# Lagrangian mechanics - Euler Lagrange Equation

by brisingr7
Tags: functional, lagrange equation
 P: 3 Euler Lagrange Equation : if y(x) is a curve which minimizes/maximizes the functional : F$$\left[y(x)\right]$$ = $$\int^{a}_{b}$$f(x,y(x),y'(x))dx then, the following Euler Lagrange Differential Equation is true. $$\frac{\partial}{\partial x}$$ - $$\frac{d}{dx}(\frac{\partial f}{\partial y'})$$=0 Well.... I don't understand why the function f has only three variables x, y(x) and the derivative of that. what about y'' or y$$^{(3)}$$? I think it could be possible.(physically) All files related to this topic states that the function f as a function of variables x, f(x), and f'(x). i.e. can function f be like : f(x,y(x),y'(x),y''(x),.....) ??? or.... is it unnecessary to think about the second derivative and furthermore?