Modelling torsion in an elastic cable in space

When an imperfectly flexible, elastic cable is suspended in a vertical plane under the sole influence of gravity and boundary conditions involving axial twist are then applied to the endpoints of the cable, its shape extends from the original vertical plane to a three-dimensional configuration in space. The aim of this paper is to develop a mathematical model (consisting of differential equations) for the configuration of and tension in such a twisted cable. The model is solved numerically for different boundary conditions. Although the final model delivers satisfactory results for small amounts of twist (inside the elastic deformation domain of the cable), realistic bounds for the amount of twist that may be applied (before plastic deformation of the cable causes model inaccuracies) are yet unknown. However, the effect of an increase in the amount of torsion applied at the endpoints of the cable is investigated numerically. The model seems capable of capturing first points of twisting bifurcation, when so much twist is applied at the endpoints that the cable jumps from un unstable equilibrium configuration to a more stable one.