A preamble: I know to convert quaternion in Eulerian Angles, I have to know the rotation orders adopted in that situation (i.e ZYX, or 321, YZX, or 231).
Now, let's assume:
q = (q0, q1, q2, q3)
I could write the quaternion rate as an ODEs set:
dq/dt = M * q
where M is a 4x4 matrix.
The preamble is to be sure that the matrix M does not depend on the order of the rotations used, but instead that its construction is invariant to the adopted rotations order.
In fact M should be set up only with angular velocity on X, Y and Z axis for any conventional system of rotation.
Am I right?