Steady motions of gyrostat satellites and their stability

The steady motions of a rigid body rotating about its maximum principal axis of inertia, while the radius vector lies in the direction of its minimum principal axis of inertia, is known to be stable in the sense of Lyapunov. Due in part to their stowed configuration in launch vehicles, however, satellites typically have an initial rotation about their minimum principal axis of inertia. Such rotation may be unstable in the presence of some dissipations. This paper investigates the effect of momentum wheels on the stability of steady motions. It is proved that the momentum wheels increase the effective moment of inertia of the gyrostat-satellite system about some desired axis. Stability of the steady rotation about the desired axis can be established only for the case when the moment of inertia of the axis aligned with the radius vector is smaller than that of the axis of linear momentum. A new set of stability criteria is obtained which includes the effects of the coupling between the orbital and attitude dynamics and may be useful in the design of attitude control systems for large spacecraft in low Earth orbit