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W. Poth, M. Matzl, W. Auzinger, A. Steindl, H. Troger:
"Comparison of Displacement Versus Natural Variables for the Numerical Simulation of a String Pendulum";
in: "Nonlinear Dynamics, Chaos, Control and Their Applications to Engineering Sciences", J. Balthazar, P. Goncalves, R. Brasil, I. Caldas, F. Rizatto (ed.); American Academy of Mechanics, 5, 2002, 127 - 136.

Simulation of the dynamic behavior of tethered satellite systems requires the numerical solution of a system of coupled nonlinear partial and ordinary differential equations. Due to the design of tethered satellite systems this set of equations of motion is a stiff system. To integrate this system of equations of motion numerically creates a number of problems. In order to address and solve some of these problems we consider the simpler mechanical model of the string pendulum which, however, displays all relevant features of a tethered satellite system.

In this paper a comparison of two different choices of variables and of various different choices of time integrators is presented in their influence on the efficient and accurate numerical integration of large amplitude motions of the string pendulum. Our results show that for stiff strings a description of the deformation of the string alternative to the usual description by displacements may result in a substantial increase both of accuracy and reduction of computation time. Further the proper choice of the time integrator has great influence as well.