The steady motions of a gyrostat suspended on a rod in a central gravitational field

The problem of the existence, stability and bifurcation of the steady motions of two bodies in an orbital tethered system, when one of the bodies is a symmetrical satellite with a rotor on the axis of symmetry, is considered. One-parameter families of steady motions are indicated, and their stability and bifurcations are investigated. The conditions which relate the parameters of the system for which stabilization of the families obtained is possible using a rotating rotor are obtained.