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V. Ph. Zhuravlev, "A generalized Foucault pendulum controlled with respect to the precession angle," Mech. Solids. 37 (5), 1-4 (2002)
Year 2002 Volume 37 Number 5 Pages 1-4
Title A generalized Foucault pendulum controlled with respect to the precession angle
Author(s) V. Ph. Zhuravlev (Moscow)
Abstract The controlled Foucault pendulum [1] free with respect to the precession angle is a gyro integrator. This means that it can be used as a sensor of the integral of the projection of the angular velocity onto the sensitive axis.

Three such integrals of three respective projections of the angular velocity onto three mutually orthogonal axes are quasi-coordinates that cannot be utilized straightforwardly for determining the angular position of an object. To that end, in practice, one usually confines oneself to small increments of the quasi-coordinates which are then utilized in Poisson's equations.

Certain advantages can be provided by a scheme in which the precession angle is constrained to be kept in a small neighborhood of a fixed value, while the information about the angular velocity is obtained by observing the control signal.

Such a gyro becomes an angular velocity sensor. When operating in such a mode, this device preserves all familiar advantages of a gyro integrator but is free from some of its disadvantages, such as, for example, a dependence of errors on the precession error.

A number of problems arise as regards the formation of algorithms for the control of the precession angle, stability analysis of the closed-loop system, and control performance. These problems are considered in the present paper.
References
1.  V. Ph. Zhuravlev, "A controlled Foucault pendulum as a model of a class of free gyros," Izv. AN. MTT [Mechanics of Solids], No. 6, 1997, pp. 27-36.
2.  J. S. Burdess and T. Wren, "The theory of a piezoelectric disc gyroscope," IEEE Trans. Aerospace and Electronic Systems, Vol. AES-22, No. 4, pp. 410-418, 1986.
Received 13 February 2001
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