Analysis Seminar

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Vibrodynamics of constrained mechanical systems

Speaker: Theodore Drivas, Stony Brook University

Location: Warren Weaver Hall 1302

Date: Thursday, April 3, 2025, 11 a.m.

Synopsis:

We study the effect of rapid vibration of constraining surfaces of arbitrary codimension on a confined mechanical particle. The slow dynamics experience an effective potential force coming from the geometry of the vibrating surface, which can introduce new equilibria and change stability character of existing ones. A classical example is Kapitza's stabilization of the inverted pendulum with a vibrating pivot. After developing this formalism for finite dimensional systems, we generalize to infinite dimensions by analogy and study the resulting vibrogenic forces for inextensible threads and incompressible fluids. The thread effectively becomes elastic, and the fluid evolves as a variant of the incompressible inhomogeneous system. This is joint work with D. Glukhovskiy.