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Double pendulum: energy and chaos

Two bobs on rigid massless rods, both swinging under gravity, with the lower bob pinned to the end of the upper rod. The Lagrangian gives coupled velocity-dependent equations of motion; the qualitative behavior ranges from quasi-periodic at low energy to fully chaotic above the lowest saddle in the potential. Drag a bob to set its initial angle; double-click the canvas to zero out velocities.

Figure 1. Planar double pendulum integrated with velocity-Verlet plus a predictor-corrector for the qdot-dependent Christoffel terms (physics dt = 1 ms). Method: `shared/js/engine/symplectic.js`.
m1 1.0 kg
m2 1.0 kg
l1 1.00 m
l2 1.00 m

WHAT TO TRY

  • Vary each control and watch the rail readouts respond.
  • Compare the diagnostic plot against the live scene.