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

Uchechukwu Opara
2020 Journal of Mathematics Research  
This paper is purposed to exploit prevalent premises for determining analytical solutions to di erential 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 conservation law is observed also admits a symmetry of invariance (Olver, 1993, pp.242; Dresner, 1999, pp.60-62 ). As an illustration, the infinitesimal symmetries for Ordinary Di erential Equations (O.D.E’s) of geodesics of the
more » ... 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.
doi:10.5539/jmr.v12n5p37 fatcat:lnjgfyaumrhkpdcvxpjwjxcu6q