Nonlinear dynamics for cylindrical resonator of wave solid-state gyroscope with different number of electrostatic control sensors
The purpose of this work is to determine differences in the nonlinearities of mathematical models of dynamics and nonlinear effects of dynamics for the cylindrical resonator of wave solid–state gyroscope using a different number of electrostatic control sensors. Methods. In this article r...
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Saratov State University
2025-07-01
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| Series: | Известия высших учебных заведений: Прикладная нелинейная динамика |
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| Online Access: | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2025/07/and_2025-4_maslov-maslov_466-484.pdf |
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| author | Maslov, Alexander Anatolyevich Maslov, Dmitry Alexandrovich |
| author_facet | Maslov, Alexander Anatolyevich Maslov, Dmitry Alexandrovich |
| author_sort | Maslov, Alexander Anatolyevich |
| collection | DOAJ |
| description | The purpose of this work is to determine differences in the nonlinearities of mathematical models of dynamics and nonlinear effects of dynamics for the cylindrical resonator of wave solid–state gyroscope using a different number of electrostatic control sensors. Methods. In this article resonator oscillations nonlinearity caused by finite ratio of the small deflection of the resonator to the small gap of the electrostatic sensor is considered. To construct approximate mathematical models Tikhonov’s theorem on the passage to the limit is used and a small parameter singularly included in the system of differential equations is also taken into account. The equations of resonator dynamics are averaged by using the Krylov–Bogolyubov method. Results. The difference between the nonlinear terms in the equations of resonator dynamics with eight and sixteen control sensors is determined. It is found that nonlinear effects are more pronounced in the case of the gyroscope with sixteen control sensors. The angular drift velocity and the displacement of the resonant peak of the amplitude-frequency response are greater than in the case of eight control sensors. It is shown that in the case of eight control sensors, the angular drift velocity has a variable value and also contains a small uncompensated component. Conclusion. Mathematical models of the dynamics for the cylindrical resonator of wave solid-state gyroscope taking into account the nonlinearities caused by the excitation of oscillations by eight and sixteen electrostatic control sensors are deduced. The difference between the nonlinear effects of the resonator dynamics for wave solid-state gyroscope with different number of control sensors is shown. The angular drift velocity and the displacement of the resonant peak of the amplitude-frequency response are obtained. Conclusions about the applicability of gyroscope with eight control sensors are discussed. |
| format | Article |
| id | doaj-art-18c5de40aadb48d5965cbf7abfc0d6a3 |
| institution | Matheson Library |
| issn | 0869-6632 2542-1905 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия высших учебных заведений: Прикладная нелинейная динамика |
| spelling | doaj-art-18c5de40aadb48d5965cbf7abfc0d6a32025-07-31T03:31:27ZengSaratov State UniversityИзвестия высших учебных заведений: Прикладная нелинейная динамика0869-66322542-19052025-07-0133446648410.18500/0869-6632-003161Nonlinear dynamics for cylindrical resonator of wave solid-state gyroscope with different number of electrostatic control sensorsMaslov, Alexander Anatolyevich0Maslov, Dmitry Alexandrovich1Moscow Power Engineering Institute (MPEI), 111250 Moscow, st. Krasnokazarmennaya, 14Moscow Power Engineering Institute (MPEI), 111250 Moscow, st. Krasnokazarmennaya, 14The purpose of this work is to determine differences in the nonlinearities of mathematical models of dynamics and nonlinear effects of dynamics for the cylindrical resonator of wave solid–state gyroscope using a different number of electrostatic control sensors. Methods. In this article resonator oscillations nonlinearity caused by finite ratio of the small deflection of the resonator to the small gap of the electrostatic sensor is considered. To construct approximate mathematical models Tikhonov’s theorem on the passage to the limit is used and a small parameter singularly included in the system of differential equations is also taken into account. The equations of resonator dynamics are averaged by using the Krylov–Bogolyubov method. Results. The difference between the nonlinear terms in the equations of resonator dynamics with eight and sixteen control sensors is determined. It is found that nonlinear effects are more pronounced in the case of the gyroscope with sixteen control sensors. The angular drift velocity and the displacement of the resonant peak of the amplitude-frequency response are greater than in the case of eight control sensors. It is shown that in the case of eight control sensors, the angular drift velocity has a variable value and also contains a small uncompensated component. Conclusion. Mathematical models of the dynamics for the cylindrical resonator of wave solid-state gyroscope taking into account the nonlinearities caused by the excitation of oscillations by eight and sixteen electrostatic control sensors are deduced. The difference between the nonlinear effects of the resonator dynamics for wave solid-state gyroscope with different number of control sensors is shown. The angular drift velocity and the displacement of the resonant peak of the amplitude-frequency response are obtained. Conclusions about the applicability of gyroscope with eight control sensors are discussed.https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2025/07/and_2025-4_maslov-maslov_466-484.pdfwave solid-state gyroscopemathematical modelelectrostatic sensorscylindrical resonatornonlinear oscillationsangular drift velocity |
| spellingShingle | Maslov, Alexander Anatolyevich Maslov, Dmitry Alexandrovich Nonlinear dynamics for cylindrical resonator of wave solid-state gyroscope with different number of electrostatic control sensors Известия высших учебных заведений: Прикладная нелинейная динамика wave solid-state gyroscope mathematical model electrostatic sensors cylindrical resonator nonlinear oscillations angular drift velocity |
| title | Nonlinear dynamics for cylindrical resonator of wave solid-state gyroscope with different number of electrostatic control sensors |
| title_full | Nonlinear dynamics for cylindrical resonator of wave solid-state gyroscope with different number of electrostatic control sensors |
| title_fullStr | Nonlinear dynamics for cylindrical resonator of wave solid-state gyroscope with different number of electrostatic control sensors |
| title_full_unstemmed | Nonlinear dynamics for cylindrical resonator of wave solid-state gyroscope with different number of electrostatic control sensors |
| title_short | Nonlinear dynamics for cylindrical resonator of wave solid-state gyroscope with different number of electrostatic control sensors |
| title_sort | nonlinear dynamics for cylindrical resonator of wave solid state gyroscope with different number of electrostatic control sensors |
| topic | wave solid-state gyroscope mathematical model electrostatic sensors cylindrical resonator nonlinear oscillations angular drift velocity |
| url | https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2025/07/and_2025-4_maslov-maslov_466-484.pdf |
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