ON THE DYNAMICS OF THREE AXISYMMETRIC BODIES - Minglibayev, M.Zh.; Kushekbay, A.K. (Academic Scientific Journal of Computer Science, 2020)
It explores the translational and rotational movement of the three free non-stationary axisymmetric celestial bodies with variable mass, size and variable compression interacting according to Newton's law. Newtonian force interaction is characterized by an approximate expression of the force function, which takes into account the second harmonic. Differential equations of translational-rotational motion of three non-stationary axisymmetric bodies with variable mass and size in the relative coordinate system, with the beginning in the center of a more massive body, are given. The axes of inertia of own coordinate system of non-stationary axisymmetric three bodies coincide with the main axes of inertia of the bodies, and it is assumed that their relative orientation remains unchanged during evolution. The mass of bodies are varied isotropically in the different rates. Canonical equations of translational-rotational motion of three non-stationary axisymmetric bodies with variable masses and sizes are obtained in the osculating analogues of the elements of Delaunay-Andoyer. Canonical equations of unperturbed motion and their integrals are given.