UC San Diego

It is common knowledge that runners' ponytails will sway from side to side when running. This thesis treats the swaying phenomenon as a stability problem and discusses solution methods and results.

Geometrically nonlinear dynamical equations are derived for a flexible rod pointing vertically down and clamped at its base that is harmonically excited. Floquet theory is used to derive numerical methods to solve the problem. Results show the ponytail is always stable when it is unforced. When it is forced, it has a complex region of instability if it is treated as a flexible string, but that region becomes more limited if it is treated as a flexible rod. Adding different different types of damping can help dissipate the energy of the ponytail motion and further reduce the instability region, so that for small enough forcing the motion is stable.