SECULAR PERTURBATIONS OF TRANSLATIONAL-ROTATIONAL MOTION IN THE NON-STATIONARY THREE-BODY PROBLEM
Minglibayev M.Zh. Kushekbay A.K.
31 March 2022al-Farabi Kazakh State National University
KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2022#113Issue 187 - 96 pp.
Modern observational data in astronomy show that real space systems are non-stationary, their masses, sizes, shapes and a few other physical characteristics change over time during evolution. In this connection, the creation of mathematical models of the motion of non-stationary celestial bodies becomes relevant. We consider a non-stationary three-body problem with axisymmetric dynamical structure, shape and variable compression. The Newtonian interaction force is characterized by an approximate expression of the force function accurate to the second harmonic. The masses of bodies change isotropically at different rates. The axes of inertia of the proper coordinate system of non-stationary axisymmetric three bodies coincide with the major axes of inertia of the bodies, and it is assumed that their relative orientations remain unchanged in the process of evolution. Differential equations of translation-rotational motion of three non-stationary axisymmetric bodies with variable masses and dimensions in the relative coordinate system, with the origin in the center of the more massive body, are presented. The analytical expression for the Newtonian force function of the interaction of three bodies with variable masses and dimensions is given. The canonical equations of translational-rotational motion of three bodies in Delaunay-Andoyer analogues are obtained. The equations of secular perturbations of translational-rotational motion of non-stationary axisymmetric three-bodies in the Delaunay-Andoyer analogues of osculating elements have been obtained. The new results obtained can be used to analyze the dynamic evolution of the translation-rotational motion of the three-body problem. The problem is investigated by methods of perturbation theory.
axisymmetric body , celestial mechanics , secular perturbation , three-body problem , translational-rotational motion , variable mass
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Al-Farabi Kazakh National University, Almaty, Kazakhstan
Al-Farabi Kazakh National University
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