The rotation operator can be derived from examining an infinitesimal rotation
where 
is the time derivative, 
is the angular velocity,
and 
is the cross product operator.
See also
Acceleration, Angular Acceleration, Infinitesimal Rotation
Explore with Wolfram|Alpha
More things to try:
Cite this as:
Weisstein, Eric W. "Rotation Operator." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RotationOperator.html