Translation and interpretation of Michael Sadowsky's paper "Theory of elastically bendable inextensible bands with applications to the M\"obius band"

TL;DR

This paper provides a translation and modern interpretation of Sadowsky's 1930 work on the theory of elastically bendable, inextensible bands, with applications to the Möbius band, including recent numerical simulation insights.

Contribution

It offers the first English translation of Sadowsky's foundational paper and adds a contemporary interpretation with numerical simulation figures.

Findings

Enhanced understanding of elastic bands' theory

Application to Möbius band geometry

Numerical simulations supporting theoretical insights

Abstract

This article is a translation of Michael Sadowsky's original paper "Theorie der elastisch biegsamen undehnbaren B\"ander mit Anwendungen auf das M\"obiussche Band" in 3. internationaler Kongress f\"ur technische Mechanik, Stockholm, 1930. The translation is augmented by an Appendix containing an interpretation of the last section of Sadowsky's original paper including figures generated from recent numerical simulations.