I don't see the difference. The motion in the version you linked is slower but I guess it can be fixed changing g. What are the visible errors in the main post?
EDIT: I just noticed someone found an error and apparently it's fixed now.
I built a physical version of this back when I was teaching HS math and science. I used two bicycle hubs, and attached metal arms to each. I put an LED on the second hub, and the end of the second arm.
For the demonstration, I'd have it under a blanket in the front of the room when students came in. I'd turn the lights out, only turn the outer LED on, and set it in motion. Then I'd cover it up, turn the lights on, and ask students to sketch what they thought was under the blanket. Then I'd turn the lights out again, turn both LEDs on, and set it in motion again.
Most people were able to sketch something pretty close to a double pendulum after that second demonstration. I also set up a camera and did some time lapses, and got pictures that look just like this online demo.
The motion is still off, as it was 2 days ago [0] in the previous submission. There's something that just doesn't look right, and some particular setups trigger very unrealistic behaviors.
Not sure if this got a second lease on life from the mods after clearing the old comments and resetting the submission date to today, or how did it make the front page again.
The system is periodical; not counting the absolute angle but the velocities, angular velocities, and the angle at the joint are all periodical functions.
When the angle at the joint is 180° the Energy and Angular momentum determines v_1 and v_2, the velocities of the masses. It is known that Energy and Angular momentum both conserve.
Therefore the system will play out the same after states when the inner joint is 180°, and all the parameters will be periodical between 2 such states.
You can observe this in the demonstration in TFA: set gravity to 0, and observe how the graph rotates, especially the furthest points from the origin (where the angle at the joint is 180°).
edit: there are probably 2 different solutions for when the joint angle is 180°? I've found a graph where one furthest place from the origin is really pointy, and then the other is rather round.
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[ 3.1 ms ] story [ 34.2 ms ] threadIf you want to see what a real physically sensible double pendulum sim looks like:
https://www.myphysicslab.com/pendulum/double-pendulum-en.htm...
EDIT: I just noticed someone found an error and apparently it's fixed now.
For the demonstration, I'd have it under a blanket in the front of the room when students came in. I'd turn the lights out, only turn the outer LED on, and set it in motion. Then I'd cover it up, turn the lights on, and ask students to sketch what they thought was under the blanket. Then I'd turn the lights out again, turn both LEDs on, and set it in motion again.
Most people were able to sketch something pretty close to a double pendulum after that second demonstration. I also set up a camera and did some time lapses, and got pictures that look just like this online demo.
Super fun project, and students loved it! :)
Not sure if this got a second lease on life from the mods after clearing the old comments and resetting the submission date to today, or how did it make the front page again.
[0] https://news.ycombinator.com/from?site=theabbie.github.io
[1] https://en.wikipedia.org/wiki/Harmonograph
(I contributed to this Wikipedia article over two decades ago!)
When the angle at the joint is 180° the Energy and Angular momentum determines v_1 and v_2, the velocities of the masses. It is known that Energy and Angular momentum both conserve.
Therefore the system will play out the same after states when the inner joint is 180°, and all the parameters will be periodical between 2 such states.
You can observe this in the demonstration in TFA: set gravity to 0, and observe how the graph rotates, especially the furthest points from the origin (where the angle at the joint is 180°).
edit: there are probably 2 different solutions for when the joint angle is 180°? I've found a graph where one furthest place from the origin is really pointy, and then the other is rather round.