English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Determining the equilibrium configuration of an elastic M\"{o}bius band is achallenging problem. In recent years numerical results have been obtained byother investigators, employing first the Kirchhoff theory of rods and later thedevelopable, ruled-surface model of Wunderlich. In particular, the strategyemployed previously for the latter does not deliver an unconstrainedequilibrium configuration for the complete strip. Here we present our ownsystematic approach to the same problem for each of these models, with theultimate goal of assessing the stability of flip-symmetric configurations. Thepresence of pointwise constraints considerably complicates the latter step. Weobtain the first stability results for the problem, numerically demonstratingthat such equilibria render the total potential energy a local minimum. Alongthe way we introduce a novel regularization for the for the singular Wunderlichmodel that delivers unconstrained equilibria for the complete strip, which canthen be tested for stability.

Computation of Unconstrained Elastic Equilibria of Complete M\"{o}bius Bands and their Stability