Four-Structure Symmetry-Constrained MEMS Ring Gyroscope
Bibliographic identity from the original PDF
Printed title: A Four-Structure, Symmetry-Constrained MEMS Ring Gyroscope: Gaussian Fluctuations, Three-Torus Calibration, Solid-Torus Elasticity, and a Möbius-Type Differential Channel
Original byline: Mr.K · Archive author: Han Jae Jun
Manuscript year: 2026. Not a claim of peer-reviewed publication.
Abstract text below is excerpted or not identified; it is not presented as the complete original abstract.
Source PDF abstract and identity / 원고 출처
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Excerpt under the original “Abstract” heading
We analyze a silicon MEMS Coriolis ring gyroscope using four mathematical structures within standard continuum mechanics and classical electromagnetism: a solid-torus elastic ring subdo- main, three-torus phase calibration, electronic Möbius-type sign parity, and Gaussian thermal- noise estimation. The accumulated R01–R26 results include symmetry and calibration theorems, conditional finite-dimensional operator certificates, executed silicon finite-element models, low-Q force calculations, discrete control screens, and finite-record Allan covariance bounds. These are separated from device-level qualification. For the current candidate with target passive mechanical Q ≤1000 and provisional range 800 ≤Q ≤1000, we prove an exact first-harmonic parallel-plate force identity and the sharp minimum over independent area, modal projection and gap tolerances. The guaranteed ideal- model coefficient is 98.358773 µN, compared with 55.512680 µN of worst-corner required resonant dissipation, giving a force ratio at least 1.771825. A separate one-sided fluctuation–dissipation √ calculation yields a worst-corner thermal white-rate-noise density of 8.140185 (◦/h)/ Hz under the stated 300-K input envelope. A separately proven uniform stiffness bound gives a unique frozen-phase static equilibrium with at least 98.3411 percent tangent-stiffness margin in the ideal one-mode plate model. None of these results proves a self-consistent nonlinear periodic orbit or its physical realization. The R28 extension executes a fixed-input 3D P1/P2 mode calculation on the preliminary five- knot spoke geometry and a 65-µm width candidate, solves a finite-element thermoelastic heat equation, derives a passive resistor-loaded Q with its necessary Johnson force noise, and estab- lishes a uniform … [source excerpt; see full PDF]
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