Numerical accuracy in the integration of cable dynamics equations

Abstract

Numerical accuracy considerations for motion of a cable modeled by a chain of rigid links are investigated. Two different systems of equations which are mathematically equivalent are integrated numerically. Effects of small changes in initial conditions, integration tolerance, equation set and integration method are studied. This highly non-linear system exhibits pronounced sensitivity to small parameter changes. Solutions which initially agree closely are found to have differences which grow exponentially with time. The instabilities inherent in numerical solutions of such systems are illustrated using some simple one-degree-of-freedom problems having known exact solutions. Thestrong dependence such systems have to minor changes in physical and numerical parameters suggested that caution should be exercised regarding credibility of results predicted by long-time simulations.