Classical Mechanics (Kibble & Berkshire) · Problem 13.3

Hamilton's equations and phase space — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · euler-lagrange-equation

Problem

Find the extremal of the path length functional

L[y] = \int_0^1 \left[1 + \left(\frac{dy}{dx}\right)^2\right]^{1/2} dx

that satisfies

y(0) = y(1) = 0

and show that it does provide the global minimum for

L