Nutational Stability and Core Energy of a Quasirigid Gyrostat

Abstract

The asymptotic nutational stability of a quasirigid gyrostat is analyzed. The primary purpose of this analysis is to resolve a debate concerning the use of the energy-sink method of analysis for systems containing driven rotors. It is shown that when the work done by the motor torque is not taken into account, the analysis leads to a contradiction even when the total energy is dissipative. A proper application of Landon's original idea yields a relationship between the time rate of change of Hubert's "core energy" and the energy dissipation rate of the damping mechanisms in the spacecraft. The analysis shows that the core energy might increase during a rotor despin condition; hence, the minimality of core energyﾃ__a previous criterionﾃ__is not always guaranteed. A criterion for the design of the damper to insure dissipation of the core energy is presented; this condition is always satisfied for the case of a constant relative rotor spin speed that facilitates a "closed-form" solution to the nutation angle time history of an axisymmetric gyrostat. The stability condition resulting from this analysis is consistent with the Landon-Iorillo stability criterion.