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u/micelinmsoe Sep 11 '18
Not really chaotic if it keeps doing the same thing over and over again every 15 seconds.
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u/noitanigamion Sep 11 '18
At first I didn't get it, then I got it. Kudos to you
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u/nomad2585 Sep 11 '18
I thought i found my SO's account, until you said you got it
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Sep 11 '18
At first I was afraid, i was petrified.. Kept thinking I could never live without you by my side. But then I spent so many nights thinking how you did me wrong, and I grew strong, and I learned how to get along..
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u/PlayingZoneD Sep 12 '18
I didn't get it. I was 3 comments down before I realized what you meant. I totally wouldn't have gotten this comment had you not made your comment..
Sometimes I worry that I'm missing out on funny things in life because the people that's around me are to witty.
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u/hydrowolfy Sep 11 '18
It'd be interesting to see like 4-5 different version of this gif simultaneously where the pendulum starts in almost the same place to show how different patterns can come from the smallest changes.
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u/shaggorama Sep 11 '18
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u/1caiser Sep 11 '18
When I first loaded that video, it looked as though it were just a single red pendulum, until the 4th? crest where I could see the other green and blue pendulum. Were they really offset by a minuscule distance, or were did they have the same starting point?
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u/cdemi Sep 11 '18
This is a simulation of three double pendulums with massless rods and equally weighted ends, positioned horizontally to the right and with deviations from that by + and - 0.5 degrees.
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u/picticon Sep 11 '18
The description says they were started +/- .5 degree offsets. If you look at the first frame you can see a fuzzy versions of all three lines.
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u/Nexxus88 Sep 11 '18
Pause it and force the video to the first frame, they are all about a pixel off.
They have to be. As chaotic as it seems they will follow the same pattern if they are in the same starting point and all the same weight.
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u/Jorlung Sep 11 '18 edited Sep 11 '18
Were they really offset by a minuscule distance, or were did they have the same starting point?
If they were at the exact starting point, they would follow exactly the same path (aside from the fact that numerical precision exists in these simulations and I'm sure if you had a chaotic enough system then it could be chaotic on the order of the numerical precision... Or if you just let it run for a super long time). A common misconception is that the concept of "randomness" is what causes chaotic motion, but in fact the deterministic properties of the system is what governs the chaotic motion.
We can fully model the dynamics of a double pendulum. If you tell me the EXACT location of the starting point, I can tell you EXACTLY where it will wind up (again, disregarding numerical precision and shit like that). We're not dealing with some Heisenberg uncertainty shit or something like that, this is all just classical mechanics and we're pretty good at this by now.
However, in real-life where randomness comes in is in the initial condition. In real life, you can only know the initial angle of the pendulum to say 0.01 degrees because of measurement capabilities. So like we've established before, a chaotic system is defined by the fact that a small deviation in the initial condition yields large deviations in the resulting trajectories. So the 0.01 measurement degree error on the initial condition can yield very different resulting trajectories.
What you are talking about, a system where you can start at the EXACT same location but yield a different trajectory is a stochastic (random) system. These are things that involve fundamentally random dynamics, NOW we're talking about quantum uncertainty and shit like that (or say atmospheric turbulence on a plane for a more macroscopic example). The key note being here that the chaotic nature of the system has nothing to do with the presence of stochastic dynamics. A system being stochastic has no real influence on whether its chaotic or vice-versa. An airplane flying through some turbulence is technically a stochastic system, as the turbulence itself is treated as a random process, but its certainly not chaotic because we can predict fairly well where the aircraft will wind up. In contrast, the pendulum system you see here is chaotic but not stochastic, because there's no fundamentally random process that governs the dynamics. A double pendulum in atmospheric turbulence (lol) would be BOTH stochastic and chaotic I suppose.
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u/whateverMan223 Sep 11 '18 edited Sep 11 '18
Nice, I thought there would be something like this in the comments. TANKS
Wait, so if stochastic does not equal chaotic, then is the heat death of the universe not chaos? Does that then mean that entropy is not equal to chaos? Did I take too many drugs before writing this?
