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The Hannay-Berry Phase of the Vibrating Ring Gyroscop

dc.contributor.advisorKrishnaprasad, Perinkulam S.en_US
dc.contributor.authorAndersson, Sean B.en_US
dc.contributor.authorKrishnaprasad, Perinkulam S.en_US
dc.description.abstractIn 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.en_US
dc.format.extent378149 bytes
dc.relation.ispartofseriesISR; TR 2004-4en_US
dc.relation.ispartofseriesCDCSS; TR 2004-2en_US
dc.subjectSensor-Actuator Networksen_US
dc.titleThe Hannay-Berry Phase of the Vibrating Ring Gyroscopen_US
dc.typeTechnical Reporten_US

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