A beautiful solution of the gravitational 4-body problem. But keep watching, because it's not stable!https://twitter.com/simon_tardivel/status/1215728659010670594 …
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this one is static under perfect conditions, right? perfect symmetry, no perturbations, etc.? the fact that it starts out symmetric at least tells me it can't end the way it does in the animation
That’s the thing it’s *not* perfectly symmetric, it just looks that way to our monkey brains. There is a ever so slight difference in initial conditions that breaks the symmetry
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In nature, increases in the energy of the orbit inevitably describe a precession. Why do people spend time solving problems of n-bodies?
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so they can eventually study n+1
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It may be symmetric, but if solved with a numerical scheme there will be truncation and representation errors plus the scheme will have finite order accuracy. These will introduce small perturbations which will be amplified in a mathematically unstable system.
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Yes but I’m assuming OP accounted for that
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but isn't there a symmetric setup that looks very similar? if so, that's what I'm asking about
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Yes, I bet there's a perfectly symmetrical solution of the 4-body problem that looks a lot like this one but stays symmetrical forever. People study highly symmetrical solutions of the n-body problem by proving theorems. Cris Moore found a bunch: http://tuvalu.santafe.edu/~moore/gallery.html …pic.twitter.com/33Sk7bxYqS
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