The numerical solution of the pre-elimination models of cable configurations

摘要

The pre-elimination model of the segmented representation of cable shape consists of a system of n nonlinear algebraic equations with the orientations of the n discrete segments as unknown variables. In this paper the banded structure of the Jacobian of the system is utilised to derive an efficient Gauss-Newton solution of the nonlinear equations. It is shown that the finite difference approximation to the Jacobian can be obtained with only three vector function evaluations instead of n. It follows that the computational effort for each iterative adjustment to the approximate solution is linear in n, which means that such pre-elimination cable modelling with the associated numerical solution method is an economical way of solving cable problems.