This page says that Quaternion Angular Velocity is given by
$$\frac{d\vec{s}}{dt} = \vec{w} \bigotimes \vec{s}.$$ Where this is interpreted as Quaternion multiplication.
He derives this by arguing angular velocity is orthogonal to position and therefore the scalar part of the quaternion is zero, therefore the above is the same as
$$\frac{d\vec{s}}{dt} = \vec{w} \times \vec{s}.$$
This argument from my understanding is not correct, since position vector and angular velocity may not be orthogonal.
So how do you correctly derive this?
