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How do we know the principle of least action is true?

  1. Mar 24, 2007 #1
    How do we know that it is true? Most people don't give me a very straightforward answer, but I don't like that. Lagrange must have gotten it from somwhere.
  2. jcsd
  3. Mar 24, 2007 #2
    It gives the right answers. What more do you expect?
  4. Mar 24, 2007 #3
    How Was It Discovered!?
  5. Mar 24, 2007 #4


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    In some sense, it's a mathematical abstraction of things we already knew [like "shortest distance between two points is a line", geometric optics, newton's laws of motion]... and we take pleasure to find that newer theories [developed after (say) Lagrange] seem to fit into this scheme... for example, quantum mechanics.

    Implicit in this discussion is how one finds action that yield the equations of motion.

    If you are interested in Lagrange's motivation, that's more of a historical question... which might be answered in (say) Lanczos's The Variational Principles of Mechanics.

    You might find some starting points here in this wikipedia article
    http://en.wikipedia.org/wiki/History_of_variational_principles_in_physics (standard caveats apply).

    You might find this section from The Structure and Intrepretation of Classical Mechanics interesting

    If you want something deeper, then you might have to look at (say) Arnold or Abraham-Marsden.
    Last edited: Mar 24, 2007
  6. Mar 24, 2007 #5
    Back when I was an undergrad, my analytical mechanics TA briefly mentioned that the principle of least action arose from some sort of theological argument. Unfortunately I don't have any further details on that.
  7. Mar 24, 2007 #6


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    another good book to learn these stuff is the "classical" Classical Mechanics book by Goldstein.

    to understand these, need to get your mind around Hamilton's or D'Alembert principle
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