Approximate Solution for the Spinup Dynamics of Near Axisymmetric Axial GyrostatsUsing the Method of Multiple Scales

摘要

Approximate solutions for the spinup of a near axisymmetric gyrostat are derivedusing the straightforward expansion method and the method of multiple scales. Two method of multiple scale solutions are presented. The first is derived using cartesian coordinates while the second is derived using cylindrical coordinates. The multiple scales solutions are compared to numerically integrated results for oblate and prolate configurations. A comparison for flat spin recovery is also accomplished. Excellent results are obtained for oblate configurations. Trajectory separatrix crossings hindered the results for prolate configurations and flat spin recoveries. Spacecraft, Dynamics,, Approximation (Mathematics), Multiple scales, Fresnel integrals, Dual-spin spacecraft.