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The axis of a rotation

The axis of a three-dimensional rotation. The initial coordinate axes are in green. The final platform orientation is in orange. You can modify this final orientation by changing the Yaw-Pitch-Roll angles. The resulting net rotation, from the green to the orange, can be achieved smoothly by rotating around an axis (yellow). The rigid blue frame smoothly rotates between the green and orange, via the one-parameter group of rotations that fixes the yellow vector.
The stable direction is determined using Cramer's rule.