This paper reports on findings relating to catenaries since the publication in Expositiones Mathematicae of Denzler and Hinz’s pioneering 1999 paper, Catenaria Vera – the True Catenary. New governing differential equations and explicit solutions are derived for the catenary in positive and negative radial potentials with physical constants incorporated in the derivations. In keeping with precedent by Denzler and Hinz, a measure of historical perspective is offered as homage to Gottfried Wilhelm Leibniz, Christiaan Huygens and Johann Bernoulli, the original first-solvers of the catenary.

本文报道了自登哲勒的《数学博览会》发表以来与接触网有关的发现，以及辛兹（Hinz）在1999年发表的开创性论文《接触网-真正的接触网》。在正向和负向径向电势中，为悬链线导出了新的控制微分方程和显式解，并在推导中合并了物理常数。根据登哲勒（Denzler）和欣兹（Hinz）的先例，向悬链线的最初解决者戈特弗里德·威廉·莱布尼兹（Gottfried Wilhelm Leibniz），克里斯蒂安·惠更斯（Christiaan Huygens）和约翰·伯努利（Johann Bernoulli）致以一定的历史观点。