I envision the three fundamental rotation matrices: R (where I use R for Ryz, Rzx, Rxy) I note that if I take (dR/dt * R-transpose) I get a skew-symmetric angular velocity matrix. (I understand how I obtain this equation... that is not the issue.) Now I am making the leap to learning about Lie Algebras and Lie Groups And I understand that any Rotation matrix can be represented with the exponential map And with the exponential map, the generator of the map happens to have a form that is skew symmetric and (aside from the coefficients) of the same form as the angular velocity matrix. Of course. A rotatoin matrix is a change. The skew symmetric angular velocity matrix is a RATE of change. How is it possible for these to related to each other through an exponential map that does not involve TIME.