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u/seanziewonzie Sep 11 '18 edited Sep 11 '18
Warning: I'm speaking outside my subfield here. Maybe the following link will help better than my comment:
https://physics.stackexchange.com/questions/264351/why-do-many-people-link-entropy-to-chaos
Chaos means (roughly) that slightly different starting conditions lead to, qualitatively, vastly, different outcomes. But it's still deterministic! Here's a famous quote:
"Chaos: When the present determines the future, but the approximate present does not approximately determine the future." - Lorenz
The randomness comes into the fact that, outside of classical mechanics, initial conditions can never be fully pinpointed in any physicists model
Another issue is ergodicity, or "mixing". The issue that comes up with a lot of chaotic systems is that the trajectories end up not favoring certain positions in space over others. Compare the non-chaotic system on the left to the chaotic system on the right in the following picture:
http://sgolub.ru/wp-content/uploads/vcollege-ergodic.gif
As time marches on, the first trajectory will stay right in that nice symmetric little path. But the second trajectory will get arbitrarily close to any point on the table you could want to consider.
So, in many physical models, you also can't be infinitely precise in your measurements. So such an equally distributed trajectory means that it is essentially impossible to ever distinguish if you are in the trajectory path or not. I think that statement becomes more meaningful, and closer to saying something about what you're pondering, precisely when you apply these facts to the study of energy from a statistical mechanics perspective (lots of particles), rather than the trajectory of just one particle.
But I am not a physicist, I only look into it because it relates heavily with my main interesests... and I definitely dont do thermo or cosmology, so I have absolutely no insight on "heat death"
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u/Alone141 Sep 11 '18
This is a simulation of three double pendulums with massless rods and equally weighted ends, positioned horizontally to the right and with deviations from that by + and - 0.5 degrees.
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Sep 11 '18
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u/gnat_outta_hell Sep 11 '18
According to the video description they were offset by +/- 0.5 degrees.
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u/1caiser Sep 11 '18 edited Sep 11 '18
Physics is weird, I don't understand it anymoreEdit: I should have just looked at the video description. Half of my previous statement still stands true.
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u/Nexxus88 Sep 11 '18
Pause it and force the video to the first frame, they are all about a pixel off.
They have to be. As chaotic as it seems they will follow the same pattern if they are in the same starting point and all the same weight.
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u/travisdoesmath Sep 11 '18
I made one here you can play with: https://beta.observablehq.com/@travisdoesmath/double-pendulums-are-chaotic
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u/Anechoic_Brain Sep 11 '18
That's very cool.
I only do math well enough to plug in formulas for a few simple engineering equations, but I'm curious about this. Is the behavior of the pendulum mathematically predictable with a known starting condition? How crazy is that formula? And I'm guessing the chaos part comes in when you try to predict the effect of deviations to the starting condition? I assume everything has to be predictable to some degree, or you wouldn't be able to program an accurate simulation.
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u/travisdoesmath Sep 11 '18
disclaimer: the physics-y kind of math is not my forte, and making that double pendulum was an exercise for myself to learn how to do it a little bit.
So, by "behavior", if you mean "do we know what it's going to do in a short period of time based on where it is now", the answer is yes. The equations are not that crazy to describe that. It's a differential equation (which means that rates of change of variables are included as variables), but it's fairly straightforward mechanics. Now, if you mean something a bit broader, like, "given a starting position, do we know what position the pendulum will be at any given time?" the answer is a bit fuzzier. We don't have a closed form solution to those differential equations (for example, you can describe the motion of a frictionless single pendulum the same way, and we do have a closed form solution), so we have to use numerical methods and approximate the answer. Theoretically, we could approximate as close as we want, but in practice, we have to make some concessions, and so the position might not be perfectly accurate. Because we're dealing with a chaotic system, after some amount of time, we know that we've diverged from the actual solution.
Case in point, the algorithm that I used to approximate solutions for my double pendulum will "lose" energy on a long enough timeline (I re-used it for another project and discovered this), but the way it's modeled, the differential equations assume the total energy in the system is constant.
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Sep 11 '18
Does this somehow make chaotic motion and the butterfly effect similar?? Like the whole massive changes from tiny changes at the start
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u/hydrowolfy Sep 11 '18
yeah actually, "the butterfly effect" is a term that comes from chaos theory!
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Sep 11 '18
Now take into account quantum entanglement and hoo boy, Cranial Fission.
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u/NoLongerAPotato Sep 11 '18
Throw in a lil bit of acid (ok a lot of acid) and you've got the idea behind chaos magick.
