Nonlinear Damping of the 'Linear' Pendulum

Abstract

This study shows that typical pendulum dynamics is far from the simple equation of motion presented in textbooks. A reasonably complete damping model must use nonlinear terms in addition to the common linear viscous expression. In some cases a nonlinear substitute for assumed linear damping may be more appropriate. Even for exceptional cases where all nonlinearity may be ignored, it is shown that viscous dissipation involves subtleties that can lead to huge errors when ignored.