On the stability and bifurcation analysis of dual-spin spacecraft

The dynamics of dual-spin spacecraft under effects of energy dissipation are considered in this paper, where the damper masses in the platform (P) and the rotor (R) cause energy loss in the system. The Floquet theory is employed to obtain stability charts for different relative spin rates of the subsystem R with respect to the subsystem P. Based on the general model for the system with nutation dampers on both P and R, models are presented for a system whose nutation damper exists only in P as well as a system without nutation damper. The results obtained from the Floquet theory agree with the energy sink analysis in the literature. The bifurcation analysis based on the movement of loci of the Floquet multipliers as the system passes through the flutter stability boundary indicates that the system experiences the secondary Hopf (Neimark-Sacker) bifurcation. The investigations show that for spacecraft whose nutation damper exists only in one of the subsystems, there is no need to apply Floquet theory, and the Routh-Hurwitz criteria provides necessary and sufficient conditions for stability. Furthermore, for the case that only P has damping, the Lyapunov stability criteria agree with Routh-Hurwitz criteria.