Double Pendulum Simulator

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.

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.

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.

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.

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.

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.

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.

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.

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.