Assume there is an object whose orientation is q_1 now and it's rotating at angular velocity q_r (according to some references I guess the angular velocity is 0.5 * w * q_1). It's expected to change its orientation to q_2 and stop rotating over a time interval dt. How to calculate the angular acceleration?
How to calculate angular acceleration in quaternion form?
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After some effort, I've found a solution but I'm not quite sure its correctness. Here is my induction.
(I don't know how to edit math formulas in StackOverflow so I post a image)
Here q' is the initial angular velocity.
The part of the induction of which I'm not quite sure is if q(t) = q' + t * q'' is correct.