Chaotic Motion with Two Coupled Pendulums in Resonance
- 3 years ago
The pendulums rotate clockwise and counterclockwise in the most unexpected and surprising fashion, changing directions or suddenly increasing speed just when you think you know what they're going to do next. (A quote from Harvard Natural Sciences Lecture Demonstrations).
This is "a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions" (American Journal of Physics, 1993, about double pendulum).
The pendulums execute simple harmonic motion when displacements from equilibrium are small. However, when large displacements are imposed, the non-linear system becomes dramatically chaotic in its motion and demonstrates that deterministic systems are not necessarily predictable (Harvard Natural Sciences Lecture Demonstrations, paraphrased).
Notice, particularly near end of video, how the two pendulums exchange momentum.
You can watch other chaotic pendulums in action at:
Double Pendulum Displays Chaotic Motion: https://youtu.be/AwT0k09w-jw
Triple Pendulum Chaotic Acrobatics: https://youtu.be/J85gpcjvqzs
Rott's Pendulum Chaotic Motion: https://youtu.be/-ncV0WYkrhE
Source of design: Make Magazine, http://www.youtube.com/watch?v=d2E5oojoXjk
This is "a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions" (American Journal of Physics, 1993, about double pendulum).
The pendulums execute simple harmonic motion when displacements from equilibrium are small. However, when large displacements are imposed, the non-linear system becomes dramatically chaotic in its motion and demonstrates that deterministic systems are not necessarily predictable (Harvard Natural Sciences Lecture Demonstrations, paraphrased).
Notice, particularly near end of video, how the two pendulums exchange momentum.
You can watch other chaotic pendulums in action at:
Double Pendulum Displays Chaotic Motion: https://youtu.be/AwT0k09w-jw
Triple Pendulum Chaotic Acrobatics: https://youtu.be/J85gpcjvqzs
Rott's Pendulum Chaotic Motion: https://youtu.be/-ncV0WYkrhE
Source of design: Make Magazine, http://www.youtube.com/watch?v=d2E5oojoXjk