What are the applications of Euler-Lagrange equations?

[MidnightR]

Below is the question:

[PLAIN]http://img706.imageshack.us/img706/7549/42541832.jpg

I don't even know where to start. there's nothing about this topic in my notes & I can't remember doing it before. I've tried searching for the key words but that didn't help much.

Does anyone have any links or suggestions as to how to start the question?

Thanks

 

[radou]

The keywords in the brackets are a good point to start - it is fundamental to classical mechanics that the Euler-Lagrange equations are equivalent to the action integral having a stationary value.

 

[MidnightR]

The keywords in the brackets are a good point to start - it is fundamental to classical mechanics that the Euler-Lagrange equations are equivalent to the action integral having a stationary value.

Hmm I've done more reading, the differential equation I want is

dL/dx - d/dt[dL/dxdot] = 0

I believe? That gives the functional a stationary value... (ie stationary point, I'm guessing that's what extremal means)

Just seems a little silly that all I have to do is state a DE...

 

[radou]

Yes, it seems like a basic theoretical question.

The equation you wrote down is the Euler Lagrange equation. Its solution are the functions for which the action functional is stationary.