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Homework Help: Euler Lagrange Equation trough variation

  1. Nov 4, 2011 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

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

    3. 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 thats not helpful. Any suggestion on how to avoid this problem?
  2. jcsd
  3. Nov 4, 2011 #2
    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
    \delta q(t_1) = \delta q(t_2) = 0
    And follow that with what [itex] \delta S [/itex] becomes :)
  4. Nov 4, 2011 #3
    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?
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