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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?

Layn
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    That's called the inverse problem of Lagrangian mechanics (and Douglas' theorem there solves it, in a sense) – ACuriousMind Dec 05 '14 at 20:35
  • Possible duplicates: http://physics.stackexchange.com/q/20298/2451 , http://physics.stackexchange.com/q/20188/2451 , http://physics.stackexchange.com/q/3500/2451 and links therein. – Qmechanic Dec 05 '14 at 20:47
  • Jacobi's Last Multiplier http://arxiv.org/abs/0709.3231 & http://books.google.ie/books?id=_i6IAwAAQBAJ&pg=PA15&dq=%22Jacobi%27s+Last+Multiplier%22+Lagrangian&hl=en&sa=X&ei=Z8yxU66UPM-g7Abz4oDoDQ&ved=0CCEQuwUwAA#v=onepage&q=%22Jacobi%27s%20Last%20Multiplier%22%20Lagrangian&f=false 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! – bolbteppa Dec 05 '14 at 21:05

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