The True Catenary a Case Study of Modern Applied Mathematics

The problem of the catenary can be used as an illustrating example for the methods of modern applied mathematics. Starting oo from a practical problem, modelling consists in transforming this into a mathematical problem, using physical principles and empirical laws. The mathematical question is then imbedded into an appropriate theory and solved. The solutions have to be analyzed with respect to their implications for the original problem (appropriateness of the model) and numerical aspects (usefulness of the model). Algorithms have to be designed and a code has to be realized in order to respond to the needs of the practitioner. The twentieth century has witnessed a dramatic development of the mathemat