Linear Stability Boundary of a Spinning Spacecraft with a Ball-in-Tube Damper

Spin stabilization is a commonly used form of passive attitude control for spacecraft. The use of ball-in-tube dampers has been studied extensively for oblate spacecraft. It is widely known from classic rigid-body dynamics that, in the presence of energy dissipation, pure spin is stable only when performed about the axis associated with the maximum central principal moment of inertia. In this study, the Routh-Hurwitz criterion is used to obtain modifications to the classic rule for asymptotic stability of the major axis spin for two configurations, in which the tube is either parallel to or orthogonal to the spacecraft spin axis. A graphical comparison of the linear stability regions, which does not appear elsewhere in the literature, is presented for the two configurations. It is evident from the linear stability diagram that the conditions required for stability are stricter for a nutation damper than for a precession damper. The stability boundaries are subsequently confirmed with numerical solutions of the nonlinear equations of motion.