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The BKE is.....

e d/dt(Vector) = u d/dt(Vector) + omega between e and u X (Vector)

sometimes an additional term is added which is the linear velocity between the frames but for some simplicity lets assume this is zero.

e is the inertial frame

and u is the working frame

omega is the angular velocity

X is the cross product operator

I know just by looking at a simple single rotation problem, the solution is trivial but does anyone know of a formal proof?