The Chaos Machine (Double Pendulum)

Every physics department needs a double pendulum, so here's how I built ours. The big improvement is that the bottom pendulum can be locked in place. This turns the chaotic double pendulum into a non-chaotic physical pendulum.

I'm going to be lazy and skip writing a big long introduction or explanation for this. The Wikipedia article on chaos thoery is pretty good and explains how chaotic systems are sensitive to initial conditions. The mathematics are too complex to accurately reproduce here, but the links below can show them correctly:

http://en.wikipedia.org/wiki/Double_pendulum

http://en.wikipedia.org/wiki/Pendulum_%28mathematics%29

http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html

http://www.myphysicslab.com/dbl_pendulum.html (simulation)

http://www.chaoticpendulums.com/chaos-theory-a9.html (simple explanation of chaos theory)

Here's a neat version made from two square plates:

http://www.physics.usyd.edu.au/~wheat/sdpend/

You can buy a double pendulum from chaoticpendulums.com, but it's more fun to build your own. Look at the pictures, look at the CAD files, watch the video, and then go make one.

Support Amazon.com for sponsoring this science fair contest, buy ball bearings online.

Safety

Standard shop and power tool warnings apply, but I have to provide a warning specific to the double pendulum. The bottom pendulum can get moving very fast and because it's chaotic, it's unpredictable. If your hand or face is in the wrong place and the wrong time, you can get seriously hurt. The best thing to do is to set it in motion and then stay out of the plane of rotation.

I fixed the video! Sorry about that. It's viewable in step 10.

Step 1 Top Pendulum - Front

This aluminum bar is half of the top pendulum. Another similar bar forms the second half. The ball bearings are 3/8" ID x 7/8" OD x 7/32" wide (McMaster-Carr P/N 60355K14) and are held in place by a #8-32 set screw. There are four bottom tapped #8-32 holes for the screws that hold the top pendulum together. There's one more #8-32 through hole for the bottom pendulum pivot. Finally, there's a 0.311" hole for the socket head shoulder bolt.

Comments

[Arnoldofingo]

you've got to check this one out...

http://vimeo.com/2952236

Mind=bender

[eviloverlord]

Very nice. Just curious - Has anyone tried a triple pendulum? Does it still exhibit the same chaotic behaviour or would the extra link damp the movement too much?

[powerfool]

here's the triple pendulum:
http://www.ne.jp/asahi/toriyama/private/pendulum6.html

But I don't know what it would be like with friction etc...

[PAWZ]

I love it. It's as hypnotic and similar to the 'Woman Falling Through Bubbles' but which I think is also slightly disturbing :-s ...but maybe that's just me!? http://www.guzer.com/animations/bubble_girl.php

[Seelos]

Raise your hand if you spent more than 4 minutes playing with this. *raises hand*

[butterknife]

Reminds me of Poi spinning.

[Mathias Re'eh]

dude thatsa awesome! thank!

[adarnell]

awesome link. thanks

[j626no]

i just played around with the masses some. it started going so fast that it exploded and the only thing left on the screen was one mass, everything else was off the screen.haha

[sssssbooom]

thank you that was fun

[n0ukf]

I let that run a while and when I came back to it, it was going faster. I guess they discovered the perpetual motion machine in that simulation. :D

[WingDings]

A teeny bit of damping would sort that out, and make it more realistic.

[sgt_pinky]

No friction assumption and creeping error in the integration method (which I assume they used Euler integration which suffers from substantial error creeping in the longer the simulation runs - compared to Runge-Kutta integration).

[CameronSS]

That's pretty darned sweet...Since I'm too lazy to read the article that you were to lazy to write, answer me this: Is the motion of the bottom pendulum truly unpredictable, or is it simply unpredictable without 43 pages of equations, three overclocked supercomputers, and a Ph.D. in quantum physics?

[electrick]

It is completely impossible to predict for any moderately long length of time.(say a second) This is because of the erratic motion of submolecular and molecular particles that move in an unpredictable fashion due to the fact that at that level, things often move without a cause. So the atoms at the point where the pendulum bends might have more or less friction than another pendulum with the exact same conditions. (it's a quirky part of quantum mechanics)

[Spokehedz]

Also true that gravity is NOT a constant like everybody thinks, as the internal molten core that comprises the earth is constantly moving. Also that air currents will effect the result from the previous swing. Combine that with the lights are imposing a bit of force on the bars... As you can see, while all of these things are very, very tiny and wouldn't normally make much of a differance--as any good engineer will tell you: "The devil is in the details" To really bake your noodle... Make two of these things and try to make them as alike as you can, and then put them side by side and holding the ends straight up and letting them go. Within the first oscillation, they will be out of sync. The science of chaos my friend!

