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Symbolic calculations in studying the problem of three bodies with variable masses

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Abstract

The classical problem of three bodies with variable masses is considered in the case when the masses of all three bodies vary isotropically. Solutions to the equation of motion in terms of the osculating elements of the aperiodic quasi-conical motion and the secular perturbations of the orbital elements of the system are examined. An algorithm for calculating the secular part of the perturbing functions and derivation of the differential equations determining the secular perturbations of the orbital elements are discussed. All the relevant symbolic calculations are carried out using the Mathematica computer algebra system.

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Authors and Affiliations

  1. Warsaw University of Life Sciences, ul. Novoursynovska 159, Warsaw, 02-776, Poland

    A. N. Prokopenya

  2. Innovation High School Collegium of Mazovia, ul. Sokolowska 161, Siedlce, 08-110, Poland

    A. N. Prokopenya

  3. Al-Farabi Kazakh National University, pr. al-Farabi 71, Almaty, 050040, Kazakhstan

    M. Zh. Minglibayev & G. M. Mayemerova

  4. Fesenkov Astrophysical Institute, Observatoriya 23, Almaty, 050020, Kazakhstan

    M. Zh. Minglibayev

Authors
  1. A. N. Prokopenya
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  2. M. Zh. Minglibayev
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  3. G. M. Mayemerova
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Correspondence to A. N. Prokopenya.

Additional information

Original Russian Text © A.N. Prokopenya, M.Zh. Minglibayev, G.M. Mayemerova, 2014, published in Programmirovanie, 2014, Vol. 40, No. 2.

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Prokopenya, A.N., Minglibayev, M.Z. & Mayemerova, G.M. Symbolic calculations in studying the problem of three bodies with variable masses. Program Comput Soft 40, 79–85 (2014). https://doi.org/10.1134/S036176881402008X

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  • DOI: https://doi.org/10.1134/S036176881402008X

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