Drag either moving joint to choose its angle. Rod lengths stay fixed; dragging stops the motion and sets both starting speeds to zero. Drag the anchor to move the whole pendulum. Press Play to release it; Restart repeats your latest setup.

Each colored curve plots one arm’s angle against its angular speed. These are two projections of a four-dimensional state, not the full phase space. Angles wrap at ±180°; lines break there rather than crossing the graph.

Two 1 kg point masses, two massless rigid 1 m rods, gravity 9.81 m/s². No friction or air resistance. A small fixed-step numerical solver approximates the motion; very long chaotic trajectories are sensitive to numerical error.

Keyboard: 1 / 2 selects a moving joint, arrow keys adjust its angle (Shift for fine adjustment), 0 selects the anchor, Space plays or pauses. Numeric fields also set angles and initial speeds.

Equations and derivation