Simplification of a System of Geodesic Equations by Reference to Conservation Laws

Abstract

This paper is purposed to exploit prevalent premises for determining analytical solutions to differential equations formulated from the calculus of variations. we realize this premises from the statement of Emmy Noether's theorem; that every system in which a conservative law is observed also admits a symmetry of invariance. As an illustration, the infinitesimal symmetries for Ordinary Differential Equations (O.D.E's) of geodesics of the glome are explicitly computed and engaged following identification of a relevant conservation law in action. Further prospects for analysis of this concept over the same manifold are then presented summarily in conclusion.