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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Assuming its not a numerical issue, I am not sure I understand why symmetry should fall apart.
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If it's not perfectly symmetrical at the start, it can become extremely asymmetric later. Or maybe it's symmetrical at the start but the numerical errors are asymmetric for some reason. In the real world, outside influences can introduce the asymmetry.
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I was assuming perfect symmetry was the idea. I dont read French so there may be things I am missing. Thanks.
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That’s the point with dynamical instability. Unless the system is perfectly free of noise/disturbances or inaccuracies in initial state, the instability will occur. In the simulation that may be numerical error (which there always is), but that just illustrates the principle.
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Not a physicist, but am aware of instability inherent to n-body problems. I suppose we can summarise as a) initial conditions (unknown here I think) b) numerical issues (perhaps ever present?) and c) external perturbations (again unknown here). Thanks to all with comments+links.
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Perfect symmetry and instability are compatible. The classic example is a perfectly sharp, symmetric pencil balanced on its tip. Any perturbation, no matter how small, will break the symmetry and cause the pencil to fall.
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Yes, I’m wondering if the order of operations in X and Y “favors” one direction? Some balancing needed?? I’ve seen this with operator splitting using ADI (alternating direction implicit).
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