Originally published at: https://boingboing.net/2020/02/12/chaotic-pendulum-wanders-field.html
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Looks like me, dancing.
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Looks like me, 25 years ago, trying to figure out which movie to rent
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It qualifies for a grant from the Ministry of Silly Walks.
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would this count as a perpetual motion machine or would it stop at some point?
do the magnets discount it as they provide energy?
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Magnets don’t provide any energy, and perpetual motion is impossible.
Eventually the magnet on the pendulum will slow, bouncing between two or three magnets until it comes to a rest at equilibrium between the the force from several magnets.
Think of it like a marble dropped into a bowl, that rolls back and forth until it changes all of it’s potential energy into kinetic energy, and eventually stops at the lowest part of the bowl.
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this is slightly different though, right? there is nothing in the bowl that is pushing the marble away. there is another video he has where there is one magnet and it is directly where you would expect the pendulum to rest. you think this would come to rest if left long enough?
Looks like i need to get me some magnets and the kids and i need to do an experiment. fun!
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Is it really chaotic or is it just very complex so it appears chaotic? I bet if you knew the values of all the magnetic fields involved as well as other forces it could be modeled without much difficulty and the motion accurately predicted.
The pendulum with the single magnet would eventually find equilibrium. It bounces because of the change from potential to kinetic energy from raising it up and having gravity take over. I’m not an expert, but I assume the magnetic fields interacting provides the same kind of “push” that a spring would when compressed. Kinetic energy (movement against spring) becomes potential energy (spring compresses) becomes kinetic energy (spring expands). Once that energy has dissipated, with smaller and smaller bounces, the magnetic field of the pendulum and that of the stationary magnet would rest against one another, with no further motion. It would probably take a while, because of the low friction. And then a much, much longer time later, the magnetism of the permanent magnets would dissipate, and the pendulum would rest wherever its potential energy was lowest.
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So, um, that’s actually the definition of a chaotic system. Yes you could predict it if you knew every variable, but every variable is extremely difficult to know. We could predict weather perfectly if we could simulate every bit of heat transfer in every molecule in the atmosphere. Chaotic != Random
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Another way to think about this is that the magnets are not pushing the pendulum. They are only steering it. Gravity is doing the swinging, and ultimately the kinetic energy is used up just like any other pendulum. Magnets do not violate thermodynamics, despite it sometimes feeling like they could if only we arranged them cleverly enough. 
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Can someone with a physics background answer whether this an example of the n-body problem, or something else?
I have one of these on my desk at work. It’s mesmerizing. My work is not.
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As the points are stationary aside from the magnet, it should be completely feasible to find an exact solution for points where the pendulum can eventually come to rest.
Now float another magnet above each of the stationary magnets, using small vertical pins or somesuch as guides, to introduce a degree of freedom … I imagine that the pendulum will interact with the floating magnets to emergentify form bee-like dancing patterns.
Lay out the two-stage magnets on a grid, cellular-automaton style … Conway’s Game of Magneto-Chaotic Life – !
Good point. Let’s hear an explanation on that, BB physicists!
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The stable resting points should be “easy” to find. I think putting a paper on top and using iron filings will identify them, otherwise you’ll have to resort to math.
The path of the pendulum and which one of them it ends up in is chaotic. Even the tiniest change in starting conditions will mean that a pendulum passes the first magnet at a different distance giving it a slightly different deflection, and for every magnet it passes that deviation will become larger until the path is totally unpredicatable.
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So at what point does a system move from simply being complex to being chaotic? Is there really enough going on in this magnet example to qualify as chaotic? Unlike weather this one (I think) shouldn’t be too hard to model for someone who knows about these sorts of things.
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