Classical Mechanics (Kibble & Berkshire) · Problem 13.1

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[x] = \int_1^2 \frac{\dot{x}^2}{t^3}\, dt

that satisfies

x(1) = 3

and

x(2) = 18

. Show that this extremal provides the global minimum of

J