Equations of translational-rotational motion of the problem of three axisymmetric bodies with variable masses, sizes and shapes

Abstract

It explores the translational and rotational movement of the three free axisymmetric celestial bodies with
variable 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 system
are obtained. The axes of own coordinate system of unsteady axisymmetric three bodies are directed along the principal
axes 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 of
non-stationary axisymmetric three bodies in a relative coordinate system are obtained, starting at the center of the more
massive body.
An analytical expression of the force functions of the Newtonian interaction of three non-stationary axisymmetric bodies
with variable masses, sizes and variable compression are given.