School of Physics Nonlinear Science & Mathematical Physics Seminar: Prof. Andy Ruina, Cornell University

Two classes of (interesting, at least to me) physical behavior follow from the impossibility of integrating some formulas that involve derivatives. First, systems with wheels or ice skates can be conservative yet have asymptotic stability. This is relevant to braking cars, flying arrows and the balance of skateboards and bicycles. Second, is the well known possibility that a system with zero angular momentum can, by appropriate deformations, rotate without any external torque. This effect explains how a cat that is dropped while upside down can turn over and of how various gymnastic maneuvers are performed. Both rolling contact and constancy of angular momentum are examples of the "non-integrability" of a "non-holonomic" equation. There are various simple demonstrations of these phenomena that can go bad. Cars can crash, bikes fall over and, in terrestrial experiments, various effects can swamp that which one wants to demonstrate. The talk describes the basic theory and then a collection of simple experiments that fail various ways for various reasons.