> I'll leave the math aside (I have some links below) but say that a 
> quaternion corresponds to a rotation and scaling transformation.  You can 
> convert back and forth from quaternions to 3x3 transformation matrices. 
> The advantage with quaternions is that you can do quaternion 
> interpolation. You can use two quaternions representing different 
> rotations/scalings and a parameter t to calculate an intermediate 
> rotation/scaling about the appropriate axis.  Very cool.

Also if you are going to calculate your rotations from applied forces and 
torques then using quaternions makes matters much simpler.

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