Abstract
We consider a variational problem posed by Tadjbakhsh and Odeh to describe the shape of an elastic ring in the plane under uniform pressure. Regarding the ring as a smooth closed curve, the Euler-Lagrange equation reduces to a second order ordinary differential equation for the curvature with the periodic boundary condition. The asymptotic form of solutions is presented as the external pressure tends to infinity. This is done by studying a singular perturbation problem for the Euler-Lagrange equation.
Information
Published: 1 January 2007
First available in Project Euclid: 16 December 2018
zbMATH: 1143.34010
MathSciNet: MR2387266
Digital Object Identifier: 10.2969/aspm/04720709
Rights: Copyright © 2007 Mathematical Society of Japan