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Anyone know how to interpret the euler-lagrange differential equation?

  1. Dec 1, 2009 #1
    Hi,
    I am having a calculus class now and these days the instructor is introducing the Euler-Lagrange differential equation. I have no idea why the formula (general form) is like that way. Is anyone here know how to interprete the formula and help me to understand it?

    dF/df-(d/dx)dF/df'=0

    Many thanks.


    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 1, 2009 #2

    Pengwuino

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    Gold Member

    The way it's introduced in physics is how it satisfies least-action principles using variational calculus; that is the variation of the action is 0: [tex]\[
    \delta \int {L(\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}
    \over x} } ,\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}}
    \over x} ',t)dt = 0
    \]
    [/tex]

    The Euler-Lagrange equations determine your equations of motion.
     
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