@inbook{7debd565a648466d971daeeb25b3666a,
title = "Dynamic curling of an Elastica: a nonlinear problem in elastodynamics solved by matched asymptotic expansions",
abstract = "We consider the motion of an infinitely long, naturally curved, planar Elastica. The Elastica is flattened onto a rigid impenetrable substrate and held by its endpoints. When one of its endpoints is released, it is set off in a curling motion, which we seek to describe mathematically based on the non-linear equations of motions for planar elastic rods undergoing finite rotations. This problem is used to introduce the technique of matched asymptotic expansions. We derive a non-linear solution capturing the late dynamics, when a roll comprising many turns has formed: in this regime, the roll advances at an asymptotically constant velocity, whose selection we explain. This contribution presents an expanded version of the results published in Callan-Jones et al. (Phys. Rev. Lett. 2012).",
keywords = "Constant Curvature, Master Curve, Matched Asymptotic Expansion, Nonlinear Problem, Physical Review Letter",
author = "B. Audoly and A. Callan-Jones and Brun, \{P. T.\}",
note = "Publisher Copyright: {\textcopyright} 2015, CISM, Udine.",
year = "2015",
month = jan,
day = "1",
doi = "10.1007/978-3-7091-1877-1\_3",
language = "English",
series = "CISM International Centre for Mechanical Sciences, Courses and Lectures",
publisher = "Springer International Publishing",
pages = "137--155",
booktitle = "CISM International Centre for Mechanical Sciences, Courses and Lectures",
}