Model Development and Code Verification for Simulation of Electrodynamic Tether System

We develop a numerical model of an electrodynamic tether system composed of two finite end bodies and a flexible tether. The equations of motion of the system are presented along with two methods of discretizing the partial differential equations governing the tether vibrations. The first method is the assumed modes method in which the tether displacements are represented as series of generalized coordinates and assumed mode functions, and the second is a finite element method in which displacements and slopes at points along the tether are interpolated by shape functions. The method of manufactured solutions is used to verify that the computer codes written to simulate the system motion implement the discretization methods properly. Both the assumed modes method and the finite element method perform well for relatively low discretization levels; however, as the number of longitudinal assumed modes is increased, the mass matrix for the longitudinal vibrations becomes poorly conditioned, resulting in numerical errors that can cause the tether vibrations to improperly diverge. This behavior is not seen in the finite element method because the mass matrices for both the transverse and longitudinal vibrations are always well-conditioned.