The double pendulum gives an example of chaotic motion

RadHazGsays...

IT WON'T STOP! Sat glued to this thing praying for it to stop and cease the hypnotic random motion...

also - those have to be some *crazy* good bearings in that thing. wonder how much $?

poolcleanersays...

If you drop it from the precise point it was dropped from in this video and observe again, will it be random? What other conditions would factor into its perceived random movement? (These aren't rhetorical questions. I'm curious.)

arvanasays...

>> ^poolcleaner:
If you drop it from the precise point it was dropped from in this video and observe again, will it be random? What other conditions would factor into its perceived random movement? (These aren't rhetorical questions. I'm curious.)


It is indeed chaotic motion -- if you attempt to recreate the exact same conditions of movement you will get different results. The reason is that there are many "balance points" where the motion could go either one way or the other, and there is no way to predict which way it will move. Sort of like balancing a ball exactly at the top of a curve -- you know it will fall one way or the other, but you can't predict which.

xxovercastxxsays...

^There's nothing truly random about it, though. It certainly appears random, but if it were released again in identical conditions the exact same thing would happen.

Of course it's probably not possible to replicate identical conditions. You'd probably need to simulate it on a computer in order to make it completely identical.

HaricotVertsays...

Attach an LED to the end, turn off the lights, and then take a long exposure picture until the motion gets boring.

Do this as many times as you want with different colored LEDs. Post all results onto DeviantArt. Profit.

Ornthoronsays...

>> ^syncron:
I'm sure it's not hard to write a formula to calculate the moment and potential of a double-pendulum system given initial conditions and duration.


It is hard actually, because the second pendulum rotates around a moving axis, which fucks up your equations royally.

sheckeysays...

For these types of systems, the resulting motion varies wildly given very small changes in the initial conditions. So, for all practical purposes, you can't make it do the same thing twice, since you will always have some error in your knowledge of the initial conditions and even that small difference (the error) will result in a wildly different result. For the same reason, you can't practically tell what it's going to do either even if you know the equations since tiny error in your knowledge of the initial conditions again yields wildly different results. Stable systems, like the earth's orbit, feature negative feedback for deviations so that small errors are brought back into line making it stable. I think systems like this one are the opposite. I think that's what's going on anyway.

swedishfriendsays...

It is not a matter of just practicality. The frikken moon and sun would have to be in the exact same positions never mind the constantly shifting magnetic field of the earth. You would have to rewind all the vibrations in the universe to get the same motion when it goes on for that long with so many moments where either pendulum could go either way. Nature is soft and wave-like so there is no same spot one could start them at and the waves that we see as atoms will never be the same ever again so there is no same thing to line up the same. And you don't even have precise moments in time since movement and geography of nature is smooth and not step-like so you cannot even release the waves that make up the object at a certain time. In short: Too many variables in a system like this to reproduce it (it is cause and effect but causes that go back into infinity).

-Karl

deathcowsays...

> and the waves that we see as atoms will never be the same ever again

I doubt quantum variations are a major player here. Air motion, temperature? Maybe to some degree. Temperature of the metal in the axis of the pivots? (Resulting in differing dimensions and clearances) Probably.

Difficulty of setting up the exact same starting dimensions, temperatures, motions... a huge YES

blackjackshellacsays...

I remember modelling these types of systems in University using Calculus of Variations. The technique involves considering the energy (kinetic, potential) of the various components. It's really very powerful, and was a ton of fun to model, but this was way back in the early 80s so the details are a bit fuzzy. Anyway, go lookup Calculus of Variations if you want to grok more.

sheckeysays...

LOL Karl. I guess I should have prefaced that I was talking about a macroscopic level. The earth orbit is regular and this thing isn't. It isn't a matter of starting it in the same position either. You know what I meant, but I take your point about the one time, forward-only experiment of the universe.

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