Classical Mechanics (Kibble & Berkshire) · Problem 13.4
Hamilton's equations and phase space — T.W.B. Kibble, F.H. Berkshire
Physics — Mechanics · euler-lagrange-equation
Problem
An aircraft flies in the (x,z)-plane from the point (−a,0) to the point (a,0). (z=0 is ground level and the z-axis points vertically upwards.) The cost of flying the aircraft at height z is exp(−kz) per unit distance of flight, where k is a positive constant. Find the extremal for the problem of minimising the total cost of the journey. [Assume that ka<π/2.]