@inbook{10.2307/j.ctt7rjgk.10,
ISBN = {9780691154565},
URL = {http://www.jstor.org/stable/j.ctt7rjgk.10},
abstract = {This short chapter contains a purely mechanical interpretation of the Euler-Lagrange functional as the potential energy of an imaginary spring. This interpretation makes for an almost immediate derivation of the Euler-Lagrange equations and gives a very transparent mechanical explanation of the conservation of energy. Moreover, each individual term in the Euler-Lagrange equation acquires a concrete mechanical meaning.Here is some motivation for the reader not familiar with the Euler-Lagrange equations.A basic problem of the calculus of variations is to find a functionx(t) which minimizes an integral involvingxand its derivative$\dot x$: $
\smallint _0^1 L(x(t),\dot x(t))dt, \caption{(8.1)}
$ whereLis a},
bookauthor = {MARK LEVI},
booktitle = {The Mathematical Mechanic: Using Physical Reasoning to Solve Problems},
pages = {115--119},
publisher = {Princeton University Press},
title = {THE EULER-LAGRANGE EQUATION VIA STRETCHED SPRINGS},
year = {2009}
}