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

Abstract

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.

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References

  1. 1.

    S.V. Kovalevskaya, “Sur le probilème de la rotation d’un corps solide autour d’un point fixe,” Acta Math. 12(1), 177–232 (1889).

    MathSciNet  Article  Google Scholar 

  2. 2.

    V. Ph. Zhuravlev, “A strapdown inertial system of minimum dimension (A 3D oscillator as a complete inertial sensor),” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 5–10 (2005) [Mech. Sol. (Engl. Transl.) 40 (5), 1–5 (2005)]

  3. 3.

    V. Ph. Zhuravlev, “Strapdown Inertial Navigation System of Pendulum Type,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 6–17 (2014) [Mech. Sol. (Engl. Transl.) 49 (1), 1–10 (2014)]

  4. 4.

    V. Ph. Zhuravlev, P. K. Plotnikov, RF Patent No. 155046 “A three-component angular velocity meter based on a spherical gyroscope with electrostatic suspension,” MPK G01C 19/00 (2015)

  5. 5.

    P. K. Plotnikov, RF Patent No. 163835 “A three-component angular velocity meter based on a Kovalevskaya spherical gyroscope with an electrostatic suspension,” IPC G01C 19/00 (2016)

  6. 6.

    V. Ya. Raspopov, Micromechanical devices (Mashinostroenie, Moscow, 2007) [in Russian]

    Google Scholar 

  7. 7.

    N. T. Kuzovkov, Modal control and monitoring devices (Mashinostroenie, Moscow, 1976) [in Russian]

    Google Scholar 

  8. 8.

    N. P. Ermolin, Electric cars of low power (Vysshaya Shkola, Moscow, 1967) [in Russian]

    Google Scholar 

  9. 9.

    P. K. Plotnikov, RF Patent No. 175218 “A three-component angular velocity meter based on a Kovalevskaya gyroscope with a spring hanger,” MPK G01C 19/00 (2017)

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Correspondence to V. Ph. Zhuravlev or P. K. Plotnikov.

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Original Russian Text © V.Ph. Zhuravlev, P.K. Plotnikov, 2018, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2018, No. 4, pp. 6–15.

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Zhuravlev, V.P., Plotnikov, P.K. Theoretical Background of Rationale for the Possibility of the Kovalevskaya Gyroscope Usage by a Three-Component Angular Velocity Meter. Mech. Solids 53, 361–369 (2018). https://doi.org/10.3103/S0025654418040015

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Keywords

  • Kovalevskaya gyroscope
  • spherical electrostatic suspension
  • mechanical suspension
  • resonance
  • self-centering
  • error
  • angular velocity meter