Answerer

Hi guys, I'm been disturbed by the principle of least action lately. I know how the "action integal" is mathematically defined but what I really want to know is that whether the "action integal" has any physical interpretation or representation and also the disturbing question of why for most physical frames, we had to take the minimum value(that is the least action)?

So, anyone?

Friar Bellows

Answerer, have you read the chapter in Feynman's lectures which talks about the principle of least action? It might be helpful.

Answerer

Acutally, no because his explanation always seem to be quite brief to me. Anyway, where could the principle of least action could be found? In his "six easy pieces" or "six not so easy pieces" or "six hard pieces"?

Friar Bellows

In Chapter 19 of Volume 2 of the Feynman Lectures on Physics.

Answerer

Thanks, anyway, before I go and search for that book, I hope to know whether Noether's theorem is derived from the principle of least action or not?

Feather

Noether's theorem is related to the action integral in that they both pertain to the Hamiltonian of a system. But Noether's Theorem (as I've used/seen it, anyway) is used mainly for finding constants of the motion, whereas the canonical equations (derivatives of the Hamiltonian) are/can actually be derived by invoking the principle of least action.

Feynmann's Lectures is a good place to get just about any interpretation of stock physics concepts that were around before or during his time. So it's probably a lot clearer than what I just wrote. More accurate, likely, as well.