Spacecraft reorientation via slewing about nonorthogonal axes

A mathematical procedure was developed which determines the exact slews relative to any known axes. The axes may be completely arbitrary; their coordinates merely reside on a data base which can be changed at any time without affecting the software. Given the desired reorientation, the procedure then determines all of the two-legged or three-legged slews which will accomplish the reorientation. For example, there are 12 possible permutations of three axes, and if they are orthogonal each always has two solutions. The nonorthogonal case, on the other hand, gives some surprising results, including the nonexistence of a solution: Consider a large reorientation where the three axes are nearly collinear. In this connection, it can be shown that every three-axis reorientation can be accomplished by three successive slews, if and only if the middle axis is perpendicular to the other two.