Classical Dynamics of Particles and Systems · Problem 6-14

Hamilton's Principle—Lagrangian and Hamiltonian Dynamics — Marion & Thornton

Physics — Mechanics · geodesic-conical-surface

Problem

Find the shortest path between the

(x, y, z)

points

(0, -1, 0)

and

(0, 1, 0)

on the conical surface

z = 1 - \sqrt{x^2 + y^2}

. What is the length of the path? Note: this is the shortest mountain path around a volcano.