Problems in the dynamics of shells and time-optimal control: From abseiling spiders to singing saws

Abstract

In the first part of this thesis, we study localized vibrational modes in shells with spatially varying curvature. In particular, we describe how localized modes arise in two musical instruments, the steelpan and the musical saw. We find that confined modes are caused by two distinct mechanisms in singly curved shells, like the saw, and in doubly curved shells, like the steelpan. The second part contains two applications of optimal control theory to animal (including human) behavior. The first application concerns two related uses of dragline silk by spiders: As a safety line in case of a fall, and to control their orientation in mid-air during a jump. By studying these behaviors from the perspective of control theory, we obtain insight into the sensory control of dragline release. Finally, we study a time-optimal control problem related to the Estonian sport known as kiiking. Comparison with data from kiiking athletes shows that they employ a nearly optimal strategy.