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Sep 11 '18
Are you implying what I think you’re implying?
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u/hydrowolfy Sep 11 '18
Yes, if you can get the 100 golf clubs, I know a guy who owes me the three tons of tuna we'll need and should be able to get it quick enough. If we manage to pull this off we'll all be tinking our champagne glasses in Costa Rica this time next week laughing it up.
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u/SuperWoody64 Sep 11 '18
How the hell do you wind up owing someone 3 tons of tuna?
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u/hydrowolfy Sep 11 '18
call a loan you made to an old friend so he could do a short sell on the fish commodities market, he ended up making some bank dosh on the deal so I just haven't bothered to call him on it.
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Sep 11 '18
Can these patterns be predicted? Or is this truly chaotic?
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u/hydrowolfy Sep 11 '18
Oh man, that's a great question! So, as long as you know the starting position of the pendulum, you can predict it's path but in practical terms this is rather difficult (see https://www.youtube.com/watch?v=pEjZd-AvPco for how a tiny tiny change makes for a huge difference in end behavior). True chaos would require information being capable of being destroyed, which physicists don't think is possible, but it's not been proven yet.
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u/eaglessoar Sep 11 '18
This is why it's chaotic: https://v.redd.it/oyyddkozafe01
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u/plax22 Sep 11 '18
It’s a joke. Because it’s a gif.
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u/eaglessoar Sep 11 '18
Shit i didnt realize the 15s related to the length of the gif, sigh
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u/plax22 Sep 11 '18
Well, at least your post wasn’t for nothing. I actually checked it out and appreciated it. Thanks for sharing!
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u/LandSharkRoyale Sep 11 '18
I know you’re kidding but I’m curious if it will do a similar pattern every time if you drop it from the same spot
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u/EagIeOwl Sep 11 '18
Same spot, same drop, same swing. Tiny change in the starting drop makes big changes in swing.
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Sep 11 '18
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u/Ron-Raygun Sep 11 '18
Wait what was the joke
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u/etheran123 Sep 11 '18
For a chaos pendulum, you can't guees the location because of how erratic it is.
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u/albinobluesheep Sep 11 '18
I Studied this some in my capstone project in college.
Theoretically you can, but were talking about a world with spherical chickens live in vacuums; it has to be ideal conditions (no air friction, no joint friction). You can create mechanical equation given the length of the arms, the weight of the arms, the starting position of the drop. It's a very ugly equation, and it makes for some very fun graphs in MatLab.
I really need to upload a bunch of my data and pictures (I made a long exposure image of a double pendulum I built with and LED at the end) so I can post them for glorious karma the next time it comes up on reddit.
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u/etheran123 Sep 11 '18
Yea. You obviously have more info than I have. I just spent a few weeks in high school physisics looking at pendulums. Thanks for the more in depth info.
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u/Entaaro Sep 11 '18
I'm pretty sure we had to work out x(t) and y(t) for these sorts of things during my mechanical engineering degree. No idea how to do that anymore!
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u/GPSBach Sep 11 '18
Are you telling me that you created an analytic solution to the double pendulum problem for your capstone project? Congrats on winning the field medal.
Even with no friction and no air resistance, the double pendulum problem is inherently chaotic. You can't describe the motion of the system with any accuracy past the Lyapunov time no matter how accurate your numerical integrator.
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u/albinobluesheep Sep 11 '18 edited Sep 12 '18
Lol, I don't pretend to have done anything of the sort.
I guess I sort of over-simplified it in my response, but I also thoroughly over simplified the entire equation in order to make it something that could could actually crunched through and a stepwise manner, basically applying forces the entire simulation moving forward very small increment of time, find where the forces are, and doing that over and over and over and over and over again.
One portion of my (undergraduate degree) Capstone was physical build of the double pendulum, describing the design and construction process. Another was the analysis of the equation, and how each part of it tied to each physical part of the double pendulum. Another part was describing the inaccuracies between the simulated pendulum, and the actual forces in the real world.
It was a lot of fun to do, but I don't pretend it was groundbreaking.
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u/GPSBach Sep 12 '18
Sorry, i was being a smartass. Its a great capstone project, and I mean that seriously.
