Double Pendulum: Chaos & Poincaré Section

Hamiltonian chaos visualized via phase-space cross-sections

Click canvas to add orbits. Left: pendulum motion. Right: Poincaré section (θ₁=0 plane)
The double pendulum exhibits Hamiltonian chaos: KAM tori appear as closed curves in the Poincaré section for low energies, while chaotic orbits fill 2D regions. As energy increases past a critical value, KAM tori break (Chirikov criterion) and phase space becomes dominated by chaos.