Translation of Michael Sadowsky's paper "An elementary proof for the existence of a developable Möbius band and the attribution of the geometric problem to a variational problem"

Abstract

This article is a translation of Michael Sadowsky's original paper "Ein elementarer Beweis für die Existenz eines abwickelbaren Möbiusschen Bandes und die Zurückführung des geometrischen Problems auf ein Variationsproblem." which appeared in Sitzungsberichte der Preussischen Akademie der Wissenschaften, physikalisch-mathematische Klasse, 17. Juli 1930, Mitteilung vom 26. Juni, 412-415. Published on September 12, 1930.

arXiv comment5 pages, 3 figures, to appear in a special volume of the Journal of Elasticity entitled "The Mechanics of Ribbons and Möbius Bands", citations of this translation should refer also to Sadowsky's original paper, as cited in the Abstract

Cited by in corpus (12)

• Variational analysis of inextensible elastic curves
• Interface geometry of binary mixtures on curved substrates
• Bistability and equilibria of creased annular sheets and strips
• Influence of material stretchability on the equilibrium shape of a Möbius band
• Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons
• Stability of boundary conditions for the Sadowsky functional
• A ribbon model for nematic polymer networks
• Nonrigidity of flat ribbons
• Computation of Unconstrained Elastic Equilibria of Complete Möbius Bands and their Stability
• Paper Moebius bands with T Patterns
• A variational model for anisotropic and naturally twisted ribbons
• Existence of optimal flat ribbons