Whirling skirts and rotating cones

Whirling skirts and rotating cones

Steady, dihedrally symmetric patterns with sharp peaks may be observed on a spinning skirt, lagging behind the material flow of the fabric. These qualitative features are captured with a minimal model of traveling waves on an inextensible, flexible, generalized-conical sheet rotating about a fixed axis. Conservation laws are used to reduce the dynamics to a quadrature describing a particle in a...

Twirling and whirling: viscous dynamics of rotating elastic filaments.

Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by coupled PDEs for twist and bend evolution. Analytical and nu...

Twirling and Whirling: Viscous Dynamics of Rotating Elastica

Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by a novel pair of coupled PDEs for twist and bend evolution. A...

Bolivian Wrestlers in Skirts

Bifurcation and Hunting Phenomena of Rotating Speed in a Flexible Rotor System Caused by Whirling Motion

This paper presents the discussion of experimental results and numerical simulation of nonlinear phenomena in a flexible rotor system under mechanical resonance. The whirling motion of the first flexural mode of the rotor causes the hunting of its rotating speed. Hysteretic jump phenomena exist between the charge and the discharge of the rotation. It is shown that the quasi-periodicity of the w...