Pendulum Gyrations

Fractals and Chaos

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This movie shows meanderings of attractor basins for the forced damped pendulum, 2014, by Evelyn Sander and James A. Yorke. In this movie, we show how the basins of attraction of the forced damped pendulum change as the forcing amplitude is varied. Both the number and topology of the basins often change quite drastically, quickly changing from laminar to chaotic, and in some cases with a surprising number of distinct attractors.

Link for the high quality version plus details of how it was made: http://math.gmu.edu/~sander/EvelynSite/pendulum-gyrations.html

 

Title page from the movie.

 

This is a still from the movie with \(\rho = 1.5175\).

 

This is a second still from the movie at \(\rho = 2.1600\).

 

This is the third still from the movie. Parameter \(\rho = 2.2925\).

Author Institutional AffiliationGeorge Mason University and University of Maryland
Author Email
Author Postal MailGeorge Mason University, 4400 University Dr. Fairfax, VA, 22030, USA University of Maryland, College Park, MD 20742, USA
KeywordsBasins of attraction, Forced-damped pendulum, chaos
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