35% aqueous glycerol solution with Kalliroscope as tracer
Credits: CK, Akshita Sahni
The Poincare Map for a damped, periodically driven pendulum is developed. Each time the forcing function passes through its maximum, the phase plane location of the pendulum is recorded as a red dot. When the pendulum passes over the top, it gets out of sync with the driver, resulting in erratic motion. The fade transition occurs between 10 and 10000 periods of the driver. The end of the transition reveals a fully developed Poincare Map,which characterizes the underlying strange attractor. Though the motion appears random, it is actually chaotic, the result of deterministic equations of motion.
A simulation of a double pendulum, where the balls have equal mass and the (massless) sticks connecting them is 0.1 meters long. The simulation is made in MATLAB, exported frame by frame (4000 frames) and converted to a 80 seconds long video (50 fps, real-time) using ffmpeg.
This was a bonus task regarding differential equations and numerical methods in our “Continued mathematical analysis” at Chalmers University of Technology.
Here is a triple pendulum which has 3 degrees of freedom. It falls freely under the influence of gravity. It looks quite chaotic.
Non-repeating. Have fun watching it all!
My favorite part is probably the one right after 8:15:35. So fascinating!!!