants that correspond to physical conservation laws and establishing criteria for equivalence of Galilean motions.

Contribution

It introduces a novel classification framework for space-time curves based on Galilean invariance and provides explicit conditions for their equivalence.

Findings

Identified invariants related to conservation laws

Derived necessary and sufficient conditions for Galilean motion equivalence

Applied Cartan's method to classify space-time curves

Abstract

In this paper, we classify space-time curves up to Galilean group of transformations with Cartan's method of equivalence. As an aim, we elicit invariats from action of special Galilean group on space-time curves, that are, in fact, conservation laws in physics. We also state a necessary and sufficient condition for equivalent Galilean motions.