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IssuesArchive of Issues2018-4pp.361-369

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Total articles in the database: 4893
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V.Ph. Zhuravlev and P.K. Plotnikov, "Theoretical Background of Rationale for the Possibility of the Kowalevskaya Gyroscope Usage by a Three-Component Angular Velocity Meter," Mech. Solids. 53 (4), 361-369 (2018)
Year 2018 Volume 53 Number 4 Pages 361-369
DOI 10.3103/S0025654418040015
Title Theoretical Background of Rationale for the Possibility of the Kowalevskaya Gyroscope Usage by a Three-Component Angular Velocity Meter
Author(s) V.Ph. Zhuravlev (Ishlinsky Institute for Problems in Mechanics RAS, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, zhurav@ipmnet.ru)
P.K. Plotnikov (Yuri Gagarin State Technical University of Saratov, 77, Politechnicheskaya street, Saratov, Russia, 410054, plotnikovpk@mail.ru)
Abstract The TGAVM schemes based on the Kowalevskaya 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.
Keywords Kowalevskaya gyroscope, spherical electrostatic suspension, mechanical suspension, resonance, self-centering, error, angular velocity meter
References
1.  S.V. Kovalevskaya, "Sur le problème de la rotation d'un corps solide autour d'un point fixe," Acta Math. 12 (1), 177-232 (1889).
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.  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.  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.  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.  V.Ya. Raspopov, Micromechanical devices (Mashinostroenie, Moscow, 2007) [in Russian]
7.  N.T. Kuzovkov, Modal control and monitoring devices (Mashinostroenie, Moscow, 1976) [in Russian]
8.  N.P. Ermolin, Electric cars of low power (Vysshaya Shkola, Moscow, 1967) [in Russian]
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)
Received 25 February 2018
Link to Fulltext https://link.springer.com/article/10.3103/S0025654418040015
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