Double Pendulum

Nudge the start by a billionth; watch it become a different pendulum. Two rods, two bobs, and the most famous demonstration of deterministic chaos — the exact Lagrangian equations, no small-angle approximation, integrated with Runge–Kutta 4.

Why it is hard

The two angles

The whole state is four numbers: the two angles each rod makes with straight down, and how fast they are changing.

Forces on the upper bob Forces on the lower bob

Gravity pulls each bob down and each rod's tension resolves that pull — but the lower rod pulls back on the upper bob, so neither rod can be solved on its own. That coupling is the whole difficulty, and the nonlinearity in it is the whole chaos.

Every run reports its energy drift: energy is exactly constant in the real system, so the drift is the one honest measure of whether the picture can be believed at all.

Try it

⚗️ Watch it run — one screen: the pendulum going, its trail drawing itself behind the bob, the setup under it and the five releases a click away. Run 90°/90°, then change the lower angle to 90.01° and watch the whole future come apart.
📖 How it works — the equations, the integrator, and why the drift is measured the way it is.

_{Rebuilt from the Systemorph Cloud Double Pendulum notebook as a MeshWeaver node type — the force diagrams above are the originals. The motion is DATA: integrated once from the node's parameters and handed to the browser as SVG keyframes, so every viewer sees the same run and nothing is mutated to show it.}