Stability of 2-degree-of-freedom gyro in a spinning vehicle

Conditions for the stability of motion of the spin axis of a two-degree-of-freedom (2DF) control moment gyroscope (CMG) mounted with spin axis parallel to the vehicle spin axis are formulated, using the Liapunov approach. Motion of the gyro symmetry axis about the equilibrium state is studied. Conditions for stability of symmetry axis motion with respect to the vehicle axis about the equilibrium state are derived using an appropriate Liapunov function. Motion of the gimbals is studied with no damping assumed, but the conditions derived would apply to asymptotic stability in the completely damped case. The existence of a multiplicity of 2DF CMG equilibrium states is established.