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IssuesArchive of Issues2009-6pp.818-827

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N. I. Amel’kin, "On Estimates of the Balanced Gyro Drift and the Accuracy of the Magnus Formula," Mech. Solids. 44 (6), 818-827 (2009)
Year 2009 Volume 44 Number 6 Pages 818-827
DOI 10.3103/S0025654409060028
Title On Estimates of the Balanced Gyro Drift and the Accuracy of the Magnus Formula
Author(s) N. I. Amel’kin (Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudny, Moscow District, 141700 Russia, namelkin@mail.ru)
Abstract We construct efficient estimates of the balanced gyro drift due to nutation oscillations. We show that, for oscillation amplitudes not exceeding one degree and for a majority of gyro motions, the relative error in the drift rate calculations on the basis of the obtained estimates does not exceed tenths of one percent. The numerical results show that the accuracy of the Magnus formula is not worse than predicted by these estimates.
Keywords gimbal gyro, oscillations, average drift rate, Magnus formula
References
1.  K. Magnus, Kreisel. Theorie und Anwendungen (Springer, Berlin, 1971; Mir, Moscow, 1974).
2.  Kh. L. Smolitskii, "On the Motion of a Gyro in Gimbal Mount," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 2, 17-22 (1966) [Mech. Solids (Engl. Transl.)].
3.  A. I. Kobrin and Yu. G. Martynenko, "On a Method for Constructing Asymptotic Solution of the Problem of Motion of a Gyro in Gimbal Mount," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 3, 40-47 (1971) [Mech. Solids (Engl. Transl.)].
4.  A. D. Bryuno, Local Method for Nonlinear Analysis of Differential Equations (Nauka, Moscow, 1979) [in Russian].
5.  V. Ph. Zhuravlev, "To the Problem of Estimates of the Magnus Effect," Dokl. Akad. Nauk SSSR 226 (3), 541-543 (1976).
6.  V. Ph. Zhuravlev and D. M. Klimov, Applied Methods in Vibration Theory (Nauka, Moscow, 1988) [in Russian].
7.  V. V. Rumiantsev, "On the Stability of Motion of a Gyroscope on Gimbals," Prikl. Mat. Mekh. 22 (3), 374-378 (1958) [J. Appl. Math. Mech. (Engl. Transl.) 22 (3), 513-520 (1958)].
Received 29 November 2007
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