Abstract: Euler angles are used to describe the angle motion and the relationship between coordinate systems, but there must be a adventitions solution in the angle motion equations when some euler angle is equal to π/2. Usually, attitude angles varied within a large range in all of a process of a satellite reentering, especially ballistic reentering, so it is difficult to avoid the singular point.By adopting a quaternion rule, the singular point problem has been settled once and for all, and the calculating speed and precision have effectivelly been impoved.In this fashion, this paper presents a simple method used to establish reentry motion equations of a satellite.

Key words: Equation of motion, Calculation method, Reentry trajectory, Recoverable satellite