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Douglas_Knight comments on Beyond Statistics 101 - Less Wrong
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Are you familiar with Noether's Theorem? It comes up in some explanations of Buckingham pi, but the point is mostly "if you already know that something is symmetric, then something is conserved."
The most similar thing I can think of, in terms of "resources for finding symmetries," might be related to finding Lyapunov stability functions. It seems there's not too much in the way of automated function-finding for arbitrary systems; I've seen at least one automated approach for systems with polynomial dynamics, though.
Noether's theorem has nothing to do with Buckingham's theorem. Buckingham's theorem is quite general (and vacuous), while Noether's theorem is only about hamiltonian/lagrangian mechanics.
Added: Actually, Buckingham and Noether do have something in common: they both taught at Bryn Mawr.
Both of them are relevant to the project of exploiting symmetry, and deal with solidifying a mostly understood situation. (You can't apply Buckingham's theorem unless you know all the relevant pieces.) The more practical piece that I had in mind is that someone eager to apply Noether's theorem will need to look for symmetries; they may have found techniques for hunting for symmetries that will be useful in general. It might be worth looking into material that teaches it, not because it itself is directly useful, but because the community that knows it may know other useful things.
In what sense do you mean Buckingham's theorem is vacuous?
It's a quite bit more general than Lagrangian mechanics. You can extend it to any functional that takes functions between two manifolds to complex numbers.