Jochen Denzler, Andreas Hinz: Catenaria vera – the true catenary. Expositiones Mathematicae 17 (1999), 117-142

We give an explicit solution of the catenary problem in a −1/r potential, including full discussion of the boundary value problem arising and of the existence question (which is more delicate than in other classical variational problems and is therefore somewhat neglected in the textbooks even for the classical catenary). Numerical examples illustrate the results. While reviewing some history, we also attempt a style that makes the discussion feasible for teaching purposes, in particular by bridging the gap between classical textbooks and the more modern tools. The appearance of the logarithmic spiral as a solution is a nice surprise in addition. Our existence proof by direct methods, enhanced with a priori estimates, generalizes to other central potentials.