Well, the title pretty much sums it up. I''m trying to figure out how to determine the orientation of a spinning object. Obviously there is a certain axis it is spinning around, and it has a certain angular spin rate, so axis-angle rotation does that. However, I would also need to have a transformation to bring the object to the proper "initial orientation". What''s more, I need to figure out how this initial orientation changes when an angular impulse (torque applied for some time) is applied to the object. And this of course all needs to be done without floating-point errors creeping in over time... Is there some better way to represent a spinning object?

Quaternions. Google will tell you all you need to know.

Wow. I was thinking that this whole quaternion thing was just hype, but it seems to be very useful, due to the Poinsot equation and its easy normalisation.

Yep.