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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Are they stable?
just as stable as any other mode of oscillation .. if you perturb it you change the mode and so wont be an eigenmode ..
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But are those modes chaotic or not?
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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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