Semi-analytical theory for long-term rotational motion of uncontrolled satellites

Analytical solutions/integrals of the free rotational motion of uncontrolled satellites which contain spinning rotors are employed in conjunction with a suitable analytical/numerical averaging approach to predict long-term attitude motion. This semi-analytical method of averaging is basically similar to the one used in purely analytical 'general perturbation' theories. However, in view of the complexities involved in analytical treatment of the problem, its application is primarily numerical in character. An example is presented illustrating the use of the theory to predict the attitude motion of an axisymmetric satellite containing symmetrical constant-speed rotors under gravity-gradient torque. The use of the theory is considerably more efficient than straightforward numerical integration of the complete set of equations of motion.