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Article · BULLETIN of the L N Gumilyov Eurasian National University MATHEMATICS COMPUTER SCIENCE MECHANICS Series · January 1, 2019

Equations of Translational-rotational Motion of the Problem of Three Axisymmetric Bodies with Variable Masses, Sizes and Shapes

M. Zh. Minglibayev, A.K. Kushekbay

Mukhtar Minglibayev
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Abstract

It explores the translational and rotational movement of the three free axisymmetric celestial bodies withvariable mass, size and variable compression interacting according to Newton’s law.Differential equations of translational-rotational motion of axisymmetric three bodies in the absolute coordinate systemare obtained. The axes of own coordinate system of unsteady axisymmetric three bodies are directed along the principalaxes of inertia of the bodies, and it is assumed that during the evolution their relative orientation remains unchanged.Based on the equations of motion in the absolute coordinate system, the equations of translational-rotational motion ofnon-stationary axisymmetric three bodies in a relative coordinate system are obtained, starting at the center of the moremassive body.An analytical expression of the force functions of the Newtonian interaction of three non-stationary axisymmetric bodieswith variable masses, sizes and variable compression are given.

Dynamics and Control of Mechanical SystemsSpacecraft Dynamics and ControlFluid dynamics and aerodynamics studiesthree-body problemaxisymmetric bodiesvariable mass

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