Article
New approach to regularise the perturbed two-body problem
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Abstract
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.
Keywords
Perturbed two-body problem, regularisation, bipolar coordinates, 70H05, 70H07, 70F05, 70F15, 70F16
Citation
Alhowaity, S., Selim, H. H., Gao, F., Pathak, N. M., & Abouelmagd, E. I. (2021). New approach to regularise the perturbed two-body problem. Applied Mathematics and Nonlinear Sciences, 6(2), 1245–1258. https://doi.org/10.2478/amns.2021.2.00324
S. Alhowaity, H. H. Selim, F. Gao, N. M. Pathak and E. I. Abouelmagd, “New approach to regularise the perturbed two-body problem,” Applied Mathematics and Nonlinear Sciences, vol. 6, no. 2, pp. 1245–1258, 2021, doi: 10.2478/amns.2021.2.00324.
Alhowaity S, Selim HH, Gao F, Pathak NM, Abouelmagd EI. New approach to regularise the perturbed two-body problem. Applied Mathematics and Nonlinear Sciences. 2021;6(2):1245–1258. doi:10.2478/amns.2021.2.00324.
Alhowaity, S., Selim, H. H., Gao, F., Pathak, N. M. and Abouelmagd, E. I. (2021), ‘New approach to regularise the perturbed two-body problem’, Applied Mathematics and Nonlinear Sciences, 6(2), pp. 1245–1258. Available at: https://doi.org/10.2478/amns.2021.2.00324.
Alhowaity, Sawsan, et al. “New Approach to Regularise the Perturbed Two-body Problem.” Applied Mathematics and Nonlinear Sciences, vol. 6, no. 2, 2021, pp. 1245–1258. https://doi.org/10.2478/amns.2021.2.00324.
Alhowaity, Sawsan, H. H. Selim, Fabao Gao, Niraj M. Pathak, and Elbaz I. Abouelmagd. “New Approach to Regularise the Perturbed Two-body Problem.” Applied Mathematics and Nonlinear Sciences 6, no. 2 (2021): 1245–1258. https://doi.org/10.2478/amns.2021.2.00324.
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- DOI: 10.2478/amns.2021.2.00324
- Type: article
- Source: Applied Mathematics and Nonlinear Sciences
- Published: 2022-11-25
- OpenAlex ID: W4383271050
Published by: Engineering Journals
