Space walks and Amusement Rides: Illustrations of Geometric Phase

摘要

Geometric phase in a dynamical system can be visualized as the interplay between two periodic functions which go in and out of "synch." Using illustrations of a boy's walk in space and a dizzying fun park ride, we demonstrate that in certain simple mechanical systems we can compute geometric phase directly from a symmetry—we don't even need to solve the system of differential equations. We can also use geometric phase to explain how cats （almost） always land on their feet. We conclude with an interpretation of geometric phase in terms of the geometric notions of connection and curvature.