Although the double pendulum is the poster boy of Chaos Theory, there are actually two "special" modes of oscillation (called "eigenmodes") in which the masses move in perfect harmonypic.twitter.com/CnivjtF8Hg
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But are those modes chaotic or not?
no .. you don't usually call a mode chaotic .. the system's sensitivity to initial conditions determines if it's a chaotic system .. these happen to be two special initial conditions
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So what I'm getting is, with a chaotic system like the double pendulum, any small perturbation from any initial point will eventually diverge exponentially from the original trajectory, right? So these aren't stable modes of oscillation
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well no they can't be stable since it's a chaotic system .. if you perturb it you're essentially getting a new pendulum with new initial conditions
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