@realcaseyrollins It's actually a really important subject in my field. "Perturbation analysis" is a method of calculating how something reacts to being disturbed from the condition it's supposed to be in. For example, let's say you have an aircraft that's supposed to be flying level, and a gust of wind or something causes it to dip just slightly below level (it's been "perturbed" from level flight). It's important to know whether the aircraft will tend to return to level flight (the perturbation tends to diminish, so it's stable) or tend to dip further away from level flight into a steep dive (the perturbation tends to grow, so it's unstable).
@realcaseyrollins I'm glad it interests you!
Here's a simple demonstration. Grab something like a DVD case and toss it in the air three times, spinning it a different way each time:
- First, toss it with a flat spin around the shortest axis
- Second, toss it with an end-over-end spin around the median axis
- Third, toss it with a lengthwise spin around the longest axis.
What you'll likely notice is that the first and third spins maintain their direction a lot better, while the second one starts tumbling and twisting in midair, no matter how careful you are to spin it evenly. This is because a rotating object's response to a perturbation depends on its axis of rotation, and random currents and eddies in the air start affecting the DVD case as soon as it leaves your hand.
- If it spins around the axis with the greatest moment of inertia, the perturbations diminish, leading to stable frisbee-like throws.
- If it spins around the axis with the least moment of inertia, the perturbations diminish, leading to stable football-like throws.
- But if it spins around its intermediate axis, the perturbations tend to grow, so even small imbalances end up having large effects, and the motion is wild and chaotic.
The [Wikipedia article on the subject](https://en.wikipedia.org/wiki/Tennis_racket_theorem) has videos and shows the mathematical analysis.
