A system is considered, consisting in a carrying body and carried ones of variable masses. The motion of that system around a fixed point of the carrying body, in a field of given exterior forces and reactions, is studied. Under determined conditions, concerning the motion of carried bodies and the rate of change of their masses, the equations of motion of the system are derived and an integral, analagous to the classical integral of energy, obtained. Two cases are found for which the differential equations of motion are completely integrable.