Double pendulum is a canonical chaotic system. Two unit-mass unit-length pendulums
obey the full nonlinear Lagrangian equations — no small-angle approximation.
The Poincaré section (right) records (θ₁, ω₁) every time θ₂ crosses 0 with ω₂ > 0.
Regular motion traces closed curves; chaotic motion fills a 2D region.
Multiple trajectories with slightly different initial conditions diverge exponentially (positive Lyapunov exponent).