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首页> 外文会议>Saint Petersburg International Conference on Integrated Navigation Systems; 20060529-31; Saint Petersburg(RU) >ON DYNAMICS AND CONTROL OF VIBRATORY GYROSCOPES WITH SPHERICAL SYMMETRY
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ON DYNAMICS AND CONTROL OF VIBRATORY GYROSCOPES WITH SPHERICAL SYMMETRY

机译：球形对称振动陀螺的动力学与控制

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摘要

It was shown in 1985 by Acad. V. Zhuravlev that the angular rate of a pure vibrating mode excited in a vibratory gyroscope with spherical symmetry is proportional to an inertial angular rate of the gyroscope. The effect is three dimensional and hence, it could be potentially used as a conception of a spatial inertial rotational sensor. Furthermore these effects are important in acoustics, geophysics and astrophysics. The effect was investigated qualitatively without specifying of a coordinate system and determination of the scale factors. In the present paper the effect of vibrating pattern precession is considered in a spherical coordinates. On the basis of exact solution of 3-D equations of motion of thick isotropic sphere, which are obtained in the spherical Bessel and the associated Legendre functions, the effects of rotation are investigated and scales factors are determined for different vibrating modes of the spherical body, spheroidal and torsional. Corresponding scales factors are calculated depending on nature of vibrating modes and their number. For realization of a three axes sensor it is necessary to realize three orthogonal spherical coordinate systems. Elements of control of vibrating spherically symmetric body are considered and possible imperfections are discussed.
机译：1985年由Acad展示。 V. Zhuravlev认为，在具有球对称性的振动陀螺仪中激发的纯振动模式的角速率与陀螺仪的惯性角速率成比例。该效应是三维的，因此可以潜在地用作空间惯性旋转传感器的概念。此外，这些效应在声学，地球物理学和天体物理学中也很重要。在不指定坐标系和确定比例因子的情况下，对效果进行了定性研究。在本文中，在球坐标系中考虑了振动模式进动的影响。根据在球形贝塞尔（Bessel）中获得的各向同性厚球形球体的3-D运动方程式及其相关的Legendre函数的精确解，研究了旋转的影响并确定了球体不同振动模式的比例因子，球形和扭转。根据振动模式的性质及其数量来计算相应的比例因子。为了实现三轴传感器，必须实现三个正交球坐标系。考虑了振动球对称体的控制要素，并讨论了可能的缺陷。

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