As our reference textbook, Fundamentals of Spacecraft Attitude Determination and Control relies upon a quaternion multiplication convention of $\bar{q}\otimes q$ it is necessary to provide the equivalent equation as expressed with the standard quaternion convention given Simulink requires it. Denoted as $\bar{q}\odot q$ in the textbook, the conversion relation given is:

$$ \bar{q}\otimes q = q \odot \bar{q} $$

Source: Fundamentals of Spacecraft Attitude Determination and Control, pg. 37

<aside> 💡 Note the order of the exchange of the quaternions, mainly $\bar{q}\otimes q \neq \bar{q} \odot q$

</aside>

For quaternions, there are multiple positions in which we can place the scalar component. One representation leaves the scalar component as the first component:

$$ \mathbf{q}=\begin{bmatrix}s \\ \vec{e}\end{bmatrix} $$

Another representation leaves the scalar component as the last component:

$$ \mathbf{q}=\begin{bmatrix}\vec{}e \\ s\end{bmatrix} $$

The textbook uses the second notation whereas Simulink uses the first notation. Since we will use the internal Simulink quaternion blocks in the aerospace blockset for quaternion operations, we will also use the first notation.