Proving Euler Lagrange equations

[Frank Einstein]

Hi everybody; I am looking for the deduction of the euler lagrange equations (d/dt)(∂L/∂v)-(∂L/∂x) from the invariance of the action δ∫Ldt=0.
Can someone please tell me where can I find It?

Thanks for reading.

 

[julian]

Here I gave the proof for a simple example, should be easy for you to generalize it. Can give additional points if you like.

https://www.physicsforums.com/threads/what-is-a-lagrangian.823652/#post-5177331

 

[Frank Einstein]

Here I gave the proof for a simple example, should be easy for you to generalize it. Can give additional points if you like.

https://www.physicsforums.com/threads/what-is-a-lagrangian.823652/#post-5177331

Thanks for the anwser; I was trying to prove this for a covariant lagrangian; the only differencie I spot with your proof is that I have to write √(1-(u/c)^2)dτ instead of dt.