Say I have a gyro that outputs degrees/second, and I take the euclidean magnitude of the x,y, and z rotations:
$$
\text{magnitude} = \sqrt{x^2 + y^2 + z^2}
$$
Is this actually useful? Is magnitude now "total degrees/second"? Or does the weirdness surrounding non-commutative addition of rotations come into play?
Best Answer
Think back to basic geometry and what the individual X, Y, and Z output values of the gyro actually mean.
One way to look at them is as the components of the rotation vector. This vector is parallel to the axis of rotatation with the magnitude being the speed of rotation. The square root of the sum of the squares of the individual components of this vector is its magnitude. So yes, your magnitude value is the speed of rotation. Draw a picture and this really should be obvious.