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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 1, Pages 29–38
DOI: https://doi.org/10.31857/S0044466920010068 (Mi zvmmf11012) 		 
This article is cited in 2 scientific papers (total in 2 papers)

A study of secular perturbations of translational-rotational motion in a nonstationary two-body problem using computer algebra

S. B. Bizhanovaa, M. Zh. Minglibayevab, A. N. Prokopenyac

a Al-Farabi Kazakh National University, Almaty, 050040 Kazakhstan
b Fesenkov Astrophysical Institute, Almaty, 050020 Kazakhstan
c Warsaw University of Life Sciences, Warsaw, 02-776 Poland
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DOI: https://doi.org/10.31857/S0044466920010068
Abstract: A nonstationary two-body problem is considered such that one of the bodies has a spherically symmetric density distribution and is central, while the other one is a satellite with axisymmetric dynamical structure, shape, and variable oblateness. Newton's interaction force is characterized by an approximate expression of the force function up to the second harmonic. The body masses vary isotropically at different rates. Equations of motion of the satellite in a relative system of coordinates are derived. The problem is studied by the methods of perturbation theory. Equations of secular perturbations of the translational-rotational motion of the satellite in analogues of Delaunay–Andoyer osculating elements are deduced. All necessary symbolic computations are performed using the Wolfram Mathematica computer algebra system.
Key words: variable mass, secular perturbations, axisymmetric body, translational-rotational motion.
Received: 29.07.2019
Revised: 29.07.2019
Accepted: 18.09.2019
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 1, Pages 26–35
DOI: https://doi.org/10.1134/S0965542520010054
Bibliographic databases:
Document Type: Article
UDC: 517.93
Language: Russian
Citation: S. B. Bizhanova, M. Zh. Minglibayev, A. N. Prokopenya, “A study of secular perturbations of translational-rotational motion in a nonstationary two-body problem using computer algebra”, Zh. Vychisl. Mat. Mat. Fiz., 60:1 (2020), 29–38; Comput. Math. Math. Phys., 60:1 (2020), 26–35
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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