Calculus of variations

samgrace
Hello, here is my problem.[/PLAIN] [Broken]

http://imgur.com/VAu2sXl

My confusion lies in, why those particular partial derivatives are chosen to be acted upon the auxiliary function and then how they are put together to get the Euler-Lagrange equation?

My guess is that it's related to the turning points of the auxiliary equation, however i don't know why those derivatives are chosen and how they're related to the EL equation.

Sam

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