A comparative study of nadir attitude pointing satellite solutions

In a variety of satellite engineering problems, analytic solutions are by far the best alternatives to spacecraft attitude dynamic equations than the numerical solutions. In this paper, a refined analytic solution in the roll and yaw axis of a nadir attitude pointing microsatellite and more specifically a passive gravity gradient stabilized microsatellite, is proposed and compared with a recent linear solution from the literature. This linear approximated solution can only be used in few limited cases; however, the proposed one is valid for the more complicated problems found in spacecraft dynamics. It is shown that such a solution is very efficient to model spacecraft attitude dynamics. Simulation results clearly indicate that the proposed analytic solution is more accurate than the existing solution in the roll and yaw axis, even when applied to the worst cases.