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

Gardenharvest

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

Pengwuino

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.