Modelling of a flexible elastic tether for the motorised momentum exchange tether concept

This paper presents a more complete flexural model for the Motorised Momentum Exchange Tether (MMET) concept. A continuous sub-span string-like model is taken in which the tether sub-span is flexible and elastic, thereby allowing three dimensional displacements of the motorised tether. The spatio-temporal coordinates u(x,t) and v(x,t) are transformed to modal coordinates before applying Lagrange's equations by means of the Bubnov-Galerkin procedure. This allows the linear modes in the tether to be pre-selected. The equations of motion contain inertial nonlinearities of cubic order, and these show the potential for intricate intermodal coupling effects. The physical assumptions required to model the MMET tether analytically in this way are summarised, and the most interesting differences between rigid body models discussed by Ziegler [2], and this new flexible model, are highlighted and discussed.