According to Val Head (Senior Design Advocate at Adobe, author, and web animation expert), the reason why motion is generally left out of design systems is not knowing or being sure how to include it.
With Toolabs DSM's motion panel, it is very easy to set up your motion system and then document it or export to code.
The animation building blocks you can manage are :
Durations
You can either generate a modular timing scale or define durations manually. Check the section for Modular Scales to see how scales are generated.
Easing
You can either use the presets or manually define the bezier curves using the drag handles of the ease editor.
Named effects (Transitions)
Here are some good articles on using motion in design systems for further reading: