Initial Conditions
120°
-20°
1.0
1.0
Lyapunov Sensitivity: The double pendulum is a canonical chaotic system. Two trajectories starting just 0.01° apart diverge at rate eλt where λ ≈ 3–7 (Lyapunov exponent). The phase portrait (θ₁, θ̇₁) shows KAM tori (closed curves) at low energy but fractal chaos at higher energy. Use the chaos demo to see identical-looking starts diverge within seconds.