Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution

doi:10.1088/1674-1056/21/5/050401

中国物理B ›› 2012, Vol. 21 ›› Issue (5): 50401-050401.doi: 10.1088/1674-1056/21/5/050401

Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution

樊尚春,李艳,郭占社,李晶,庄海涵

School of Instrument Science & Opto-electronics Engineering, Beihang University, Beijing 100191, China; Key Laboratory of Precision Opto-mechatronics Techonology of Ministry of Education, Beijing 100191, China; Key Laboratory of Inertial Science and Technology for National Defence, Beijing 100191, China

收稿日期:2011-06-10 修回日期:2012-04-27 出版日期:2012-04-01 发布日期:2012-04-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 60927005), the Innovation Foundation of BUAA for Ph. D. Graduates, China, and the Fundamental Research Funds for the Central Universities, China (Grant No. YWF-10-01-A17).

Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution

Fan Shang-Chun(樊尚春), Li Yan(李艳)^†, Guo Zhan-She(郭占社), Li Jing(李晶), and Zhuang Hai-Han(庄海涵)

School of Instrument Science & Opto-electronics Engineering, Beihang University, Beijing 100191, China; Key Laboratory of Precision Opto-mechatronics Techonology of Ministry of Education, Beijing 100191, China; Key Laboratory of Inertial Science and Technology for National Defence, Beijing 100191, China

Received:2011-06-10 Revised:2012-04-27 Online:2012-04-01 Published:2012-04-01
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 60927005), the Innovation Foundation of BUAA for Ph. D. Graduates, China, and the Fundamental Research Funds for the Central Universities, China (Grant No. YWF-10-01-A17).

摘要/Abstract

摘要： Dynamic characteristics of the resonant gyroscope are studied based on the Mathieu equation approximate solution in this paper. The Mathieu equation is used to analyze the parametric resonant characteristics and the approximate output of the resonant gyroscope. The method of small parameter perturbation is used to analyze the approximate solution of the Mathieu equation. The theoretical analysis and the numerical simulations show that the approximate solution of the Mathieu equation is close to the dynamic output characteristics of the resonant gyroscope. The experimental analysis shows that the theoretical curve and the experimental data processing results coincide perfectly, which means that the approximate solution of the Mathieu equation can present the dynamic output characteristic of the resonant gyroscope. The theoretical approach and the experimental results of the Mathieu equation approximate solution are obtained, which provides a reference for the robust design of the resonant gyroscope.

关键词: resonant gyroscopes, dynamic characteristics, Mathieu equation, approximate solution

Abstract: Dynamic characteristics of the resonant gyroscope are studied based on the Mathieu equation approximate solution in this paper. The Mathieu equation is used to analyze the parametric resonant characteristics and the approximate output of the resonant gyroscope. The method of small parameter perturbation is used to analyze the approximate solution of the Mathieu equation. The theoretical analysis and the numerical simulations show that the approximate solution of the Mathieu equation is close to the dynamic output characteristics of the resonant gyroscope. The experimental analysis shows that the theoretical curve and the experimental data processing results coincide perfectly, which means that the approximate solution of the Mathieu equation can present the dynamic output characteristic of the resonant gyroscope. The theoretical approach and the experimental results of the Mathieu equation approximate solution are obtained, which provides a reference for the robust design of the resonant gyroscope.

Key words: resonant gyroscopes, dynamic characteristics, Mathieu equation, approximate solution

中图分类号: (Relativistic stars: structure, stability, and oscillations)

04.40.Dg

02.30.Hq (Ordinary differential equations) 05.10.-a (Computational methods in statistical physics and nonlinear dynamics)

樊尚春, 李艳, 郭占社, 李晶, 庄海涵. Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution[J]. 中国物理B, 2012, 21(5): 50401-050401.

Fan Shang-Chun(樊尚春), Li Yan(李艳), Guo Zhan-She(郭占社), Li Jing(李晶), and Zhuang Hai-Han(庄海涵) . Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution[J]. Chin. Phys. B, 2012, 21(5): 50401-050401.

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Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution

Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution

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