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
--------------------------------------------------------------------------------------------------------------
<<
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.
>>