Euler-lagrange definition slipping my mind

[Ai52487963]

I don't mean the actual definition of the Euler-Lagrange equation per-se, but rather a word definition that's slipping my mind. I remember that if you want to measure the shortest distance between two points, you have to minimize an integral of all possible paths or something. Is that thing you're minimizing called anything in particular?

Basically, I'm trying to remember from my classical mechanics class two years ago on how, when you minimize that thing, you're minimizing something that doesn't physically exist or something to that effect. I realize my description is butchering the whole formalism, but can anyone give me a simple fill in the blank here?

You minimize ______ to find the shortest distance between two points.

 

[Pere Callahan]

If I remember correctly from my theoretical mechanics class you need to minimize the action over all possible trajectories to find the "physical trajectory". And to carry out this minimization you can use the Euler-Lagrange equations.

Of course, in order to find the shortest distance between two points (what ever this is...) you need to minimize the distance. The distance between two points, however, is just a constant, so there is nothing be minimized

 

[Ai52487963]

Action! That's the word I was looking for, thanks!