The double pendulum is one of the simplest mechanical systems that exhibits deterministic chaos. Two rigid links connected by frictionless pins follow Newton's second law exactly — yet tiny differences in starting angle diverge exponentially, making long-term prediction impossible. This is the butterfly effect made visible.
Drag the pendulum bobs to set initial angles, then release. Use the angle sliders in the control panel to set precise values. Enable trajectory trace to draw the chaotic path. Clone the simulation with a tiny offset to directly compare how two nearly-identical starting conditions diverge over time.
Henri Poincaré discovered the mathematical foundations of chaos in the 1890s while studying the three-body problem — a related system. The double pendulum's phase space contains both stable periodic islands and chaotic seas, depending on energy level. High energy → almost always chaotic; low energy → behaves like two coupled simple pendulums.