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Double averaging approach to the study of spinup dynamics of flexible satellites

We study the dynamics of a class of flexible dual-spin satellites in which 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-Bogoliubov-Mitropolski averaging method. A second application of averaging developed herein leads to a reduction of the equations of motion from a sixth-order system to a single first-order equation describing the slow evolution of energy as a function of the axial angular momentum of the rotor. The geometrical interpretation of this reduction involves projecting solutions onto a certain bifurcation diagram. Numerical solutions of the averaged equation agree with numerical solutions to the full sixth-order system and show that the flexible spacecraft behaves essentially the same as its rigid counterpart during the spinup maneuver.