Double pendulum simulation

Is the double pendulum chaotic — does a hair's-breadth difference in where you release it change everything?

▶ Run the simulationSee the measured result

Units: dimensionless (ω_fast/ω_slow = 1+√2; secondary knowns ω_slow = √((2−√2)g/L) = 2.3971994, ω_fast = √((2+√2)g/L) = 5.7873513 rad/s)

How the lab tests it

Swing a bright pendulum next to a faint ghost released δ=0.004 rad away (watch them split), and quantify it with a Benettin twin started δ₀=1e-8 away — renormalise the phase-space separation and average its log-growth into the largest Lyapunov exponent λ.

What it looks for

λ > 0 (exponential divergence ⇒ deterministic chaos / sensitive dependence) at large amplitude, vs λ ≈ 0 (two coupled normal modes) for a gentle release