Classical Mechanics (Kibble & Berkshire) · Problem 13.12
Hamilton's equations and phase space — T.W.B. Kibble, F.H. Berkshire
Physics — Mechanics · hamiltons-principle
Problem
A particle is constrained to move over a smooth fixed surface under no forces other than the force of constraint. By using Hamilton's principle and energy conservation, show that the path of the particle must be a geodesic of the surface. (The term geodesic has been extended here to mean those paths that make the length functional stationary).