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

1. Dec 1, 2009

### 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

2. Dec 1, 2009

### 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: $$$\delta \int {L(\mathord{\buildrel{\lower3pt\hbox{\scriptscriptstyle\rightharpoonup}} \over x} } ,\mathord{\buildrel{\lower3pt\hbox{\scriptscriptstyle\rightharpoonup}} \over x} ',t)dt = 0$$$

The Euler-Lagrange equations determine your equations of motion.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook