Numerical Solution of Equilibrium Equations of Spatial Elastica

Abstract

The goal of the thesis was to simulate numerically some equilibrium equationsof spatial elastica, where the equations simulate an elastic rod that has been de-formed. The equations are taken from the article ?Analytical solution of spatialelastica and its application to kinking problem? by Y. Miyazaki and K. Kondo, [25],and these have been studied. The purpose of this thesis was to implement numer-ical discretizations for the simulation of the elastic rod and to look at numericalmethods that conserves the geometric invariants of the problem. We consider ashooting method based on second order Runge-Kutta integration for the solutionof the boundary value problem describing the elastic rod. Here we emphasize thedifference between methods that conserve the invariants exactly and those whichdo not.We also look at a multi-symplectic (or multi-Hamiltonian) formulation of theequations. We discuss numerical methods that conserve the symplecticity of theequations.