What is the source of the quaternion derivative equation in the 6D0F (Quaternion) block in the Aerospace Blockset?

The equation in the block documentation contains:

 [ q3 -q2  q1;

   q2  q3 -q0;

-q1  q0  q3;

-q0 -q1 -q2 ]

However, I have also seen this derived as:

 [-q1 -q2 -q3;

   q0 -q3  q2;

   q3  q0 -q1;

-q2  q1  q0 ]

I am wondering which is correct and exactly how the documentation version was derived.

Answer 1

[MathWorks Support Team]

This bug has been fixed in Release 2006b (R2006b). For previous product releases, read below for any possible workarounds:

There is an error within the documentation for the Aerospace Blockset for the 6DoF (Quaternion) block.

The quaternion equations shown for the 6DoF (Quaternion) block are derived with the rotation angle in the fourth position (q3). However, the actual equations used by the block (like most standard quaternion derivations, as well as the other quaternion functionality in the Blockset) have the angle in the first position (q0). This is the format of the second matrix above.

These can also be found in the following reference:

Stevens, B. L., and F. L. Lewis, Aircraft Control and Simulation, John Wiley & Sons, New York, NY, 1992.