Accession Number:

ADA439267

Title:

The Hannay-Berry Phase of the Vibrating Ring Gyroscope

Descriptive Note:

Technical research rept.

Corporate Author:

MARYLAND UNIV COLLEGE PARK

Report Date:

2004-01-01

Pagination or Media Count:

26.0

Abstract:

In an analysis published in 1890, G.H. Bryan investigated the retrograde precession of the nodal points in a vibrating, rotating shell and wrote down a formula relating the rate of precession to the rate of rotation. This effect has been utilized in the design of various vibratory gyroscopes including modern MEMS-based devices. Existing analyses model these systems with a pair of harmonic oscillators coupled through the Coriolis force the normal mode method. In this work we utilize the theory of moving systems developed by Marsden, Montgomery, and Ratiu to show that the nodal precession can be understood as a geometric phase with respect to the Cartan-Hannay-Berry connection. This approach allows us to explicitly characterize the simplifications of the linearizing assumptions common to previous analyses. Our results match those of Bryan for small amplitude vibrations of the ring. We use the inherently nonlinear nature of the moving systems approach to calculate a small correction to the rate of precession of the nodes.

Subject Categories:

  • Electrical and Electronic Equipment
  • Mechanics
  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE