Keyframing angular velocity (linear acceleration of orbiting bodies)

I am creating the visuals for a collaborative ambisonics project, and have run into an issue.

An orbiting body has initial frequency of 0.5Hz at 0s, accelerates linearly up to 8Hz at the 30s mark and further accelerates up to 16Hz at 50s.

Is there any way to keyframe angular velocity in Blender? I am truly stumped.

Many thanks in advance,

Franky

Spontaneous hand waving answer is to use animation nodes. Lots of tutorials on it, easy to understand and good for stuff like animating rates of change or integrals of your typical loc/pos/rot settings. I bet this could solve it.

The more ad hoc solution is to do the math yourself. Looking at your first segment you will be expecting a totalt of 127.5 revolutions in 30 seconds.
Now, the problem lies in the linear acceleration, and here my only hope is that it is not super crucial to get right because I have no idea how to. I made an example here (749.0 KB) where I just estimated the general cubic (=2nd order polynomial) behavior of the actual integral

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If the linear acceleration is a must, then you could make a driver to do the calculation every frame, on the basis of “frame”. But the more changes you get, the more complicated the driver becomes.