Resonant motion of a spin-stabilized thrusting spacecraft

The attitude instability of a spin-stabilized, thrusting upper stage spacecraft is investigated based on a two-body model consisting of a symmetric main body, representing the spacecraft, and a spherical pendulum, representing the liquefied slag pool entrapped in the aft section of the rocket motor. Exact time-varying nonlinear equations are derived and used to eliminate the drawbacks of conventional linear models. To study the stability of the spacecraft's attitude motion, both the spacecraft and pendulum are assumed to be in states of steady spin about the symmetry axis of the spacecraft and the coupled time-varying nonlinear equation of the pendulum is simplified. A quasi-stationary solution to that equation and approximate resonance conditions are determined in terms of the system parameters. The analysis shows that the pendulum is subject to a combination of parametric and external-type excitation by the main body and that energy from the excited pendulum is fed into the main body to develop the coning instability. When one of the resonance conditions and real flight data are used in the original time-varying nonlinear equations, the results match well with the observed motion before and after motor burnout of typical spin-stabilized upper stages. Some numerical examples are presented to explain the mechanism of the coning angle growth and how disturbance moments are generated.