Diskrete Dynamik am Beispiel der Atwoodschen Fallmaschine

Abstract

Simple mechanical machines like Atwood’s fall machine or genuin pulleys can be modelled in the framework of discrete mechanics without the notion of the derivative. One then arrives at difference equations the solutions of which can be calculated easily and which describe the discrete dynamics of the machines completely. Furthermore this point of view allows for deep insights into the behaviour of solutions of difference equations with respectto the conservation law for energy. If compared to physics one can view the discrete approach as discretisation procedure of equations from continuum mechanics. Then it ispossible to draw out detailed information about the order of approximation of the discrete formulation.