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What you have animated in a gimbal. Gyroscopes are often mounted on gimbals to demonstrate how they resist changes to their axis of rotation. This is why many people associate gimbals with gyroscopes. I guess many people don't know the term gimbal, or have forgotten it.
Anyway, as I said in a top-level comment, you should look up "gimbal lock" which is what happens when all the rings of the gimbal end up in the same plane.
Replied to your other comment. Thanks interesting