Approximate symmetries of geodesic equations on 2-spheres

TL;DR

This paper investigates the approximate symmetries of geodesic equations on 2-spheres, revealing that no non-trivial approximate symmetries exist for these spaces, which impacts understanding of particle paths under perturbations.

Contribution

The study provides a detailed analysis of approximate symmetries of geodesic equations on 2-spheres and demonstrates the absence of non-trivial approximate symmetries using two different methods.

Findings

No non-trivial approximate symmetries found

Exact symmetries of geodesic equations identified

Two approaches confirm the symmetry results

Abstract

Approximate symmetries of geodesic equations on 2-spheres are studied. These are the symmetries of the perturbed geodesic equations which represent approximate path of a particle rather than exact path. After giving the exact symmetries of the geodesic equations, two different approaches to study the approximate symmetries of the approximate geodesic equations show that no non-trivial approximate symmetry for these spaces exists.