Double Pendulum: Chaos & Sensitivity to Initial Conditions (2D)

This 2D companion drives the same Lagrangian double-pendulum equations as the 3D version through a plain canvas view built for reading the physics rather than orbiting a scene: a side panel exposes both arm lengths, both masses, both release angles and a "chaos seed" offset, a phase-space plot traces θ2 against its angular velocity so you can see the system never repeats a loop, and a translucent twin pendulum — released a fraction of a degree away from the main one — visibly peels apart from it within seconds, making the sensitive dependence on initial conditions that defines chaotic systems directly visible instead of implied.