Chaotic 1,2 pendulum

This is an unforced coupled pendulum system with one upper and two lower pendula. Also see the 1,3 pendulum here: http://www.youtube.com/watch?v=Lz8B2ek9o84

The initial condition for this film was with the upper pendulum straight up, and the lower pendula straight down, and the movie began about three seconds after the pendula were released.

Chaotic systems exhibit a property called sensitivity to initial conditions. That means that no matter how exactly you tried to duplicate the initial angles and velocities for each experimental run, the motion would soon be very different from experiment to experiment.

This is one member of the family of compound pendulums known as 1,n, because there is one upper and n lower pendula. It is chaotic in the limit of zero friction, but has a little bearing friction and viscous damping from air friction.

This was built in the dynamics lab in the physics department of the University of Colorado at Denver (Dr. Randall Tagg, proprietor) a few years ago while I was working on my Ph.D.

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• pendulum
• chaos
• physics
• chaotic

[Asdam12]

Boy that is lookin' pretty chaotic! But I'm not sure the definition really applies in the right way...

[jstarret]

If there was no friction at all, then it would be truly chaotic.

[Acrimonius1408]

Would I be correct in assuming that this is 'only' an assembly of steel bars on a frame?

'Cos I want to build one.

[jstarret]

They are aluminum bars, but steel would work. It would be more difficult to machine, though. I used cheap ball bearings, unlubricated so that there is little friction. But you are correct, it is as simple as it appears.

[ezekieloak]

This displays non-linear, predictable behaviour. Not chaotic.

[jstarret]

What is your definition of "chaotic"?

[profiley]

i used to date a girl that danced like that.

[ChopSockeyJockey]

Am i the only one reminded of John Cleese and the ministry of silly walks ?

[kyufan1]

@ezekieloak our prof showed us this model to illustrate chaotic motion...

[TacoDude314]

Run, Forrest, Run!!!!!!!!!!!

[TaterGumfries]

22 people don't like chaos.

[haakondahl]

@ezekieloak I don't feel that it;s predictable, except in a gross sense, e.g., we know it won't leap to the ceiling. Within reasonable parameters though, predictable is not an adjective that leaps to mind. I lack the math (been years), but I think I have the concept.

[DogBoots77]

Best riverdancer ever

[sacr3]

@pgroot26 The only real equation that predicts what happens was created by a program. An Evolutionary Program that went over the many equations humans made and came out with one that was correct

[iloverikku714]

i think it want to kick me

[pgroot26]

@ezekieloak

I'm pretty sure this does display what is defined as "chaotic behavior". I found the equation to predict the motion of one of these for a class I took. The definition of chaotic doesn't mean that it can't be predicted, but that it is extremely sensitive to -and can produced vastly different results due to- specific initial conditions. 

[magicalhats15]

I feel like this just doesn't have the understated elegance of a normal pendulum.

[allismind]

@ezekieloak actually this IS a chaotic pendulum... it's time evolution varies greatly with only a small change in initial conditions... hence chaotic...which is nonlinear... such as the 3 (or more) body problem in physics