What is the characteristic of a system that turns it into a chaotic system?

[Boyphys]

Is there a way to predict the positions of a double pendulum? What is the characteristic of a system that turns it into a chaotic system? I’ve always had this doubt!

 

[anuttarasammyak]

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

explains sentitivitiy to initial condition to flip as illustrated above. What kind of doubt do you have ?

 

[sophiecentaur]

What is the characteristic of a system that turns it into a chaotic system?

Some form of nonlinearity and an appropriate choice of appropriate input conditions (within the chaotic region)
I made a double pendulum and it was predictable until one of the pendulums went 'over the top'. Fascinating. Slo mo makes it more fun. I have tried to put a youtube video on that link. I have to press the re-wind button for the demo to start. Anyone know why?

 

[Tom.G]

Video not accessible. YouTube states:

Private video
Sign in if you've been granted access to this video

 

[sophiecentaur]

Video not accessible. YouTube states:

Private video
Sign in if you've been granted access to this video

Thanks for responding - I'll look into it. Never used YouTube to post before

 

[sophiecentaur]

@Tom.G . I found the private / public buttons. You may be able to see my handywork now.

 

[Ibix]

I have to press the re-wind button for the demo to start. Anyone know why?

I think it's the &t=221s at the end of the URL. 221s is 3m41s, which corresponds to the end of the video. Deleting that seems to make it work.

Nice demo.

 

[sophiecentaur]

I think it's the &t=221s at the end of the URL. 221s is 3m41s, which corresponds to the end of the video. Deleting that seems to make it work.

Nice demo.

Correctamundo my boy. Thanks very much. PF is a magic source of cleverness.

So many URLs are a mile long and read like gobbledegook but every character is relevant. It's just a blur to me until someone explains it, piece by piece. I guess it should be a case of RTFM as usual.

 

[sophiecentaur]

Try this link; it seems to work. It's entertaining and takes you by surprise near the end. Just when you think it is dying, the energy from both rods goes into the short one and it does a 360 again.

 

[Herman Trivilino]

What is the characteristic of a system that turns it into a chaotic system?

Small quantitative differences in initial conditions lead to large qualitative differences in behavior.

 

[Peter Morgan]

For chaotic systems, it's generally only possible to predict statistics of future positions. Steve Brunton's YouTube channel is pretty reliable about this kind of thing as well as being mostly at an Intermediate level, as in this playlist. A look at Brunton's channel will teach almost anybody some cool physics they didn't know.
Brunton and a few coauthors have an Open Access review of Koopman Theory, as one branch of the use of statistics for dynamical systems is now called, "Modern Koopman Theory for Dynamical Systems". Parts of that would have to be called Advanced more than Intermediate, but it's well-written.

 

[hutchphd]

"Modern Koopman Theory for Dynamical Systems". Parts of that would have to be called Advanced more than Intermediate, but it's well-written.

Just looked at the paper: very well written and interesting. Well worth a look.