The dynamics of pendulums on surfaces of constant curvature (Q1029254)

A pendulum problem on a surface of constant curvature is defined as a pivot point and a mass connected to the pivot by a rigid massless rod of fixed length. Assume that the pivot is constrained to move along some fixed curve with prescribed motion. The rod provides the only force on the mass in order to keep the mass a fixed distance from the rod. No torque is applied to the rod and so the acceleration of the mass is always in the direction of the rod. Then, a number of 4 theorems on the dynamics of pendulums are proved together with a conservation law involving the intrinsic angular speed.