(ongoing revision persists...)
Iteration of DCM with angular velocity in body frame. (This is the module. Import it in Python to use the iteration method.)
An example. (A test code.)
The background theory is in this post (in Chinese language though, I want to translate it into English but it takes time. Hope someone is interested in translating it!). And it has a python simulation of a rotating symmetric top in 3D motion.
The approximation of rotation by iteration of DCM is discussed in this textbook. The approximation of rotation ωdt is also discussed. Here I use ω(t+dt)dt to approximate the rotation from t to t+dt. This is discussed in the same post.
 D.H. Titterton and J.L. Weston, Strapdown inertial navigation technology, Peter Peregrinus
Ltd., London UK, 1997