DOUBLE AVERAGING APPROACH TO THE STUDY OF SPINUP DYNAMICS OF FLEXIBLESATELLITES

We study the dynamics of a class of flexible dual-spin satellites in w hich the rotor is spun up by a small constant torque T applied by the platform. We use a previously published zero torque solution that was obtained using the Krylov-Bogolinbov-Mitropolski averaging method. A s econd application of averaging developed herein leads to a reduction o f the equations of motion from a sixth-order system to a single first- order equation describing the slow evolution of energy as a function o f the axial angular momentum of the rotor. The geometrical interpretat ion of this reduction involves projecting solutions onto a certain bif urcation diagram. Numerical solutions of the averaged equation agree w ith numerical solutions to the full sixth-order system and show that t he flexible spacecraft behaves essentially the same as its rigid count erpart during the spinup maneuver.