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Whirling skirts and rotating cones

Abstract : 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 three-parameter family of potentials. One parameter is associated with the stress in the sheet, another is the Noether current associated with rotational invariance and the third is a Rossby number which indicates the relative strength of Coriolis forces. Solutions are quantized by enforcing a topology appropriate to a skirt and a particular choice of dihedral symmetry. A perturbative analysis of nearly axisymmetric cones shows that Coriolis effects are essential in establishing skirt-like solutions. Fully nonlinear solutions with three-fold symmetry are presented which bear a suggestive resemblance to the observed patterns.
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Jemal Guven, J. A. Hanna, Martin Michael Mueller. Whirling skirts and rotating cones. New Journal of Physics, Institute of Physics: Open Access Journals, 2013, 15, ⟨10.1088/1367-2630/15/11/113055⟩. ⟨hal-01513425⟩

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