### 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.