On one case of reducibility of the equations of motion of a complex mechanical system

A mechanical system, consisting of a non-variable rigid body (a carrier) and a subsystem, the configuration and composition of which may vary with time (the motion of its elements with respect to the carrier is specified), is considered. The system moves in a uniform gravitational field around a fixed point of the carrier. Obtained are conditions for the existence of the integral, which is a generalization of the kinetic moment projection integral in the case of variable mass. The system is reduced to an autonomous type. Case of an algebraic integral of the Kovalevskaya type existence is distinguish.