Rotation as a vector
This very interesting thread seems to come to the clear conclusion that angular displacement is NOT a vector - although there are a few voices saying that angular position IS a vector. I can't figure out what the differene between position and displacement is.
I have a practical problem where I know the angular position of an object in an orthogonal 3D space but I want to know it's angular position in another orthogonal 3D coordinate system that is rotated with respect to the original.
Before reading this discussion, I had naively assumed that I could treat the angular position as a vector (direction=axis, magnitude=angle), combine the three orthogonal positions by vector arithmetic then project the resultant vector onto the new space.
If angular position is NOT a vector, this is clearly invalid. So, after a long winded intro - my question is:
If angular position/dispacement is not a vector - what IS it? and what mathematics do I need to use to work with it. Can any of you erudite people help?