Stability of a Dual-Spin Spacecraft with a Flexible Momentum Wheel P. M. BAINUM* Howard University, Washington, D.C. AND P. G. FUECHSEL AND J. V. FEDOR

The attitude stability of a dual-spin satellite with damping in the momentum wheel as well as the "despun" portion is analyzed. Wheel energy dissipation is modeled by assuming the wheel can flex with two degrees of freedom relative to the hub. The nonlinear attitude equations are derived for small wheel flexural motion and are a ninth order nonautonomous set. If the main body damper mass and wheel transverse moment of inertia are assumed small when compared with main satellite masses and inertias, an averaging process can be used to determine the zeroth and first order secular perturbations on the behavior of the system nutation angle. From this a general analytic stability criterion is established. A numerical evaluation of this criterion using parameters and measured wheel damping data for the Small Astronomy-A satellite indicates that stability about a zero degree nutation angle is insured by a factor of 128 under normal operating conditions. Numerical integration of the nonlinear equations confirms the analytic results for special cases.