I'm using quaternions to describe 3D rotations which necessitates that the quaternion is normalized. I'm getting more interested in quaternions and I tried to check what the quaternion magnitude represents, though I couldn't find any information. Searching on the internet for possible literature only returns results for using quaternions in orientation, frame transformation or translation, for which only unit quaternions are used.
So the question is, can anyone tell what the magnitude of the quaternion represents or how and when it is used? If someone knows about relevant literature, that would be great.