Euler Lagrange Equation trough variation

[BasharTeg]

Homework Statement

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

Homework Equations

[itex]S =\int dt q[/itex]

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 [itex]\delta S=\int dt \delta q=0[/itex]
and that's not helpful. Any suggestion on how to avoid this problem?

 

[JHamm]

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

 

[BasharTeg]

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

[itex] \delta S = \int dt (f(q+\delta q) - f(q))= \int dt \frac{\partial f}{\partial q} \delta q = \int dt \delta q[/itex]

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