The function transform of spatial acceleration is inconsistent with the theory in a course

[wly2014]

The function transform of spatial acceleration is inconsistent with the theory in the course: lec8-1 Rigid Body Dynamics. In this course, the transform of spatial acceleration between two frames is (at 1:31:00 of this video)

However, in the RigidBodyDynamics.jl, the transform of spatial acceleration is realized as url.

These seem to be two inconsistent formulas. It seems that there is an extra calculation for se3_commutator in RigidBodyDynamics.jl. Are these two calculation methods equivalent? Or is there any existing literature on the calculation method you use?

Thank you very much.