I am faced with a problem where I have a quaternion which represents rotation and three arbitrary axis about which I can make rotations, thus three unit vectors.
What I would like to know is angles (or real parts of the quaternions) by which I should rotate around given axis such that I would make the same rotation as original quaternion represents.
$$q=q1∗q2∗q3$$
Note: When the first rotation is being made, the second and third axis is being rotated also, and the second rotation affects the third axis in the same manner.
The solution I am looking for is the one which makes the least rotations, thus minimising rotations angles about the first, second and third axis.