Date of Award
Doctor of Philosophy (PhD)
Billiard systems, broadly speaking, may be regarded as models of mechanical systems in which rigid parts interact through elastic impulsive collision forces. When it is desired or necessary to account for linear/angular momentum exchange in collisions involving a spherical body, a type of billiard system often referred to as no-slip has been used. Previous work indicated that no-slip billiards resemble non-holonomic systems, speciﬁcally, systems consisting of a ball rolling on surface. In prior research, such connections were only observed numerically and were restricted to very special surfaces. In this thesis, it is shown that no-slip billiard and rolling systems are directly related to each other under very general conditions. Our main result shows that no-slip billiards are truly the non-holonomic counterpart to standard billiard systems. In addition, to the best of our knowledge, we use a novel from of the rolling equations, showing that these systems are a one-parameter perturbation of the geodesic equation on a Riemannian manifold. This opens up a new area of investigation in the theory of geometric dynamical systems, concerning what we call rolling ﬂows. We introduced the main concepts related to the rolling ﬂow but we leave further development for future research.
Chair and Committee
Zhao, Bowei, "Geometry and Dynamics of Rolling Systems" (2022). Arts & Sciences Electronic Theses and Dissertations. 2758.