Double pendulum modes | chaos fractals

Surface of section (or Poincaré map) for the double pendulum with low energy. The Poincaré map is acquired by mapping angle and angle momentum of the first pendulum each time the second pendulum crosses a certain angle. This is done simultaneously for 36 double pendulums that all have the same energy. The resulting map shows regular trajectories (closed orbits) and some seemingly random and chaotic motion (irregular orbits). The orbits never intersect and the chaotic orbits will therefore reveal modes hidden within the chaotic regions of the double pendulum. The video shows a survey of the Poincaré map. More precisely it shows the motion of the double pendulum at selected positions of the map and a zoom near the center. The simulation was done using high order explicit symplectic integrators. This type of simulation requires exact time evolution in phase space and can not be performed properly using regular integration methods. 0:00 intro (chaotic 🔥) 0:15 Poincaré map (36 double pendulums) 0:28 regular 0