[sbtroy]

Make two of these things and try to make them as alike as you can, and then put them side by side and holding the ends straight up and letting them go. Within the first oscillation, they will be out of sync.

There used to be a website that showed exactly that, but I haven't been able to find the video.

[James (pseudo-geek)]

somethings wrong here though. if you could calculate ALL that, the friction, earths gravity, the difference in materials, etc, etc, etc. then it would be completely predictable.

[thinkdunson]

chaos simply means that there are so many variables that it is 100% impossible to know them all.

if you knew every variable, and how they affected each other, then you could predict it.

some people say chaos means that there are things that are literally unpredictable.  this is not true.  what is true is that there are too many of them, and that the vast majority are to minute for us to even imagine.

if it were somehow possible to combine every computer on the planet with every human mind on the planet, i seriously doubt that it would come close to being even .00001% fast enough to calculate all the variables involved with this simple machine.  and that’s assuming we were even able to detect all of them.  and that’s assuming that we’re even able to know what they all are.  and that’s all assuming we can describe how they interact.  all of these things taken on their own are impossible, therefore…

i think we’re safe calling it chaos, for now.

[lll3nto]

you cannot calculate all, because if you'd also know all phisics variables, unfortunately you don't know so well what is inside your mind ( this is nothing personal, of course :)

: your mind, you *are* part of the experiment, and your mind, you affect the experiment, and you are inside the experiment: can you measure yourself?
... interesting

[James (pseudo-geek)]

I believe the "etc, etc" covers all that. if you knew all those variables, it would literally kill you, your mind could not handle all that information, you would need a more powerful mind.

[dentsinger]

Things are predictable to certain degrees, hence the theories we apply. The sweetness of chaos theory is that we found a way to somewhat predict unpredictability. We can predict the earth's revolution around the sun will take 365 days, but we can't predict some kind of catastrophic bifurcation occuring within that period of time.

[Edgar]

You should have a field day, browsing trough this: https://sites.google.com/site/buildyourstuff/reuleaux%2Clearnfromthemasters

[Closet_RAt]

The real killer (the reason the patterns cannot be predicted) about trying to figure out the patterns is that scientific theories are usually proven wrong.

While this is *relatively* trivial when it comes to whether the Earth is flat, or the moon is made of cheese, it does pop up when to matters that can be proven on the spot (such as this experiment).

I became irate at this when I asked my biology teacher why books say it's impossible to travel at the speed of light. His answer was that at the speed of light mass becomes infinite. When I challenged him that as we've never gone that fast before, how would anyone know, his reply was that it was just a proven fact, just like how it's impossible to twirl your arms in opposite directions. When I showed him that I could do just that, he said I was doing it "wrong", because it's physically impossible.

So, I showed him a second time, explaining that I'd heard that one before, and practiced doing so for a few minutes (based on my own theory) before nailing it perfectly.

But he still wouldn't budge.

For the record, I'm referring to pointing your fingers at each other (arms held roughly at shoulder level, and spinning from the elbows to make the fingers trace the same circle in opposite directions. People will normally follow one arm on accident within the first few minutes. But I have proven that if you plot out the course the opposing arm needs to take in your head, and keep focussed on that objective while subconsciously twirling the dominant arm, then it is quite easily possible. I now actually have to let my arms do it the normal way...

Science is chaos, zero predictability (go Doctor Malcolm!!!)

[wjbeaty]

> scientific theories are usually proven wrong

No, it's *new* theories which are usually wrong (like the stuff in Science and Nature journals.) Theories that have made it through the filters, all the way to college textbooks and encyclopedias, are only rarely proven wrong.  But it does happen. (Don't trust authorities entirely, because your most cherished theory might be the one that turns out to be flawed.)

> When I challenged him that as we've never gone that fast before

Of course we've gone that fast. It was done back around 1910-1920. Kids were doing it themselves in the 1960s using the VandeGraaff plans from Scientific American. What's the Superconducting supercollider for? It's not for accelerating particles, since those particles go right up to the speed of light immediately. The SSC is there for adding more energy, which pushes them closer and closer to lightspeed. But they never get there. They just get heavier and heavier, so that it takes more energy to get to 99.9999% of lightspeed.

> just like how it's impossible to twirl your arms in opposite directions I started doing that as a kid. Then I heard about Feynman Bongo tricks with two different hands, so I had to teach myself to spin my arms in two different directions backwards AT TWO DIFFERENT SPEEDS. Turn one finger eight times around, the other seven, so they slowly approach each other every eight turns. :) Then learn to switch directions. Then learn to change speeds on the fly. (Then teach yourself to speak with an echo. I'm still working on learning to talk backwards in English: Yeeerth, wuOOst, nOouuw, one two three.)

