[The entire message from which the below was quoted was supposed to be a private note rather than to the whole list, so I didn't check it quite as carefully as I would have. Just getting used to the new mailing list. hint: when you reply to sender, it goes to the "reply-to" address, not the "from" address]. At 04:24 PM 11/8/2002 -0800, I wrote:
The basic thought is that t is time and rotations proceed as a function of time.
This *is* what I really meant, though I see that I got the time parameterization wrong. What A(t) and B(t) really are are matrices that express the instantaneous rate (and direction) of rotation per unit time at time t. So when they are constants over time, the product integral of one of them over time is a matrix that expresses an increasing rotation with time, like the usual parameterized (by some factor times angle) rotation matrix. This is a pretty nice analogy to a linear function being the integral of a constant. --Shel