Configuration of an inelastic flexible anchored cable

Abstract

Consider an inelastic, perfectly flexible cable with given external forces acting on the total length of the cable. The one end-point is fixed in the origin and the other end-point is anchored at a given point (a;b;c) in space. The resulting configuration of the cable in space can be modelled by a system of non-linear differential equations. In this article it is shown that this continuous model of the cable can always be solved in terms of an integral. In the special case of a constant (i.e. independent of the position on the cable) external force per unit length the solution is given explicitly in terms of three constants that describe the tension at the origin. These three constants are determined by the boundary values a, b and c at the other end-point, and must be calculated in general by a numerical procedure from the three resulting simultaneous non-linear equations. A few applications of this method are shown.