STEADY MOTIONS OF GYROSTAT SATELLITES AND THEIR STABILITY

The motion of a rigid body moving in a central gravitational field has been studied by many investigators. The steady motions, or relative e quilibria, of a rigid body rotating about its maximum principal axis o f inertia, while the radius vector lies in the direction of its minimu m principal axis of inertia, is known to be stable in the sense of Lya punov. Due in part to their stowed configuration in launch vehicles, h owever, satellites typically have an initial rotation about their mini mum principal axis of inertia. Such rotation may be unstable in the pr esence of some dissipations. This paper investigates the effect of mom entum wheels on the stability of steady motions, It is proved that the momentum wheels increase the effective moment of inertia of the gyros tat-satellite system about some desired axis. Stability of the steady rotation about the desired arris 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. The Hamiltonian s ystem, obtained through reduction, is shown to have a noncanonical str ucture. For this reduced system Casimir functions can thus be used to assess stability properties through the method of Lagrange multipliers . A new set of stability criteria is obtained which includes the effec ts of the coupling between the orbital and attitude dynamics and may b e useful in the design of attitude control systems for large spacecraf t in low Earth orbit.