The Use of Differential Forms to Linearize a Class of Geodesic Equations

Abstract

Lie was the first to consider linearization of differential equations many years ago. Since then, a great deal of research has been done on linearization of differential equations using various methodologies. Surprisingly, there has not been much progress in linearizing geodesic differential equations. In particular, the use of differential forms to linearize a class of geodesic equations is not documented in the literature. Differential forms are used to linearize a class of geodesic differential equations in this research. Geodesics on a plane, geodesics on a cone, and geodesics on a sphere are examples. The solutions to these equations were discovered during the linearization process, as the findings of this study are distinctive, innovative, and original.