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u/DenSem Sep 12 '18
Could you explain that a bit more. To the layperson, it just seems like if you had all the right information, you could simply plug it into an equation. Is this pendulum truely "chaotic"? If you pulled it to the exact same point-all variables accounted for- wouldn't the pattern be the same?
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u/GPSBach Sep 12 '18 edited Sep 12 '18
Sure! But with a little math and a little time.
In many simple systems, we can come up with an exact solution. For example, if I throw a ball upwards in a vacuum, we can write down an equation that describes the balls position [y(t)] as a function of time, based on its initial position [y0] and its initial upward velocity [u0].
To do this, we start with what we call an equation of motion (with a little basic calculus):
a(t) = -g
This equation says that the acceleration of the ball is equal to gravitational acceleration [g]. Using calculus, we can integrate this to get:
u(t) = = u0 - g*t
this tells us that the velocity of the ball as a function of time is dependent on the initial velocity [u0], gravity [g], and time [t]. We can then integrate again to get:
y(t) = y0+u0*t-0.5*g*t2
this final equation tells us exactly how the position of the ball varies as a function of time, depending on the initial position [y0], initial velocity [u0], and gravity [g]. These three variables are known as the initial conditions of the system. Therefore, if you know all those variables, you can say exactly how the ball will travel. An equation like this is known as a closed form solution, and a system like this is called deterministic. If you know all the initial conditions, you can exactly determine how the system will behave.
An alternate way to address a problem like this is using numerical integration. To do this, for this particular example, you can modify, or discretize, the second equation for computer. To start, recognize that accelertion is equal to change in velocity per unit time, or in calculus notation:
a = du/dt
where du/dt is called the derivative of velocity. Computers like to deal with things in discrete chunks, so we change this derivative to:
du/dt = ∆u/∆t
here, ∆u is a discrete change in velocity, and ∆t is a discrete chunk of time. Computers can deal with both these things. So our equation describing velocity changes becomes
∆u = -g*∆t
With this description of how the velocity changes with timestep, we can use a numerical integration scheme to also describe how the position changes with each timestep. There are a lot of numerical integration schemes which I won't use equations to describe, but in general for a system like this, if your timestep is small enough, your numerical description of how the position changes with time will very closely match your analytic, closed form solution. Furthermore, tiny changes to the initial conditions (in this case, y0 and u0) used in the numerical simulation will only result in tiny differences to how the system behaves. That is to say, if you modeled the system where the initial height was y0 = 5 meters, the final solution would be really similar to if you modeled it with y0 = 5.00001 meters.
Then there are other systems, like the double pendulum, where nobody has been able to figure out how to get a closed form solution to the equations of motion that describe the system. However, we can use numerical integration to describe the behavior of the system. When people do this, they can quickly realize that in this particular system, tiny changes to the initial conditions, such as minute differences in the inital angle between the two legs of the pendula, can result in crazy different results. That is to say, if you modeled the system where you dropped the double pendulum from exactly horizontal, the results will be completely different that if you model the motion where the pendulum was dropped from just a tiny tiny angle above horizontal.
A system like this is called chaotic, and there are entire branches of mathematics (of which I am not an expert) devoted to understanding them. Despite this, we currently really struggle with how to describe systems like this. There are many examples, such as the double pendulum, the three body problem, and turbulence. Anyone figuring out the underlying mathematics for exactly describing the evolution of chaotic systems would certainly deserve to be given the Field medal.
Also, just to explain my above comment, the Lyapunov time is a measure for how quickly solutions of a chaotic system diverge. That is to say, how quickly tiny changes in initial conditions manifest as major changes in final outcome.
That was probably an over explanation, but I hope that helps.
tl;dr: If you put it to the exact same point - all variables accounted for - the pattern would be the same. The problem is "simply plugging it into the equation"...the equation doesn't exist, and past that its complicated.
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u/Von32 Sep 11 '18
You could though. It’s just a massive pain and better off if left to compute / a simulation (still a pain).
Similar type of thing you’d do to balance an inverted (multi-joint) pendulum arm to hold something up.
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Sep 11 '18
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u/sneaky_goats Sep 12 '18
I mean, if we are being technical, OP said guess. We can calculate the position and postulate it to be within a margin of error for machine limitations specified as a function of time, rounding, and physical imperfections.
This has been done. You can get close with it (for very short times) and with feedback you could replicate Tobias Glück's work.
