Rotations about nonorthogonal axes.

Abstract

Given a desired three-axis reorientation, it is well known that there are, in general, twelve possible sequences of three successive rotations about orthogonal axes which will perform the reorientation. The present paper determines whether the maneuver can or cannot be accomplished with three successive rotations aobut arbitrary (not necessarily orthogonal) axes. This result is then employed to derive conditions on the axes which insure that every rotation may be so generated. The associated angles of all the possible three-legged slews are exhibited by a closed analytical procedure which requires no assumptions concerning the degree of nonorthogonality nor any approximations. The classical orthogonal case (Euler angles) is then an immediate consequence as a special case of the generalized solution.