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A Study of Secular Perturbations of Translational-Rotational Motion in a Nonstationary Two-Body Problem Using Computer Algebra

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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.

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Authors and Affiliations

  1. Al-Farabi Kazakh National University, 050040, Almaty, Kazakhstan

    S. B. Bizhanova & M. Zh. Minglibayev

  2. Fesenkov Astrophysical Institute, 050020, Almaty, Kazakhstan

    M. Zh. Minglibayev

  3. Warsaw University of Life Sciences, 02-776, Warsaw, Poland

    A. N. Prokopenya

Authors
  1. S. B. Bizhanova
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  2. M. Zh. Minglibayev
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  3. A. N. Prokopenya
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Correspondence to A. N. Prokopenya.

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Translated by N. Berestova

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Bizhanova, S.B., Minglibayev, M.Z. & Prokopenya, A.N. A Study of Secular Perturbations of Translational-Rotational Motion in a Nonstationary Two-Body Problem Using Computer Algebra. Comput. Math. and Math. Phys. 60, 26–35 (2020). https://doi.org/10.1134/S0965542520010054

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  • DOI: https://doi.org/10.1134/S0965542520010054

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