Efficient tether dynamic model formulation using recursive rigid-body dynamics

Abstract

A computationally efficient discrete model for low-strain tethers used in many engineering applications is developed without the use of elastic elements. The tether is modelled using N links, with each link treated as a body of revolution where it is assumed the tether spin is negligible to the dynamics, resulting in each link having only two degrees of freedom. A recursive algorithm is developed for the dynamic equations, with the solution procedure being an order N method requiring only a 2×2 matrix inversion, resulting in approximately half the computations of the general recursive algorithm. A comparison between the proposed efficient recursive rigid-body model and a lumped point mass model shows that the absence of stiff elastic elements eliminates high-frequency axial vibrations that appear in many lumped point mass tether models. The absence of high-frequency axial vibration facilitates numerical integration of the equations, providing further improvement in computational speed.