I have a sensor at some arbitrarythat gives me its orientation in space using quaternions. I would like to track its motion (non-zero roll say i rotate the sensor about [1, yaw0, pitch)0], then I would like to get this information. The only variable is the initial orientation. This could be anything.
For example, let say the sensor is at some arbitrary orientation given by quaternion q0. I then pitchrotate the sensor about [1,0,0] to orientation q1. When I compute the
relative relative rotation between the two as
r = q1 q0^{-1}
Then I notice that the relative rotation has rollcomponents along the x, pitchy and yaw componentsz axes. Why is this and? And how do I recover the axis of motion, i.e., [1,0,0] ? In the more general case, I would like to get a pure pitch from rthe direction of motion (no matter what axis it is about), irrespective of the initial orientation?