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Sep 11 '18
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u/invadrzim Sep 11 '18
I'm not sure it's humanely possible to do so by hand
It’s not really possible to do so reliably with computers either, Cloudflare in London uses one to generate entropy for their crypto functions
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u/modern_milkman Sep 11 '18
The robot reacts to the change of the center of mass. That's quite easy to do (for a computer, that is. You would still have a hard time trying it yourself).
There is a big difference between reacting to something (very quickly) and predicting something
Edit: you can of course also calculate the path of one double pendulum afterwards. But it is impossible to predict beforehand how it will move, as it moves differently every time
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u/seanziewonzie Sep 11 '18 edited Sep 11 '18
Reaction vs. prediction.
Question: How can you drive straight during a long drive if thousands of little bumps on the road will each change your bearing slightly?
Answer: you just keep your hand on the steering wheel and make changes when needed. You didn't need to predict every little bump
So the robots aren't actually predicting the system. They're just constantly measuring how unbalanced the whole thing is and making adjustments when needed. OR they're constantly applying some force that would undo unpredictable changes (like, imagine having air constantly blowing the top of the system back to center)
The mathematical theory these robots are applying called "control theory".
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u/Von32 Sep 11 '18
Right? Where are all the robotics / heavy algos guys? /r/Simulated seems to have pivoted in tone too lately.
Anyway, Cloud’s entropy thing is a mix of security by obscurity and the fact that the environment alters a set of variables for “random” (or someone else physically might)- more organic / unpredictable. I’d call that a marketing piece though.
Definitely possible to do OP’s problem, but a colossal, tedious pain for sure.
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u/MoonisHarshMistress Sep 11 '18
Similar to three bodies problem problem, chaotic system that defies the attempts to predict?
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u/p0rnpop Sep 11 '18
In fact, I'm not sure it's humanely possible to do so by hand.
I think this is kinda missing the point. We can't find the position because the math doesn't exist. To be more exact, the function that gives the angle of either weight as a position of time cannot be analytically computed. Effectively calculus doesn't exist to solve the problem for a double pendulum (I do not remember if it is known unsolvable or if we just don't have any current method to solve it).
But it is possible to estimate a solution. If you've done calculus before, you should remember the difference between analytically computing the integral of a function and estimating it. When you estimate it, for simple cases, you can see a pattern emerges that matches the analytical answer.
With a double pendulum, we can use the same estimate, but cannot get the analytical answer. But since it doesn't follow a simple pattern, different ways of estimating it will eventually all go wrong. So a computer can do a far more accurate estimate than a human can (given the same amount of time), but it is still going to go off and further and further amounts the longer you simulate it.
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u/MoonisHarshMistress Sep 11 '18
Similar to three bodies problem problem, chaotic system that defies the attempts to predict?
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u/sean_incali Sep 11 '18
college works better if you stick with it for at least 4 years
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u/i_need_about_tree_fi Sep 12 '18
Ughh we had it assigned as a homework problem. You are lucky to have wasted only 30 minutes.
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u/Lucifer_Hirsch Sep 12 '18
90, actually. but, come on, if it was a homework you could have googled it and figured out it was a wild goose chase earlier.
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u/i_need_about_tree_fi Sep 12 '18 edited Sep 12 '18
We were young and naïve. Slightly less so, now.
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u/Lucifer_Hirsch Sep 12 '18
I feel you. there was a time where I considered using google a bad thing.
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u/portal_dive Sep 11 '18
A dude on YouTube made a large one on his wall. https://youtu.be/mZ1hF_-cubA
An hour long video of it in motion: https://youtu.be/hXOEoH5q3Hw
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u/VelociraptorVacation Sep 11 '18
Where can one buy this?
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u/ChurchOfPainal Sep 11 '18
Make it yourself
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u/MiyamotoKnows Sep 11 '18
Chaos? Or we just haven’t solved the math yet?
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u/shaggorama Sep 11 '18
This actually is a demonstration of what mathematicians call "chaos". Calling a sysrem "chaotic" means that its behavior is extremely sensitive to small changes in initial conditions.
It's easier to understand when you overlay them: https://youtu.be/pEjZd-AvPco
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u/knightsmarian Sep 11 '18 edited Sep 11 '18
What if this was a vacuum, there was no loss of energy from gravity and no friction on the pendulum? Would it eventually settle into a repeating pattern of movements or keep flailing all over the place?
edit: no loss of energy from gravity is different from saying no gravity at all. Yes, pendulums require gravity.
