Double Pendulum Ring and Bar v.redd.it/i1gbbwurmro71
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Double pendulum chaos demonstration v.redd.it/mgjx62ylxgx71
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Double Pendulum Chaos Demonstration v.redd.it/mo195pijwvo71
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Double pendulum ring and bar. v.redd.it/gaog6e5f8uo71
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Double pendulum simulation/animation. v.redd.it/lbcqr7aczsb71
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Double Pendulum
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How chaotic is a double pendulum really?

The double pendulum is widely known for being chaotic, in stark contrast to the well behaved single pendulum. But can it be analyzed statistically? I tried to get to the bottom of this by doing some simulations to find, whether the pendulum would have a kind of average frequency.

I simulated a double pendulum in python and recorded the displacement of the first bob. I then did a Fourier transform on the displacement. This essentially filters out the most important frequencies of the signal. I found out that for small initial displacements (10Β° - 20Β°) the double pendulum is very well behaved, having a main frequency similar to a single pendulum the length of the entire double pendulum and a pretty strong higher frequency 2.4 times higher.

When I started the pendulum with a higher initial displacement, there were more overtones. At a certain point, the pendulum undergoes an abrupt transition. For an initial displacement of 79.141958Β°, the pendulum still has distinct frequencies, but for 79.141959Β° there are no discernible frequencies at all.

Imgur album with diagrams: https://imgur.com/a/rpJ0QcJ

PS.: Was for some reason deleted in r/physics, I thought it would fit pretty well here though.

Edit: I tried the simulations with the initial condition being the first rod being dsiplaced to the right, the second rod to the left by the same angle (the Energy for a given angle stays the same as before). This results in a different picture https://imgur.com/a/klkGtg4 (just 100 samples though), kinda the opposite of bifurcation. To get results that are only dependent on input energy, I'd have to do much longer simulations, which aren't really useful with runge kutta. The "transition to chaos" is more gradual but still finishes about 70-80Β°.

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100 Double Pendulums Simulation ( Chaos Theory is Beautiful <3 ) v.redd.it/9tqvkskduai71
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Double pendulum. Insights reddit.com/gallery/rmjhvb
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Interactive Double Pendulum Playground theabbie.github.io/Double…
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Butterfly-effect simulation using 500 double pendulums v.redd.it/qihy2mtmdts71
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Interactive Double Pendulum Playground theabbie.github.io/Double…
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Double-double pendulum v.redd.it/8haq9kzy8h381
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Double Pendulum
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Interactive Double Pendulum Playground Using SVG theabbie.github.io/Double…
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Whoa Amazon! I just want a double pendulum, for science. Didn’t even know Amazon had this type of thing! Certainly wouldn’t expect them as suggested results! [Not sure if this quite fits here. But I def said Hol’Up!]
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Interactive Double Pendulum Playground theabbie.github.io/Double…
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[OC] I made a double pendulum fetch for gifs! gfycat.com/ablecookedcygn…
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Interactive Double Pendulum Playground theabbie.github.io/Double…
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Simon Lancaster showcasing a β€œDouble pendulum chaos demonstration” v.redd.it/czxjtw5n56q71
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How did you you enjoy the double pendulum?
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Interactive Double Pendulum Playground theabbie.github.io/Double…
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Interactive Double Pendulum Playground github.com/theabbie/Doubl…
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200,000 Double pendulums with slightly different initial conditions [compute shader] v.redd.it/i7c1pwn5j8y61
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Saw a full-sized version of the double pendulum here yesterday. Here's a mini one my kid and I made with a Kiwico kit. May only be mildly interesting... v.redd.it/kh1y1ckxm2p71
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Little wand pendants I made so they are portable and can be worn! They double as pendulums too.
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Deriving, Solving, and Animating the Double Pendulum in Python: No Pencil Required! An introduction to symbolic and numerical computing in python. youtu.be/8ZZDNd4eyVI
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Phase space of 1000 double pendulums
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Double Pendulum

Hi everyone, I would like to share this simulation of the Double Pendulum

Link: https://www.geogebra.org/m/yjz98xay

I used the equations form MyPhysicsLab:

https://www.myphysicslab.com/pendulum/double-pendulum-en.html

Double Pendulum

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Interactive Double Pendulum Playground buttondown.email/theabbie…
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Interactive Double Pendulum Playground github.com/theabbie/Doubl…
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