Perturbation solution of attitude motion under body-fixed torques

Approximate analytical solutions are established for the attitude rates and angles of a rigid body subjected to a constant body-fixed torque. The perturbation solutions obtained are valid for any arbitrary inertia parameters. The small parameter is defined as the ratio between representative transverse rotation rate and the spin or scan rate. The results should be useful for quickly evaluating the attitude response of a spin-stabilised or scanning spacecraft to a variety of torque inputs. The applicability of the theory is illustrated by means of practical examples such as the spin-down due to rate coupling of ESA's GEOS spacecraft and the prediction of the attitude drift of the HIPPARCOS satellite during payload initialisation. Furthermore, the compact first-order results should be suitable for implementation in on-board manoeuvre or attitude control software.