On the Modelling and Computation of Nonlinear Multibody Cable Systems

Lagrange's equations of motion are used to obtain a differential algebraic equation representing the nonlinear dynamics of cable systems approximated through the use of multibody modelling. The differential algebraic equation of index 3 is cast as an ordinary differential equation and integrated using the LSODAR software. The cable system consists of an arbitrary number of links between which restoring torques are placed to provide a damping effect. A cable car is introduced to ride upon the cable, where the initial conditions of the cable car system are determined by allowing the original cable system to fall into an equilibrium position. Graphs and animation indicate the chaotic behaviour of both multibody systems, and it is shown that the CPU time increases in a cubic nature as the number of bodies in the system increases. Finally, the accuracy of the results is investigated using a constraint compliance testing procedure.