Instabilities of Elastic and Spinning Systems: Concepts and Phenomena

Abstract

Bifurcational instabilities of increasing complexity are described, with instructive and intriguing applications. Multiple folds in the gravitational collapse of a star triggers a discussion about possible sequencing of folds. Columns, rings and a quirky floating log illustrate safe and dangerous pitchforks, with self-weight models as lecture demonstrations. Localized buckling is employed by biologists using magnetic tweezers to twist a DNA molecule and evaluate a cutting and de-knotting enzyme. Unfolding of complex bifurcations into “structurally-stable” forms by a number (codimension) of perturbations illuminates the imperfection-sensitivity of shells, and the interactive buckling of a guyed mast at a hyperbolic-umbilic catastrophe. Spinning of primitive planets introduces secondary bifurcations, while Kirchhoff’s analogy is displayed for rods and spinning tops. Examples of gyroscopic stabilization and levitation mimic the “traps” that are used in modern experimental physics to hold in place individual electrons and neutrons.