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- W2797444996 abstract "We consider a cylindrical vibratory gyroscope comprising a not necessarliy thin-shelled annular disc with small-plate thickness, vibrating in the m -th vibration mode in-plane and in the (m + 1)st vibration mode out-of-plane. We derive the equations of motion for this contrivance in the force-to-rebalance regime and show how a slow (three-dimensional) inertial rotation rate of the gyroscope can be calculated in terms of amplitudes of vibration and other constants, all of which can be measured experimentally or calculated when the eigenfunctions and eigenvalues of the system are known. By means of a concrete example, a numerical experiment demonstrates how varying the inner radius of the annulus as well as the thickness of the plate allows us to tune the vibration frequencies of the in-plane and out-of-plane vibrations so that they coincide (for all practical purposes), eliminating any frequency split. Conventionally, an array of at least three thin-shelled hemispherical (or thin-ring) vibratory (resonator) gyroscopes is used to measure any three-dimensional rotation of the craft to which the gyroscopes are fixed. With the design proposed here, the array can be reduced to a solitary, tuned, annular thick-disc thin-plate vibratory gyroscope, reducing both size and cost." @default.
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- W2797444996 date "2018-04-01" @default.
- W2797444996 modified "2023-10-16" @default.
- W2797444996 title "An analytical theory for a three-dimensional thick-disc thin-plate vibratory gyroscope" @default.
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- W2797444996 doi "https://doi.org/10.1088/1742-6596/991/1/012072" @default.
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