Variational Calculus: Euler-Lagrange vs. Lagrange's Equation of Motion

[babtridge]

Could someone please direct me to a good web page or comment on the main difference between the euler lagrange eqn and lagranges eqn of motion. I'm struggling to differentiate between the two...
Also, I'm struggling to grasp the concept of Lagrange density - when does one introduce this into the action integral?

Cheers

 

[dextercioby]

Well,technically,they are the same bunch of equations.The names are confusing.It would be fair,if the general ones,which don't have anything to do with physics,Lagrangians and lagrangian actions be called :"Euler's equations".

And the ones who do have everything to do with physics:"Lagrange's equations".

Daniel.

P.S.The Lagrangian density is the volumic density of lagrangian.Thay appear once people introduce the concept of (classical) field.