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.

The Generalized Sundman Transformation and Differential Forms for Linearizing the Variable Frequency Oscillator Equation and the Modified Ivey's Equation

“…Numerous academics have expressed interest in studying nonlinear ODEs, and numerous solutions have been put forth. Linearization via differential forms was put in place by authors like (Harrison, 2002), (Orverem et al, 2017) and (Orverem et al, 2022). Also, linearization through the generalized Sundman transformation was first considered by (Duarte et al, 1994) where the Laguerre form was considered.…”