A comparison of various mathematical formulations and numerical solution methods for the large amplitude oscillations of a string pendulum

The large amplitude planar oscillations of a string pendulum the length of which can be varied is studied. The string is modeled as a massive one-dimensional viscoelastic continuum and the end mass as a point mass. Two different sets of equations of motion, one in a rotating frame (shadow frame) and the other in a space fixed nonrotating frame, are presented, resulting in systems of coupled nonlinear partial and ordinary differential equations. Four different solution strategies namely a Galerkin modal approach, a finite element discretization, a finite difference discretization and the use of the FE-package ANSYS are compared with each other and with experimental results.