Periodic Solutions for Spinning Asymmetric Rigid Bodies with Constant Principal-Axis Torque

Abstract

We analyze themotion of a spinning asymmetric rigid body subject to constant torque along one of the principal axes. Periodic solutions for the angular velocity vector and the corresponding kinematic parameters are given in terms of Fourier series expansions. Three semi-analytic solution methods are presented: one-period integration, Newton’s method, and a perturbationmethod. These are compared for computationalefŽ ciency with a given error bound.The solutions apply to arbitrarily large attitudemotions.Whenmultipleperiod solutions are desired, these methods always prove more efŽ cient than straightforward numerical integration. The techniques may be applied to onboard computations, maneuver analysis, and maneuver optimization.