ON THE STABILITY OF RELATIVE EQUILIBRIUM OF A SATELLITE IN A CIRCULAR ORBIT.

A study is made of the motion of an artificial satellite with respect to the center of mass in a central Newtonian gravitational field. The satellite is a rigid body and the orbit of its center of mass is circular. In the space of inertial parameters of the satellite there are two regions in which the relative equilibrium of the satellite in the orbital coordinate system is stable in the linear approximation. In one of them sufficient conditions of stability are satisfied. In the other region, for which hitherto only stability in the linear approximation has been established, one obtains, depending on the values of the parameters, stability in the sense of Lyapunov, formal stability, or stability for the majority of initial conditions.