Physics
Double pendulum
A classic demonstration of deterministic chaos.
What happens
Two hinged pendulums, and determinism turns into chaos: launch the fan of nearly identical copies and watch them stay together for a while, then fly apart exponentially, as the divergence chart shows on a log scale. Change masses, lengths and angles; the energy drift chart proves the integrator is honest.
Equations used in the module
Equations L = ½(m₁+m₂) l₁² θ₁′² + ½ m₂ l₂² θ₂′² + m₂ l₁ l₂ θ₁′ θ₂′ cos(θ₁−θ₂) + (m₁+m₂) g l₁ cos θ₁ + m₂ g l₂ cos θ₂ d/dt (∂L/∂θ′) = ∂L/∂θ Lyapunov: δ(t) ∝ e^(λt)
