# Euler Lagrange Equation trough variation

## Homework Statement

"Vary the following actions and write down the Euler-Lagrange equations of motion."

## Homework Equations

$S =\int dt q$

## The Attempt at a Solution

Someone said there is a weird trick required to solve this but he couldn't remember. If you just vary normally you get $\delta S=\int dt \delta q=0$
and thats not helpful. Any suggestion on how to avoid this problem?

## Answers and Replies

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I believe you need to make your function $q = q(t) + \delta q(t)$ and then observe that since this new function needs to have the same ending points it implies that
$$\delta q(t_1) = \delta q(t_2) = 0$$
And follow that with what $\delta S$ becomes :)

thanks but isn't this just the general way of variation?

$\delta S = \int dt (f(q+\delta q) - f(q))= \int dt \frac{\partial f}{\partial q} \delta q = \int dt \delta q$

and there still the same problem remains that I can't find any function that makes $\delta S = 0$ for every $\delta q$ because here I would get $1=0$.
Or did i miss your point?