I have two quaternions, $q_1$ and $q_2$. I want to rotate the axis of rotation of $q_1$ by $q_2$. Is there any way of doing this directly, without extracting the axis of rotation from $q_1$, rotating it and re-inserting it again?
Please note that I am not trying to perform a combined rotation by quaternion multiplication ($q' = q_2q_1$). Instead I want to rotate the axis of rotation of $q_1$.