Double Pendulum Chaos

Lyapunov divergence — two nearly-identical pendulums, exponentially diverging trajectories

Parameters

L1 (arm 1) 1.0 L2 (arm 2) 1.0 M1 (mass 1) 1.0 M2 (mass 2) 1.0 Initial θ1 (deg) 150 Perturbation ε 0.001

Time0.00

|Δθ₁|—

|Δθ₂|—

log(divergence)—

Est. Lyapunov λ—

Orbits

Poincaré

Lyapunov

Phase portrait of θ₁ vs dθ₁/dt