Theoretical Background of Rationale for the Possibility of the Kovalevskaya Gyroscope Usage by a Three-Component Angular Velocity Meter

• Published in: Mechanics of solids Vol. 53; no. 4; pp. 361 - 369
• Main Authors: Zhuravlev, V. Ph, Plotnikov, P. K.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-07-2018; Springer Nature B.V
• Subjects: Algorithms; Angular velocity; Classical Mechanics; Computer simulation; Derivatives; Differential equations; Equations of motion; Formulas (mathematics); Mathematical analysis; Physics; Physics and Astronomy; Simulation; Velocity; spherical electrostatic suspension; self-centering; angular velocity meter; resonance; error; Kovalevskaya gyroscope; mechanical suspension
• ISSN: 0025-6544; 1934-7936
• DOI: 10.3103/S0025654418040015

The TGAVM schemes based on the Kovalevskaya gyroscope with both spherical electrostatic and spring suspensions are described. The differential equations of motion of the gyroscope are given, formulae for the output information on the three components of the angular velocity of MO. The formula for determining the third component includes the first and second derivatives on the coordinates of the translational movements of the gyroscope in the equatorial plane. To determine them, an algorithm is used to filter the interference of derivatives, based on the Luenberger identification device. The results of mathematical simulation by the derivation of the three components of the angular velocity, which confirmed the validity of the premises, are given. An analytical approximate solution of the problem is given for the self-centering mode of the gyroscope rotor and for the resonance mode. It is shown that in the second case the sensitivity of the device can be an order of magnitude higher than in the first. The approximate solution is confirmed by calculations of the third component of the angular velocity based on measuring only the coordinates of the translational movement of the gyroscope, without derivatives.