Quaternion derivative ambiguity

[softec17]

In Quaternions and Rotation Sequences by Jack B. Kuipers (pg. 264-265)
the quaternion derivative is defined as:

$$\frac{dq}{dt}=q(t)\overline{\omega}(t)$$

But in many published papers, I have seen the derivative defined instead as

$$\frac{dq}{dt}=\frac{1}{2}q(t)\omega(t)$$

Why is there a discrepancy? Is there some nomenclature that is different. I am assuming \omega(t) to be the angular velocity of the body axis wrt the fixed frame and the quaternion is used to transform a vector from the fixed frame to the body frame.

Thanks for any help.

 

[arkajad]

Probably the two definitions of $$\omega$$ differ by the factor of 2.