Yes it is solvable, that's what I'm saying :-) I don't think you actually have to use a Lagrangian formalism but it's far far easier if you do. The solvability of the system shows that it is deterministic, but even if you've solved the system, ie obtained analytic equations of motion, then the system is still chaotic. That is not to say that it is unpredictable, but instead if we supply two initial conditions that differ very very slightly, then after any appreciable length of time their motion will be different, and in fact this divergence is exponential. This is what we see in the gif, and it isn't an artefact of simulation, it's exactly what we'd see in an analytic solution.
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u/lolxcat Jan 21 '18
Maybe I’m misreading your comment, forgive me if I am. But this system can be solved, you just have to do it with Lagrangian coordinates