# La grangian

1. Feb 4, 2012

### georg gill

http://en.wikipedia.org/wiki/Lagrangian#Explanation

I am trying to prove pV=nRT and in order to do so one need to get lagrangian (not the math formula it seems)

Here is an explanation

http://en.wikipedia.org/wiki/Lagrangian#Explanation

why is

$$\frac{\delta S}{\delta \varphi _i}=0$$?

S is a point given in time and space but I guess my problem is what is
$$\varphi$$

I guess that it is the value of the field at that point in spacetime as they write does not help me much to get what it is

2. Feb 4, 2012

### strangerep

You didn't say what these symbols mean.

No. S is the action. Read a bit further on that Wiki page. It says
$$\mathcal{S} [\varphi_i] = \int{\mathcal{L} [\varphi_i (x)]\, \mathrm{d}^4x}$$
Lagrangian/Hamiltonian mechanics start from a principle of least action, meaning
that the total action is assumed not to vary under small variations of the generalized coordinates (i.e., the $\varphi_i$ in this case) and the equations of motion are
then derived from this principle.

It's a generalized configuration variable.

BTW, this question probably belongs over on the classical mechanics forum. It sounds like you really need a textbook, and someone over there could probably suggest one.