  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.
