Quaternions to Euler

[weg22@drexel.edu]

Hi all,

I've posted quaternion questions on here before and I thank you all for
your help. However, I am still a bit cofused so please bear with me.
If I have an aircraft with an Euler Angle orientaiton of (yes, my
aircraft can fly in this orientation)

Roll (phi, x-axis) = 0 degrees
Pitch (theta, y-axis) = 90 degrees
Yaw (psi, z-axis) = 20 degrees

and I measure this with a sensor, it will suffer from singularities
which will yield erroneous results. However, that same sensor will
yield the correct quaternion for that orienation:

Q = 0.696 + 0.123i + 0.696j + 0.123k

My question is how do I mathematically convert the quaternion (Q) back
to Euler Angle format *while* still avoiding the singularities present
at theta=90 degrees?

Thanks,
-weg