- #1

hideelo

- 91

- 15

It seems a little odd that we assume, without proof, that this function exists and then sort out its properties. How do we know such a function exists? Does it always exist? Are there conditions on this? Isn't it a little shady to be discussing properties of something if we haven't proved yet that it exists?

On the other hand, once we complete the derivation, it seems clear to me that a function which satisfies the Euler Lagrange equation will be a stationary function. I think.

I'm still left feeling uncomfortable however about this. Is there some outside proof which shows that this function must exist?

I shoud give the caveat that I have only seen this derivation in physics books, I don't own any math books on calculus of variations