Open AccessApplying Differential Forms and the Generalized Sundman Transformations in Linearizing the Equation of Motion of a Free Particle in a Space of Constant Curvature
Author(s) -
J. M. Orverem,
Yusuf Haruna,
Bala Ma’aji Abdulhamid,
M. Y. Adamu
Publication year - 2021
Publication title -
journal of mathematics research
Language(s) - English
Resource type - Journals
eISSN - 1916-9809
pISSN - 1916-9795
DOI - 10.5539/jmr.v13n5p5
Subject(s) - mathematics , constant (computer programming) , transformation (genetics) , constant curvature , motion (physics) , mathematical analysis , linearization , space (punctuation) , differential equation , curvature , nonlinear system , classical mechanics , geometry , biochemistry , chemistry , physics , linguistics , philosophy , quantum mechanics , computer science , gene , programming language
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.