Nonlinear Resonances in the Attitude Motion of Dual-Spin Spacecraft

The attitude motion of a class of dual-spin spacecraft which exhibit nonlinear resonances during the despin process is studied. The model adopted consists of a rigid slightly asymmetric rotor and a rigid symmetric platform that is dynamically unbalanced with respect to the rotor's axis of maximum moment of inertia. No external torques are considered. Attitude equations are derived in an unconventional form that allows easy incorporation of the integral of angular momentum. The presence of a nonlinear resonance is shown to depend on the coexistence of rotor asymmetry and platform dynamic unbalance. An approximate solution for the attitude motion near resonance is obtained for the case of zero despin-motor torque by using the generalized method of averaging. The salient characteristics of the near-resonant motion are obtained from integrals of the averaged equations.