Numerical Example
Consider the reorientation corresponding to the Euler angles relative a given base vector system
Corresponding matrix relative to this base vector system is (see Euler angles#Matrix orientation)
and the quaternion is
The canonical form of this operator
with is obtained with
The quaternion relative to this new system is then
Instead of making the three Euler rotations
the same orientation can be reached with one single rotation of size around
Read more about this topic: Rotation Operator (vector Space)
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