RESONANCE CAPTURE IN AXIAL GYROSTATS

We consider the rotational motion of axial gyrostats with axisymmetric platform and asymmetric rotor, where the rotor is spun up by a small constant internal torque, epsilon, applied by a motor on the platform, Of particular interest is a certain resonance capture phenomenon whic h has previously been reported in the literature. In this paper we pre sent a new analysis of this resonance condition by two methods: first by studying the dynamics on the unperturbed (epsilon = 0) momentum sph ere, and second by studying the slow evolution of rotational kinetic e nergy when epsilon not equal 0. Since resonance capture is related to a separatrix crossing and is an uncertain event, we discuss the probab ility of capture, and its relationship to the magnitude of the spinup torque epsilon.