My dumb question: I thought the whole thing with this is the instability/inability to predict. It starts off with the three bodies locked in to fixed motions? I guess it has to be for the user to start messing around with it?
My dumb question: I thought the whole thing with this is the instability/inability to predict. It starts off with the three bodies locked in to fixed motions? I guess it has to be for the user to start messing around with it?
Not a dumb question at all!
There is no general closed-form solution to the three-body problem. There are certain specific initial conditions which give periodic, repeating orbits. But they are almost always highly "unstable", in the sense that any tiny perturbations will eventually get amplified and cause the periodic symmetry to break.
It's analogous to balancing an object on a sharp point. Mathematically, you can imagine that if the object's center of gravity was perfectly balanced over the point, then there would be zero net force and it would stay there forever. But the math will also tell you that any tiny deviation from perfect balance will cause the object to fall over. It's an equilibrium, but not a stable equilibrium.
The example at the link demonstrates this. The numerical integration can't be perfectly accurate, due to both the finite time steps and the effects of floating-point rounding. Initially the error is much too small to see, and the orbits seem to perfectly repeat. But if you wait a couple of minutes, the deviations get bigger and bigger until the system falls apart into chaos.
Ahh okay I'll let it run as is for a while and see what happens, thanks
Not really. Any solar system proves a kind of stability. And so does the famous KAM theorem. It states that a periodic solution is indeed quasi-stable under small pertubations. And yes, small sometimes is extremely small. But still stable. Imagine a sharp point with a tiny dent.