From the standpoint of the mathematical framework behind Lagrangians and their corresponding action, is there a method to invert the process?
If not, is this an open question or is there some aspect of the formalism that does not allow this?
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3$\begingroup$ That's called the inverse problem of Lagrangian mechanics (and Douglas' theorem there solves it, in a sense) $\endgroup$– ACuriousMind ♦Commented Dec 5, 2014 at 20:35
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$\begingroup$ Possible duplicates: physics.stackexchange.com/q/20298/2451 , physics.stackexchange.com/q/20188/2451 , physics.stackexchange.com/q/3500/2451 and links therein. $\endgroup$– Qmechanic ♦Commented Dec 5, 2014 at 20:47
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$\begingroup$ Jacobi's Last Multiplier arxiv.org/abs/0709.3231 & books.google.ie/… is apparently a method to do it, though I can't make sense of the method & would love someone to explain it in a simple deriving-it style way without assuming differential operators out of the blue! $\endgroup$– bolbteppaCommented Dec 5, 2014 at 21:05
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