Mark Levi: Gaussian curvature, gyroscopes and some counterintuitive phenomena in mechanics

Submitted by Tony I Garcia on

The Department of Applied Mathematics is pleased to host this series of colloquium lectures, funded in part by a generous gift from the Boeing Company. This series will bring to campus prominent applied mathematicians from around the world.

Speaker: Mark Levi

Date: April 11th, 2019, 4pm

Location: (SMI 205)

Title: Gaussian curvature, gyroscopes and some counterintuitive phenomena in mechanics

Abstract: It is a fundamental fact of nature that a changing electric field creates a magnetic field; for instance, a rotating electric dipole creates a magnetic field perpendicular to the plane of rotation. Remarkably, a superficially analogous situation arises in mechanics: a changing mechanical force field creates a magnetic-like force upon a particle, provided, however, that the change is of high frequency.

For example, a point mass placed in the gravitational field of a rapidly spinning dumbbell behaves as if it were electrically charged and in the presence of magnetic field. In this talk I will outline this result (obtained jointly with Graham Cox), and will survey some other similarly counterintuitive phenomena, explaining some of them with the help of differential geometry. In particular, I will explain how (and why) Gaussian curvature arises in the dynamics of gyroscopes, and how this connection to differential geometry simplifies the classical exposition (found in most books on mechanics, e.g., in Arnold’s Mathematical Methods of Classical Mechanics).