final_sol - Physics 210 Final Exam Autumn 2002 Problem 2...

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Physics 210 Final Exam Autumn 2002 Problem 2: Exercise 6 of Chapter 11 For r=0 and r=10 we find a simple attractor point into which the solution decays or spirals. For r=20 the chaotic behavior starts to become apparent. For r=28 chaos sets in around t=7 in the sense that this is where the solution starts switching from one lobe to the next. Below are 2-D projections generated in MathCad. Three of the plots for r=28 are run to a large time, to show how the lobes fill in. In addition, for r=28 I also include a 3-D plot, so that you can see the orientation of the lobes. The last two plots are a Poincaré section, showing the points where y=0. The switching between lobes is clearly illustrated by the lines connecting the points. The switching back and forth is where I see most clearly the chaotic behavior. The solution seems to pick random orbits to suddenly switch from one lobe to the next. Note the seemingly random pattern, most easily seen in the Poincaré section. The V shape fills in more and more completely as I go
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final_sol - Physics 210 Final Exam Autumn 2002 Problem 2...

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