Technical question of how to transform accelration and velocity.

[cgringmuth]

Hi, I find it hard to understand how it is actually possible to transform linear acceleration and angular velocity into a different coordinate frame. As far as I understood your code, you just use the rotation from the transform. But if you consider following example

You can see despite a pure angular velocity in the base frame. The IMU experience linear displacement as well, which results in a linear acceleration from the IMU (I added several positions of the IMU to show the impact is related to the distance of the centre point of rotation). So, now I want to transform the readings from the IMU into the base frame. I would expect just an angular velocity part and linear acceleration should be zero. But if you would just rotate both vectors I would get values for lin. acceleration other than 0.
I would be very glad if you could explain my problem or point me to some resource were I could fill in my gaps.

[cgringmuth]

I think I understood my misconception. The transform does not transform the motion such that I get the motion of the base. It transforms the motion such that it is represented in the base frame. Or put it differently ego motion is transformed into IMU motion in the base frame.