On the dynamic effects of the motion of the center of mass of a rotating solid bodies in the central field

A model of motion of a solid rotating body in a central gravitational field is proposed, which takes into account the mass-geometric characteristics of the body and the factor of rotation of the body relative to its own center of mass. The axis of rotation of the body (relative to the center of mass) is the line connecting the center of mass of the body and the center of the inertial coordinate system (the center of the gravitational field). The distance from the center of mass of the body to the beginning of the inertial system is constant during movement. In this case, the mathematical model of motion is Euler's dynamic equations for a rigid body with a fixed point (the classic "Euler-Poinsot case"). The Euler-Poinsot equations are presented in projection on inertial axes, on normal axes, and also in classical form - in projection on axes connected with a body. It is established that at a "small" angular velocity of rotation relative to the center of mass, the motion of a body with a high degree of accuracy coincides with the classical model of the motion of a point mass in the central.