Nonlinear Pendulum — Driven Chaos & Poincaré Sections

A driven damped pendulum: θ'' + γθ' + sin θ = F·cos(ωt). Below the chaos threshold it settles into periodic orbits. Increase the drive amplitude and watch sensitive dependence on initial conditions emerge. The Poincaré section (right) samples phase space once per drive period.

Phase portrait: θ (angle) vs θ' (angular velocity). Poincaré section sampled each drive cycle.