Applying 3 Concurrent Angular Velocities to Vectors

[Ryoko]

This problem has me stumped. I'm toying with a stabilization platform design which has 3 gyroscopes supplying angular velocity -- one for each axis (x,y,z). The model has units vectors (x,y,z) representing the platform's orientation in space. The question is how do I apply the 3 orthogonal angular velocities to these vectors. I tried applying euler angles one at a time and just going with that. However, euler angles are sensitive to the order in which they are applied and it didn't take long for errors to accumulate.

What's the trick to applying 3 concurrent angular velocities to a vector? Is there a transform which takes the 3 angles and produces a rotation matrix or quaternion?

 

[tnich]

Call your origin vector $A$ and your destination vector $B$. Then $C = A\times B$ is the axis around which you need to rotate. If you make the rotation rates around the x,y,z-axes proportional to the x,y,z-components of $C$, the platform should rotate from $A$ toward $B$.