Double Pendulum Chaos

RK4 integration · Sensitive dependence on initial conditions · Lyapunov exponent estimation

Pendulums: 6

θ₁₀: 2.50 rad

Speed: 1.0

t = 0.00 Separation: — Est. λ: —

Double pendulum: chaotic for most initial conditions. Lyapunov exponent λ > 0 → exponential divergence of nearby trajectories. Here: δ(t) ≈ δ₀ e^{λt}, λ ≈ 2–3 s⁻¹.