An investigation of the effect of an internal spinning rotor on the attitudes and stability properties of a satellite employing gravity-gradient stabilization. This study considers all possible rotor directions and speeds, and all possible satellite inertias. The set of equilibrium orientations for each of these gyrostat configurations is investigated, and the stability of new solutions is analyzed in order to determine their usefulness in the design of future satellite systems. Also, a simple geometric visualization is presented for the set of all orientations that can be made into equilibria by proper choice of rotor axis and rate of rotation. The discovery of a continuum of equilibrium orientations for certain gyrostat configurations suggests a possible explanation for the observed sudden tumbling of some gravity-gradient stabilized satellites that use long, flexible booms. 143 pp. Ref.