Perturbation Solution for the Flat Spin Recovery of a Dual-§pin Spacecraft

Abstract

Euler's differential equations for free-body attitude motion are solved for the constant bearing axis torque recovery maneuver of a spacecraft with a symmetric rotor and asymmetric platform. The rotor bearing axis coincides with the spacecraft's centroidal principal axis of least inertia. The recovery time and the residual nutation angle are algebraically related to the initial flat spin rate, the spacecraft inertia properties, and the bearing axis torque. The differential equations are solved by use of two asymptotic parameter expansions of the multiple time scale type, which are matched to a transition expansion with a limit process matching procedure.