Motion of a Variable Body in a Time-Dependent Force Field

The problem of translational-rotational motion of a variable body is considered under the assumption that the inertial properties of the body, as well as the external forces and torques acting on it, explicitly depend on explicitly. The conditions are indicated under which the equations of motion are reduced to classical equations that describe the motion of a rigid body in a force field that does not depend on time. There are cases when the equations of motion are reduced to completely integrable ones. Elements of the discussion of the 1920–1930s about the description of the motion of a material point of variable mass in a time-dependent gravitational field are reproduced.