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.
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.
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.
It's way off. My first guess was that there was something wrong with the physics code, but after carefully checking against this[1] derivation of the Hamiltonian it seemed fine, and once I wrapped my head around the JavaScript the RK4 integration[2] checked out as well.
So, what else might be wrong I wondered. Well, it seems to move in the wrong direction... so I checked how the pendulum is displayed. And sure enough, I think there's a sign error:
Note how the upper bob uses ang0 while the lower one has -ang1. Meanwhile the physics derivation assumes both angles are against the vertical, so have same sign.
Changing -ang1 to ang1 does indeed make the pendulum move in a natural way, except now dragging it is flipped. Ie you drag it left and it moves right. Another sign error in setLowerBobPos. Fixing that as well it now works as I'd expect.
When you bring up the lower mass and let it go, it seems to push the upper mass away, which should never happen. This whole site smells off vibe coded jank.
A vibe-coded double pendulum sim should produce a much better result than the physics on this page. Claude Code made this just now off one prompt, the physics are much better: https://keir.is/swinging
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.
Super fun project, and students loved it! :)
This is hilariously bad.
If you want to see what a real physically sensible double pendulum sim looks like:
https://www.myphysicslab.com/pendulum/double-pendulum-en.htm...
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.
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.
[0] https://news.ycombinator.com/from?site=theabbie.github.io
If you tried it when it was broken, could it be you're running the old version? That is, clear your cache and try again?
If not, describe what feels off, as it feels fine to my untrained eyes after the sign fix.
Love to see someone do this for a harmonigraph [1].
[1] https://en.wikipedia.org/wiki/Harmonograph
(I contributed to this Wikipedia article over two decades ago!)
Could use a way to set some friction
Could someone explain why turning off gravity makes it path so uniform ?
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.
Because of the constant-length rigid connections, they start behaving like celestial objects in perfect orbit.
Anyone else feel like the pendulum motion seems off? Maybe the default mass settings are weird, but the movement just does not look physical to me.
It's way off. My first guess was that there was something wrong with the physics code, but after carefully checking against this[1] derivation of the Hamiltonian it seemed fine, and once I wrapped my head around the JavaScript the RK4 integration[2] checked out as well.
So, what else might be wrong I wondered. Well, it seems to move in the wrong direction... so I checked how the pendulum is displayed. And sure enough, I think there's a sign error:
Note how the upper bob uses ang0 while the lower one has -ang1. Meanwhile the physics derivation assumes both angles are against the vertical, so have same sign.Changing -ang1 to ang1 does indeed make the pendulum move in a natural way, except now dragging it is flipped. Ie you drag it left and it moves right. Another sign error in setLowerBobPos. Fixing that as well it now works as I'd expect.
[1]: https://dassencio.org/46
[2]: https://lpsa.swarthmore.edu/NumInt/NumIntFourth.html##sectio...
Just made a PR
I considered it, but had to go to work and I figured since the last commit was over 4 years ago it might just sit there idly, so I skipped it.
But no, PR was merged in short order. Lesson learned.
Hn shows this story is 3 hours old, yet your GitHub PR was made 2 days ago, linking here?
The story has been reposted to HN via the “second-chance pool”, which resets the dates.
https://news.ycombinator.com/item?id=26998308
There's a "How To Use?" section on the GitHub repo page.
https://github.com/theabbie/DoublePendulum?tab=readme-ov-fil...
Yep, it's just bad. Physics feels totally off.
Yes I think the physics is wrong
When you bring up the lower mass and let it go, it seems to push the upper mass away, which should never happen. This whole site smells off vibe coded jank.
I don't think that's fair. Also the project is 4 years old so the timeline doesn't really work out for being vibe-coded.
> This whole site smells off vibe coded jank.
A vibe-coded double pendulum sim should produce a much better result than the physics on this page. Claude Code made this just now off one prompt, the physics are much better: https://keir.is/swinging