English

Lambert W function and hanging chain revisited

Classical Physics 2019-01-23 v3

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.

Cite

@article{arxiv.1809.07047,
  title  = {Lambert W function and hanging chain revisited},
  author = {Masato Ito},
  journal= {arXiv preprint arXiv:1809.07047},
  year   = {2019}
}

Comments

11 pages, 6 figures, v2: comments added, misprints corrected, v3: corrected some typos

R2 v1 2026-06-23T04:11:10.848Z