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.
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机译：它在1985年由Acad显示。 V. zhuravlev以球形对称在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度成比例。效果是三维，因此，它可能被用作空间惯性旋转传感器的概念。此外，这些效果在声学，地球物理和天体物理学中都很重要。定性地研究了效果，而不指定坐标系和尺度因子的确定。在本文中，在球形坐标中考虑了振动模式进样的效果。基于厚同位素球的运动的精确解，将其在球形贝塞尔和相关的传说中的功能中获得，研究了旋转的效果，并确定了球体的不同振动模式的缩放因子，球状和扭转。根据振动模式及其数量的性质来计算相应的缩放因子。为了实现三个轴传感器，需要实现三个正交的球形坐标系。考虑了振动球体对称体的控制元素，并讨论了可能的缺陷。
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