Applying Differential Forms and the Generalized Sundman Transformations in Linearizing the Equation of Motion of a Free Particle in a Space of Constant Curvature

Joel M. Orverem, Y. Haruna, Bala M. Abdulhamid and Magaji Y. Adamu

Journal of Mathematics Research, 2021, vol. 13, issue 5, 5

Abstract: Equation of motion of a free particle in a space of constant curvature applies to many fields, such as the fixed reduction of the second member of the Burgers classes, the study of fusion of pellets, equations of Yang-Baxter, the concept of univalent functions as well as spheres of gaseous stability to mention but a few. In this study, the authors want to examine the linearization of the said equation using both point and non-point transformation methods. As captured in the title, the methods under examination here are the differential forms (DF) and the generalized Sundman transformations (GST), which are point and non-point transformation methods respectively. The comparative analysis of the solutions obtained via the two linearizability methods is also taken into account.

Date: 2021
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