Classical Mechanics (Kibble & Berkshire) · Problem 13.2

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

Physics — Mechanics · euler-lagrange-equation

Problem

Find the extremal of the functional

J[y] = \int_0^{\pi} (2x \sin t - \dot{x}^2)\, dt

that satisfies

x(0) = x(\pi) = 0

. Show that this extremal provides the global maximum of

J