> Science is chaos

Science is watching other scientists dishonestly fool themselves, then finding out that you're just as bad yourself. Then slowly learning how to stop doing that crap.

[timsbro2000]

I find it useful to note that on every rotation the paths of your arms will intersect twice, on opposite sides of the circle. for instance if you start at the top with your fingers pointing at each other and move them in opposite directions (relatively easy) then they will point at each other again at the bottom of the circle. then you can continue and they will pass each other at the top again, etc. i think this is an easier way to think about it than what you described and every bit as successful. but to each their own I suppose. and as for the speed of light. you can't be sure but it's a fairly accepted theory. also your science teacher was clearly full of himself.

[mr.space]

lol, maybe its impossible to go the "speed of light" because its different in different materials, but seriously, it is a fact, i'm no physics guy but think of it like how in math you have one piece information, and can work out the rest

[Ben5504]

It's impossible to travel at the speed of light because it would require an infinite amount of energy to reach that speed.

Relativistic energy is defined as E=γmc², where γ = 1 / Sqrt(1-(v/c)²). (v is the object's velocity, and c is the speed of light). If the velocity were equal to the speed of light, then γ would equal 1 / 0, which is infinite.

The best analogy I can give you is accelerating a car. It takes very little horsepower to get a car moving from rest to, say, 20 mph. However, once the car is moving 60 mph, you need much more horsepower to get it up to 80, even though you're technically still accelerating by 20 mph. Because the car already has a large amount of momentum, you need more energy to change that momentum, even if it's in the same direction. To get up to the speed of light, it's not only difficult to accelerate to that point, it's impossible, because there simply isn't enough energy in the universe.

[gannon12raiders]

How does light move at the speed of light?

[sonaps]

Light is energy, and therefor different physics apply.

[barcmjm]

It doesn't have any mass.

[Nunavutnewsrules]

well it is possible for an object to have infinite mass. It did happen in the big bang and then it moved so there is enough energy in the universe too move an abject with infinite mass. Also when a macro sized object approaches the speed of light its mass and density gets so great that it would turn into sort of a black hole. So it would modify the speed of light to what ever speed it happened to be going because light would be sucked in and wouldn't be able to escape. Will someone plz. tell me how my glob of odd logic is mistaken thanks.

[Anthony312]

The big bang did not have infinite mass, if it i did, then the universe today would be pure mass and there would be no empty space. The universe had infinite DENSITY and infintesimal size. And the big bang didn't move, it stayed the same place the entire time. Its confusing, but the big bang happened at every point in space simultaneously. Even the space you occupy now was once the big bang. Black holes don't modify the speed of light at all, so your logic is mistaken.

[temp]

How do we knowthat. has anything traveled the speed of light then turned into a black hole? Do we have proof of that? But here's something to think about. If you're driving faster than the speed of light and you turn your headlights on, what happens? The speed of light is just a thing. Just like the sound barrier is. We broke that and we didn't all die. The same should be true for the "light barrier". How does something gain infinite mass? Just because light isn't traveling as fast as it doesn't mean it can't be seen. Jets can fly faster than the speed of sound, but we still hear them.

[Anthony312]

The speed of light is NOTHING like the sound barrier. It CANNOT be broken. It is a constant of the universe. It is a speed limit. The faster something goes, the more massive it is. You weigh more while you run then while you sit down. At the speed of light, you gain infinite mass, but because that is impossible, it is impossible to go at the speed of light. This is proven in particle accelerators. Yes, we have sent things at near the speed of light and created black holes in particle accelerators. There's your proof.

[ubr.bzkr]

IF you go faster than the speed of light in a car and turn the headlights on you would see nothing but darkness because the light would be going behind you because you are going faster than it. read Michio Kakus "Physics of the Impossible" it answers alot of questions.

[Anthony312]

You are wrong. Light is always the same speed no matter how fast you are going. If you did turn you headlights on, they would act like perfectly normal headlights and speed away from you at the speed of light. Read Einstein's theory of relativity, it answers a lot of questions.

[ubr.bzkr]

Which is why you cant go faster then the speed of light. thats why i put IF.

[maruawe]

I disagree with your answer , I am not a scientist or math prodigy , but given the area of discussion mass can travel at the speed of light given the right momentum and their is enough energy in the world to do just that

[Anthony312]

the momentum needed is infinite.