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

  1. Dec 1, 2009 #1
    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?


    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


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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

    The Euler-Lagrange equations determine your equations of motion.
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