New approach to regularise the perturbed two-body problem

Alhowaity Sawsan; Selim H. H.; Gao Fabao; Pathak Niraj M.; Abouelmagd Elbaz I.

doi:10.2478/amns.2021.2.00324

Applied Mathematics and Nonlinear Sciences (Jul 2023)

New approach to regularise the perturbed two-body problem

Alhowaity Sawsan,
Selim H. H.,
Gao Fabao,
Pathak Niraj M.,
Abouelmagd Elbaz I.

Affiliations

Alhowaity Sawsan: 1Department of Mathematics, College of Science & Humanities, Shaqra University, Saudi Arabia
Selim H. H.: 2Celestial Mechanics and Space Dynamics Research Group (CMSDRG), Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan 11421, Cairo, Egypt
Gao Fabao: 3School of Mathematical Science, Yangzhou University, Yangzhou225002, China
Pathak Niraj M.: 4Department of Mathematics, Faculty of Technology, Dharmsinh Desai University, Nadiad, Gujarat, 3870001, India
Abouelmagd Elbaz I.: 2Celestial Mechanics and Space Dynamics Research Group (CMSDRG), Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan 11421, Cairo, Egypt

DOI: https://doi.org/10.2478/amns.2021.2.00324
Journal volume & issue: Vol. 8, no. 2
pp. 1245 – 1258

Abstract

Read online

This work aims to construct a new regularisation version for the perturbed two-body problem using bipolar coordinates. We mainly use two transformation techniques to deal with this problem when the distance between two bodies tends to be zero. The system exhibits a well-stabilised periodic orbit over a long time span through numerical simulations. With the increase in the oblate parameter value of the body, the periodic orbit will gradually evolve into a quasi-periodic form.

Published in Applied Mathematics and Nonlinear Sciences

ISSN: 2444-8656 (Online)
Publisher: Sciendo
Country of publisher: Poland
LCC subjects: Science: Mathematics
Website: https://sciendo.com/journal/AMNS

About the journal

Abstract

Keywords