Interactive Double Pendulum Playground

Yes I think the physics is wrong

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:

  getUpperBob() {
     const { x0, y0, ang0, l0 } = this;
     const { x, y } = this.calculateBobPosition(x0, y0, ang0, l0);
     return { x, y };
   }

   getLowerBob() {
     const upperBobPos = this.getUpperBob();
     const { ang1, l1 } = this;
     const { x, y } = this.calculateBobPosition(
    upperBobPos.x,
    upperBobPos.y,
    -ang1,
    l1
     );
     return { x, y };
   }

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...

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.

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.

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.

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.