Two identical double pendulums are released a tenth of a degree apart. They move as one, then separate completely, while a log-scale graph shows the gap doubling at a steady rate. Start it gently and it is not chaotic at all.
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Double Pendulum
About this simulation
Double Pendulum solves the full nonlinear equations of motion using a fourth-order Runge-Kutta method, with no small-angle shortcut. A pink pendulum and a cyan twin that starts only 0.05 degrees away swing together at first, then part ways. Students adjust both angles and the mass ratio, switch the twin and the trails on or off, and read the twin separation and energy drift. It is an accessible first look at chaos and sensitive dependence on initial conditions, suitable for physics and maths discussions.
What students can explore
- Keep the defaults and watch for the moment the Paths parted readout passes 0.5 m.
- Lower Angle 1 to 20 degrees and see how long the twins stay together.
- Change Mass 2 / Mass 1 and see how the trails change shape.
- Turn Trails off and on to compare the pink and cyan paths.
- Check the Energy drift readout to judge how accurate the simulation is.
Learning objectives
- 1Describe sensitive dependence on initial conditions.
- 2Compare small-angle motion with large-angle chaotic motion.
- 3Explain why long-term prediction fails even with exact equations.
- 4Interpret a trail as a record of a system's path over time.
Questions teachers ask
Is the Double Pendulum simulation free?
Yes. It is free, has no sign-up and runs in any modern browser, including interactive whiteboards and tablets.
What does chaos mean here?
The motion follows exact laws, yet a tiny difference in the starting angle grows until the two pendulums behave completely differently. That is sensitive dependence on initial conditions, the signature of chaos.
How do I use it?
Drag the angle sliders to set a start, then watch the pink pendulum and its cyan twin. Moving any slider restarts the run. Read Twin separation to see how quickly they diverge.
Why is the energy drift not exactly zero?
The motion is computed in tiny time steps, so a very small numerical error builds up. The readout shows how far total energy has moved from its starting value.
Embed this simulation
Drop it into your LMS, blog, or class site — free.
<iframe src="https://kiwibee.io/en/simulations/double-pendulum-3d-simulation/embed" title="Double Pendulum | KiwiBee" loading="lazy" allowfullscreen style="width:100%;height:min(70vh,620px);min-height:420px;border:0;border-radius:16px"></iframe>Continue exploring
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