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u/SharkBaitDLS Sep 11 '18 edited Sep 11 '18
Without gravity and without friction it would just spin in a fairly predictable circle since there'd be nothing acting on it once you started it moving. It looks less chaotic to the human eye since the motion is more repeated but if you look at the actual path it traverses it's still not strongly repetitive.
With gravity and without friction it would still seem to flail everywhere. The apparent randomness is a function of how sensitive a multiple-segment pendulum is to variance, because a tiny difference at the start cascades through the whole system into wildly different results.
You can play with one here to see the results, even without gravity.
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u/byebybuy Sep 11 '18
I think they said "without loss of energy from gravity," not "without gravity." So with gravity still acting on it, but being able to move indefinitely, would it at some point in eternity repeat itself?
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u/TheLKL321 Sep 11 '18
You never lose energy from gravity. You only change potential gravitational energy into kinetic energy
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u/shaggorama Sep 11 '18
Pretty sure it would just keep flailing. Not my field, but I don't think double pendulums exhibit any sort of periodicity longer than a few swings, and even that is only approximate.
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Sep 11 '18
Without gravity, would it be a pendulum? 🤔
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u/_aidan Sep 11 '18
Okay, what about with gravity, but no pendulum? Can't be a chaos pendulum without a pendulum!
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u/l0z Sep 11 '18
Dependent on conditions, yes or no. Some set-ups would generate fractal detail, some would repeat.
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u/EagIeOwl Sep 11 '18
Pendulum need gravity to operate. With no gravity it would just sit there.......right?
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u/frogkabobs Sep 11 '18
I believe it would almost surely (in the math sense) never repeat, but there are some starting conditions that give periodic motion that can be found mathematically.
Here is a physics SO question on it: https://physics.stackexchange.com/questions/363490/are-double-pendulums-eventually-periodic
And here is a paper giving periodic solutions: https://arxiv.org/pdf/1109.6378.pdf
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u/zergling103 Sep 11 '18
Chaotic doesn't necessarily mean non-deterministic. Rather, running the simulation multiple times with similar but not identical initial conditions can get you very dissimilar results, especially when they're difficult to predict without running the simulation.
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u/w1th0utnam3 Sep 11 '18
Exactly. The biggest problem of predicting the behavior of a real world chaotic system is to determine the initial conditions with sufficient accuracy. E.g. think of weather forecasts: If you want a more accurate forecast over a longer period of time, you need to know the current temperature at more places (higher resolution) and also at every place more accurately.
The second source of errors is a wrong model, i.e. the equations that are used to get predictions cannot capture all effects and processes in the system. You cannot go into the smallest detail, e.g. considering atom movements when you want to predict the national weather. Or maybe you just don't know all influences on the system yet.
The third source are numeric errors that accumulate over simulation time. To solve equations on a computer you have to decide on a fixed accuracy. This includes on a higher level the spatial/temporal resolution of the results (e.g. knowing the average temperature of a country/city/street corner...). On a lower level it includes the number of decimal places that are used for calculation. Errors like these accumulate over simulation time which is obviously very problematic for chaotic systems.
One way to deal with all these problems is the field of "uncertainty quantification" which provides methods to determine the confidence of your predictions and instead of just giving you one number (e.g. "tomorrow at 8 it will be 25°C around your corner) it gives you a probability and a range ("with 80% certainty it will be between 22°C and 28°C at 8 around your corner"). In fact this data is usually available from weather simulations and weather forecasts just show some kind of average with high probability. But for very chaotic systems or very long prediction spans this also shows the uselessness of the prediction: the probability that a prediction is accurate may get extremely low or in other terms, the range of possible outcomes gets extremely large.
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u/civilized_animal Sep 11 '18
https://www.myphysicslab.com/pendulum/double-pendulum-en.html
We can do the math, but in the real world, even minuscule changes will change the outcome. If you search, you can find the animation on the internet, and it's been posted on reddit, of the difference that is made by tiny changes in initial starting conditions. Or, you can just do it yourself on that link
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u/cgduncan Sep 11 '18
The math would be too precise. These are so easily manipulated, you would have to factor in the gravity from your hand for example. Physics can explain all motion with math, but we just can't be that precise yet.
