Stability Results for Elastic Rods with Electrostatic Self-Repulsion.
Connections for Women: Dynamical Systems
January 17,2007 10:30 AM to 11:00 AM
Speakers:
Hoffman, Kathleen
|
 |
Summary: |
A general theory of conjugate points for variational problems is presented. A similar approah is used to study the stability of an elastic rod with electrostatic sel-repusion. Results for the two-dimensional electric strut are presented. |
Abstract: |
Conjugate points, attributed to Jacobi, have been a part of the classical calculus of variations literature for over a century, however, the classical theory pertains only to the standard calculus of variations problems. In this talk, I will outline the classical methods of conjugate points in the standard setting, and generalize those results to calculus of variations problems with integral constraints. I will then present a general theory of conjugate points for variational problems satisfying generic assumptions. The motivation for this work is to determine the stability of an elastic rod with an electrostatic self-repulsion. The singular, non-local repulsive potential makes the problem remarkably different from the standard calculus of variations problem, yet a theory of conjugate points can still be used to identify minima, or stable equilibria. Results for the two-dimensional elastic strut will be presented. |
Keywords: |
Stability; Elastic rod; Calculus of variations; Conjugate points, |
|
|
