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Whirling skirts and other conical problems
Thu 14 March 2013, 14:00
Martin Michael Muller
Equipe BioPhysStat, Universite de Lorraine, Metz
Organiser: Mark Woodhouse
ABSTRACT
A spinning skirt forms steady wave patterns which display a well-de ned dihedral symmetry with strikingly sharp features. A minimal model of an inextensible elastic rotating conical sheet is used to explain these patterns. The resulting Euler-Lagrange equations can be solved semi-analytically. Extrinsic closure of the skirt causes the solutions to be quantised.
A thin growing elastic sheet can be treated in an analogous framework. In this case growth instead of spinning induces shape changes; a planar disc deforms into a dihedrally symmetric shape. As before, semi-analytical quantised solutions are obtained and analysed.