Physics · Study 013
Double Pendulum
Three double pendulums start 0.002 radians apart and end up nowhere near each other. A live demonstration of chaos you can restart.
What you're looking at
Each pendulum is two rigid arms and two equal masses, advanced by the exact equations of motion in small time steps. The three copies begin almost perfectly overlapped. For a few swings they move as one, then the traces peel apart and never agree again.
The idea behind it
This is sensitive dependence on initial conditions, the defining feature of chaos. The system is fully deterministic and has no randomness in it. Prediction fails anyway, because any error in the starting angle, however small, grows exponentially with time.
Try this
Click or tap to release three new pendulums from a different height.
