About possible displacements of a rigid body during rotation around a fixed axis displaced relatively to the center of mass

Based on the analysis of virtual geometric displacements when solving a kinematic problem of Applied Mechanics, representing the uniform rotation of a free rigid body around a fixed vertical axis displaced relative to the center of mass of this body. Necessary and sufficient conditions have been established for such motion in the form of portable rotation of the center of mass of the body in a circle and relative motion of the body in the form of its rotation relative to the center of mass.