REGULAR PRECESSIONS IN THE RESTRICTED PROBLEM OF THE ROTATIONAL MOTION

In this paper the rotational motion of a rigid, symmetric body that mo ves in a circular orbit in the central gravitational field is consider ed. All harmonics of the potential function were taken into account. I t was proved that, besides the only known Lagrange solution, a family of conic regular precessions exists. Assuming that the dimensions of t he body are small enough in comparison with the orbit radius, it was p roved that there exist three families of regular precessions close to that known in the truncated problem when only second order harmonics a re taken into account. Finally, a new family of regular precessions wa s found. It exists when the projection of the total angular velocity o f the body onto its symmetry axis is small.