It so happens that SO(3), being a Lie group, has a well-defined space of derivatives: its associated Lie algebra so(3) [notice lower case]. In fact, the genera

It so happens that SO(3), being a Lie group, has a well-defined space of derivatives: its associated Lie algebra so(3) [notice lower case]. In fact, the generators of the group fundamentally arise from the derivatives of rotations around the identity. http://en.wikipedia.org/wiki/Lie_group#The_Lie_algebra_associated_to_a_Lie_group http://en.wikipedia.org/wiki/Lie_group#The_Lie_algebra_assoc...