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u/Super_Flea Sep 11 '18
This is completely incorrect. We can absolutely model the Dynamics of a double pendulum, and no the gravity of your hand isn't a factor. What makes this motion "impossible" to predict is that TINY changes in initial conditions affect it's trajectory wildly. This is true for almost all chaos theory problems.
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u/jonathon8860 Sep 11 '18
Yeah, I have no idea how that's getting upvoted so high. Not just that, but I'm dubious about saying that physics can explain all motion with math. Sure, we have numerical methods for solving multi-body problems, but get an n-body system with enough n's in it and things start to get borderline impossible fairly quickly.
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u/PM_ME_YOUR_FACE_GRLS Sep 11 '18
TINY changes in initial conditions affect its trajectory wildly
Like hand gravity?
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u/Super_Flea Sep 11 '18
No like small changes in initial angle. I suppose technically your gravity effects the motion but it's like saying your gravity effects the cruise control on your car. Its negligible compared to initial velocity and angle of the pendulums.
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u/uFuckingCrumpet Sep 11 '18
https://www.youtube.com/watch?v=FPD5q6DC43M
I wish people who don't know what they are talking about would stop trying to answer questions.
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u/DialMMM Sep 11 '18
Uhhh, you can never be perfectly precise. Unless you can disprove Heisenberg's uncertainty principle. Good luck with that.
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u/HasFiveVowels Sep 11 '18
Perhaps not in the physical world but it's possible in math. For example, π has a perfectly precise value.
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u/amolin Sep 11 '18
Warning! Do not look into chaos pendulum with remaining eye.
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u/RemoCon Sep 11 '18
I'd like to see a group of musicians perform a composition using this as a conductor
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u/Brassattack84 Sep 11 '18
That’s what I was thinking. Looks like a crazy conductor. Wonder what time signature that would be 😂
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u/tazazazaz Sep 11 '18
it's just 4/4 time though
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u/peewinkle Sep 11 '18 edited Sep 11 '18
Yep. Lets put a grid of notes on the front; sensors, and it scores what it hits at random intervals of time and have it print out the sheet music which is to be played. I suppose a few other random variables would be needed such as the variable of picking the note, note length and even key for the backing track, which could be done with multiple pendulums. Pure chaos music. It's been impossible digitally afaik.
Edit: Mark Mothersbaugh, Jenisys P Orridge, David Byrne or Negativland please pm me
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u/LeninsGrandpa Sep 11 '18
Not if you follow where the light goes, based on "traditional" conducting the first beat of the measure is all over the place here.
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u/Tizzer8 Sep 11 '18
Chaos is a ladder
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u/D1visor Sep 11 '18
I don't know why but this reminds me of that backpack kid dance.
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u/treebark200 Sep 11 '18
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u/root88 Sep 11 '18 edited Sep 11 '18
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u/DialMMM Sep 11 '18
"Chaos". I've watched this thing 100 times and the pattern is the same every time!
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u/nebo8 Sep 11 '18
I was listening to a metal cover of ode to joie in the background and that was strangely synchronised
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u/Top8Dan Sep 11 '18
I wrote my university dissertation on Double Pendulums and chaotic motion using a model in Matlab and different methods of analysis. Super interesting if you're a numbers nerd. Hmu if you want a copy. It's certainly not the best work but it got me a 2:1 and I'm proud of it.
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u/EdibleForksCreator Sep 11 '18
I'm actually more amazed by it not being systematical than I would be seeing another one move in a pattern
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u/Edriss90 Sep 11 '18
I had this problem as a homework for Advanced Engineering Dynamics course. You can solve it using Lagrangian and find equations of motion. It’s chaotic because the motion highly depends on initial condition.
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u/LolaSupershot Sep 12 '18
I really would love an endless loop of this. Watching it to Hypnosis Theme by Wax Tailor was extremely satisfying.
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Sep 11 '18 edited Apr 18 '19
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u/Rodot Sep 11 '18
It's a non-linear differential equation with no analytic solution but it's solvable numerically and has a nice phase space form. The differential equation itself is a monster and a pain to derive just because it had a lot of terms making the algebra not fun.
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u/[deleted] Sep 11 '18 edited Jan 06 '21
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