Floquet Approximation for a Nearly Axisymmetric Rigid Body with Constant Transverse Torque

Abstract

We use Floquet theory to solve the problem of large angular excursions of the spin axis of a rigid body. A semi-analytic solution is presented for the attitude motion of a spinning nearly axisymmetric spacecraft subject to constant transverse torques. Based on the assumption that the spin rate remains nearly constant, we employ a Cayley› Klein representation of the kinematic equations to cast them as a linear set of differential equations with periodic coefe cients. The attitude solutions are computed using Fourier series expansions. For cases where the applied torque is small enough, we present a simple approximate solution. In addition, a lower bound is given for the truncation level of the Fourier series. For the axisymmetric case (where the assumption of constant spin rate is exact ), highly accurate solutions can be obtained with relatively few Fourier terms for typical spacecraft maneuvers with purely transverse torque. However, when the solution is applied to the nearly axisymmetric case, the errors are driven by the variation in the spin rate.