Analysis of 3D Pendulum sliding along a Rope

Abstract

The paper deals with a dynamic engineering problem in which a mass attached to a pendulum slides along a cable. In this problem, the pendulum mass and the cable are coupled in a model described by a system of algebraic differential equations (DAE). In this paper, the formulation of the system of differential equations modelling the problem is presented together with the determination of the initial conditions. The developed model is general in the sense of a free choice of support location, elastic rope properties, pendulum length and the inclusion of braking forces. This model can be used in the design of real rope structures such as zip lines. Many calculated values that can be measured on a real structure can be exported from the model and used for parameter calibration. In one example, the model is related to a real rope structure to illustrate and validate the model. The most important aspect of the model is its ability to estimate the safety of a ropeway quickly and easily.