Bending rulers and bifurcation from a simple eigenvalue

By Miles Wheeler

December 7, 2011

Abstract

After deriving equations for the bending of an elastic rod (say a plastic ruler), we'll look for small (nearly flat) solutions. The hypotheses of the usual implicit function theorem will fail, and we'll develop another tool (Crandall Rabinowitz transversality) to get a local picture. If time permits, we'll use the same method to analyze an ODE model for elastic rods. I will not assume any background beyond multivariable calculus, linear algebra, and a tolerance of samosas. If we get to the ODE there will also be variation of constants and a little bit of functional analysis.