The discussion centers on the derivation of the Euler-Lagrange equations from the invariance of the action, specifically the expression δ∫Ldt=0. A user seeks guidance on this proof, particularly in the context of a covariant Lagrangian. They note that the primary distinction in their approach involves using √(1-(u/c)^2)dτ instead of dt. The conversation includes references to a simple example proof provided in a linked forum post.
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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.julian said: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