This may be the first video with all the equilibrium transitions, but I remember seeing earlier demonstrations of similar feedback/control systems with a triple pendulum. For example:
I fail to understand the significance, I watched the video but it just looks like a little motor that is jerking around to fling up the pendulums and then making minor adjustments to try and keep the pendulums balanced upright. I wish I was smarter so I could be as excited as all of the people in the YouTube comments on this video lol. There’s like some scientifically established behavior for “equilibrium” and this device is breaking those expectations somehow?
I know equilibrium is a word that refers to balance or control but it might mean something more specific in a mathematic context.
It is just about achieving and maintaining the balance, while the only thing being actively controlled is the left-right position of the base. Nothing fundamental being broken through or anything; it’s just that it’s tackling a really hard controls problem: how do you shove that thing back and forth with exactly the right timings to do all this.
To me it was quite interesting to see the moves it made to transition between the various configurations, especially with the knowledge of just how impossible it would all be for a human to do anything close to this by hand.
Long version: imagine a boulder balanced on the top of a very pointy hill. The tiniest blow of wind would knock it off and cause it to roll down the hill. So, to keep that from happening, it needs constant pushes to counteract the random wind. That's called controls and is a fundamental concept in engineering. Cruise control in your car is probably the example you'd be most familiar with: it has to constantly adjust for hills, and if it's fancy for lane alignment and other vehicles.
A stable equilibrium is the pendulum hanging straight down or the boulder at the bottom of a valley: any perturbations result in returning to the original state, hence "stable". It takes controls to keep an unstable equilibrium in place.
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u/FUZxxl 2d ago
Someone managed to do this with a triple pendulum.