Lambert W function and hanging chain revisited

TL;DR

This paper explores the application of the Lambert W function to calculate the slack of a hanging chain, providing experimental and theoretical insights into a classical physics problem.

Contribution

It demonstrates how the Lambert W function can be used to express the slack of a hanging chain, linking mathematical physics with classical mechanics.

Findings

Slack can be expressed using Lambert W function or irrational functions.

Experimental validation of the theoretical model.

Highlights the mathematical richness of the slack calculation in physics.

Abstract

In classical physics, calculating the slack of a hanging chain is a problem that has attracted interest. This study aims to solve this problem through experiment and theory. When the length and distance of both the ends of a hanging chain are given, the length of slack can be expressed by a Lambert W function or an irrational function within a certain distance. Herein, a simple observation of the slack is presented. The result obtained is one of the applications of the Lambert W function in the field of physics. Though the shape of a hanging chain is well-known to be a catenary, the calculation of slack possesses richer aspects of mathematical physics.