Hi its me again, stuck once more. Sorry guys and gals :P(adsbygoogle = window.adsbygoogle || []).push({});

Ok a problem I found on http://en.wikipedia.org/wiki/Action_(physics)

In a 1-D case how do we get from:

[tex]\delta S = \int_{t_1}^{t_2} [L(x + \varepsilon, \dot{x} + \dot{\varepsilon})-L(x,\dot{x})]dt[/tex]

to:

[tex]\delta S = \int_{t_1}^{t_2} \left(\varepsilon \frac{\pd L}{\pd x} + \dot{\varepsilon} \frac {\pd L} {\pd \dot{x}}\right)dt[/tex]

where [tex] \varepsilon = x_1(t) - x(t) [/tex]

and where the first order expansion of L in ε and ε′ is used? I dont even know what that last phrase means, so if someone could explain that to me too, that would be great.

Thankyou very much.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Missing step: Euler-Lagrange equations for the action integral

**Physics Forums | Science Articles, Homework Help, Discussion**