Mathematics Colloquium

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Geometry of Fast Oscillations in Continuum Mechanics

Speaker: Theodore D. Drivas, Stony Brook University

Location: Warren Weaver Hall 1302

Date: Monday, November 23, 2026, 3:45 p.m.

Synopsis:

In this talk, I will describe a geometric approach to two classes of physical problems from continuum mechanics.  The first is the motion of a point mass in a steep potential well, in a situation where the mass ought to roll along the minimum set. This picture realizes D'Alembert's principle for constrained motion, with some wrinkles.  An infinite dimensional example of such motion can be found in a slightly compressible fluid.  The second problem is to determine the aggregate effect of small and fast oscillations of ideal constraints on the motion of a mass.  Kapitza's (inverted with vibrating pivot) pendulum is the prototypical example, but arbitrarily many constraints are permitted. A continuum example shows how you might keep water over oil in a bucket, if only you shake fast enough.  All of this is joint work with Daniil Glukhovskiy.