 Given the current orientation of the craft, and the desired orientation of the craft in cartesian coordinates, the required axis of rotation and corresponding rotation angle to achieve the new orientation is determined by computing the eigenvector of the rotation operator.Let

be a body fixed reference system for a 3 axis stabilized spacecraft.The initial attitude
is given by

One wants to find an axis relative the spacecraft body

and a rotation angle formula_6 such that after the rotation with the angle formula_6 one has that

where

are the new target directions.