Effects of energy addition and dissipation on dual-spin spacecraft attitude motion

Abstract

The attitude motion of an axisymmetric dual-spin spacecraft in which energy is both added and dissipated is considered. Energy addition to the spacecraft occurs because a constant spin rate of the rotor with respect to the remainder of the spacecraft (i.e., the platform) is maintained. Dissipation of energy is due to the operation of a spring-mass-dashpot nutation damper on the platform. The attitude motion is determined qualitatively and quantitatively. Qualitative results are obtained using the generalized method of averaging and energy-sink considerations. Quantitative information is obtained from the generalized method of averaging, numerical integration, and an extended energy-sink method. In applying the generalized method of averaging, it is assumed that the contribution of the damper mass to the overall transverse moment of inertia of the spacecraft is small. However, the nutation angle is not restricted. The results obtained using the generalized method of averaging agree well with numerical integration results. The extended energy-sink method produces an analytical result for the average time rate of change of the nutation angle that agrees with the result from the generalized method of averaging. This analysis substantiates the conclusion that energy-sink methods, when properly applied, lead to meaningful results even for systems containing driven rotors.