WAVESPEED AI DOUBLE PENDULUM Runs in your browser

100% FREE

Double Pendulum SimulatorWatch chaos grow from a tiny nudge.

Double pendulum, live in your browser: one pendulum hangs from the end of another, and that is enough for wild, chaotic motion. Drag the two bobs anywhere, press Play and watch the trail it paints, coloured by speed.
Release up to 50 pendulums that start a hair apart and watch them fan out, race two in butterfly mode, map which starts flip over the top, and save the result as a video clip or a PNG.

Up to 50 pendulums at onceChaos map of every startMP4 clips and PNG snapshots

No sign-up No upload No watermark

Loading the simulator…

Simulations, snapshots and videos are made on your device.

THREE SIMPLE STEPS

How to use the double pendulum simulator

Pick a start

Choose the chaotic, single, nearly periodic, fan or butterfly scene, or drag the two bobs to any angle you like.

Press Play

Watch the motion and its trail, slow it down or step frame by frame, and change lengths, masses or gravity while it swings.

Explore and export

Fan out many pendulums, open the chaos map, then save a PNG or export a vertical, square or wide MP4 clip.

Why is a double pendulum chaotic?

A double pendulum follows exact, deterministic laws: the same start always gives the same motion. Yet its two swinging arms constantly trade energy through terms that depend on the sines and cosines of both angles and on the squares of their speeds. These equations are nonlinear and, at high enough energy, have no simple repeating solution.

In this chaotic regime two starts that differ by a millionth of a degree separate roughly exponentially fast, so the difference becomes visible within seconds and the two motions soon have nothing in common. This sensitivity to initial conditions, often called the butterfly effect, is what makes long-term prediction impossible in practice even though nothing random happens.

At small swings the picture is calm: the pendulum moves like two linked springs with two natural rhythms, both arms swinging together slowly or against each other quickly, and its motion is regular. Raise the starting angles and chaos takes over, which the fan, the butterfly mode and the chaos map let you see directly.

Deterministic, not randomReplay a start and you get exactly the same motion, frame for frame. The surprise comes only from how quickly tiny differences grow.
Energy stays constantWithout damping the total energy never changes, so the motion stays bounded. Chaos rearranges the energy between the arms; it does not create any.
Some starts can never flipReleased at rest from low angles, the pendulum lacks the energy to swing an arm over the top. With equal arms and masses that is every start where 2 cos θ1 + cos θ2 is above 1: the black region of the chaos map.

Tips for striking pendulum clips

Start high for chaos

Angles above about 90 degrees give the wildest motion. Below about 30 degrees the swing stays regular and the trail repeats.

Fan out for the rainbow

In the fan, 30 to 50 pendulums that differ by a thousandth of a degree stay together for a few swings, then burst into a rainbow. Slow motion makes the moment of splitting easy to see.

Pick starts from the map

Click any point of the chaos map to load that start. Bright areas flip over the top almost at once, dark areas take much longer.

WaveSpeed AI

From pendulums to visuals

Teaching physics or making science content? Create the pictures and clips around your simulation with WaveSpeed AI.

Start creating Explore 1,000+ AI Models

1,000+ AI models
Image, video and 3D
Pay as you go

$1 in free credits for eligible new accounts. No card needed. Generators have separate account and credit requirements. The Double pendulum simulator is free.

Double pendulum FAQ

Is this double pendulum simulator free?

Yes. Every scene, setting, snapshot and video export is free, with no account, no sign-up and no watermark. It runs entirely in your browser.

How accurate is the simulation?

It solves the exact equations of motion of two point masses on rigid, weightless rods, derived from the Lagrangian, with the fourth-order Runge-Kutta method and a small fixed time step. Without damping the total energy stays constant to better than one part in a million over minutes of motion, and small swings match the textbook periods.

Why do the pendulums in the fan split apart?

Each pendulum in the fan starts a tiny angle away from its neighbour. In the chaotic regime such differences grow roughly exponentially, so after a few swings the pendulums follow completely different paths. Start the fan at small angles and they stay together.

What is the butterfly mode?

Two pendulums start almost identically, by default a hundred-thousandth of a degree apart. The graph shows their difference on a logarithmic scale as it climbs, and the readout tells you when the two outer bobs first visibly separate.

What does the chaos map show?

Every point is a start position, the first arm's angle across and the second arm's angle up, released at rest. Its colour shows how long the pendulum takes until either arm swings over the top: bright for quick flips, deep blue for slow ones, black where it never has the energy to flip. The map fills in from coarse to fine in the background, and a click loads that start.

What are the phase plot and the Poincaré section?

The phase plot draws an arm's angle against its angular speed, or the two angles against each other, as the pendulum moves. The Poincaré section marks a dot each time the first arm passes straight down moving forward: a regular motion leaves a few points or a closed curve, chaos sprays dots over a wide area.

Can I simulate a single pendulum?

Yes. Pick the single pendulum scene or untick Second arm. At small angles it swings with the familiar period 2π√(L/g), and you can watch the period grow at larger angles.

Can I export a video?

Yes. Open Export, choose 9:16, 1:1 or 16:9, full 1080p or a quick preview, 30 or 60 fps and the length, then save an MP4 (or WebM). The motion is replayed frame by frame from the start, so the clip is perfectly smooth on any computer and includes your slow-motion setting.

What do gravity and damping change?

Stronger gravity makes everything swing faster; try the Moon, Mars or Jupiter. Damping slowly drains energy, as air resistance and friction would, so a chaotic swing calms down into a regular one.

All Free Tools