A Complex Analytic Solution for the Attitude Motion of a Near-symmetric Rigid Body under Body-fixed Torques

Although analytic solutions for the attitude motion of a rigid body are available, for several special cases, a comprehensive theory does not exist in the literature for the more complicated problems found in spacecraft dynamics. In the present paper, analytic solutions in complex form are derived for the attitude motion of a near symmetric rigid body under the influence of arbitrary, but constant body-fixed torques. The solution is extremely compact, which enables efficient and rapid machine computation. Numerical simulations reveal that the solution is very accurate when applied to typical spinning spacecraft problems.