Stability of a dual-spin satellite with two dampers

The rotational stability of a dual-spin satellite consisting of a main body and a symmetric rotor, both spinning about a common axis, is investigated. The main body is equipped with a spring-mass damper, while a partially filled viscous ring damper is mounted on the rapidly spinning rotor. The effect of fluid motion on the rotational stability of the satellite is calculated, considering the fluid as a single particle moving in a tube with viscous damping. Time constants are obtained by solving approximate equations of motion for the nutation-synchronous and the spin-synchronous modes, and the results are found to agree well with the numerical integrations of the exact equations. A limit cycle may exist for some configurations; the nutation angle tends to increase in such cases.