Hi, Shel.

I'm not clear on how A(t) and B(t) depend on t in what you wrote below.

I have posted a response to math-fun that should appear any minute.

--Dan
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If A and B are thought of
as matrix-valued functions of  a parameter t where, e.g., A(1/n) ^ n = A(1),  B(1/n) ^ n = B(1),
which makes easy to see geometric sense for constant rate rotations,
then the product integral P (A(t)B(t))^dt  seems to be the continuously combined rotation
(at least according to one way of defining it),
and seems to be equal to P (B(t)A(t))^dt.
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