Equations of motion of the problem of two bodies with variable masses
Abstract
It is shown that, excluding purely mathematical generalizations, the differential equations in an absolute system of coordinates of 12th order can always be reduced to the solution of equations of relative motion of 6th order. Knowledge of the general solution of the equations of relative motion makes it possible to reduce the determination of the general solution of the initial equations to six quadratures. If the additional forces satisfy a specified condition, the equations of motion in the absolute system of coordinates admit three momentum integrals. The presence of momentum integrals makes it possible to calculate the velocity of the bodies in the absolute system of coordinates algebraically, without quadratures. The coordinates of the bodies are then calculated by three quadratures.
 Publication:

Moskovskii Universitet Vestnik Seriia Fizika Astronomiia
 Pub Date:
 February 1983
 Bibcode:
 1983MVSFA..24...62L
 Keywords:

 Celestial Mechanics;
 Equations Of Motion;
 Two Body Problem;
 Variable Mass Systems;
 Coordinates;
 Differential Equations;
 Gravitational Effects;
 Quadratures;
 Time Dependence;
 Velocity Distribution;
 Astronomy