International Applied Mechanics

, Volume 45, Issue 11, pp 1248–1256 | Cite as

Stability analysis of gyroscopic systems with integral correction

  • V. A. Storozhenko

Stability theorems for gyroscopic systems with integral correction under dissipative and nonconservative positional forces are proved. An inertial vertical gyro is used as an example to illustrate the results obtained


stability integral correction nonconservative positional force inertial vertical gyro 


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  1. 1.
    S. A. Agafonov, “Stability and motion stabilization of nonconservative mechanical systems,” J. Math. Sci., 112, No. 5, 4419–4497 (2002).MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    V. V. Bolotin, Nonconservative Problems in the Theory of Elastic Stability [in Russian], Fizmatgiz, Moscow (1961).Google Scholar
  3. 3.
    B. V. Bulgakov, Applied Theory of Gyroscopes [in Russian], Izd. Mosk. Univ., Moscow (1976).Google Scholar
  4. 4.
    A. Yu. Ishlinskii, “The equations for the positioning of a moving object with gyroscopes and accelerometers,” Prikl. Mat. Mekh., 21, No. 6, 725–739 (1995).Google Scholar
  5. 5.
    V. N. Koshlyakov, “Structural transformations of nonconservative systems,” Prikl. Mat. Mekh., 64, No. 6, 933–941 (2000).MATHMathSciNetGoogle Scholar
  6. 6.
    A. M. Lyapunov, The General Problem of the Stability of Motion, Taylor & Francis, London (1992).MATHGoogle Scholar
  7. 7.
    D. R. Merkin, An Introduction to the Theory of Stability of Motion [in Russian], Nauka, Moscow (1987).Google Scholar
  8. 8.
    I. I. Metelitsyn, “On gyroscopic stabilization,” Dokl. AN SSSR, 86, No. 1, 31–34 (1952).Google Scholar
  9. 9.
    Yu. I. Neimark, “On the distribution of roots of polynomials,” Dokl. AN SSSR, 58, No. 3, 357–360 (1947).MathSciNetGoogle Scholar
  10. 10.
    N. G. Chebotarev and N. N. Meiman, “Routh–Hurwitz problem for polynomials and integer functions,” Tr. Mat. Inst. V. A. Steklova, issue, 26, Izd. AN SSSR, Moscow–Leningrad (1949).Google Scholar
  11. 11.
    N. G. Chetaev, Stability of Motion: Studies on Analytic Mechanics [in Russian], Izd. AN SSSR, Moscow (1962).Google Scholar
  12. 12.
    E. I. Jury, “Innor’s approach to some problems of system theory,” IEEE Trans. Autom. Contr., AC-16, No. 3, 233–240 (1971).CrossRefGoogle Scholar
  13. 13.
    A. Liénard and M. N. Chipart, “Sur la signe de la partie réelle des racines d’une equation algébrique,” J. de Math. Pure et Appl., 10, No. 6, 291–346 (1914).Google Scholar
  14. 14.
    A. A. Martynyuk and A. C. Khoroshun, “On parametric asymptotic stability of large-scale systems,” Int. Appl. Måch., 44, No. 5, 565–574 (2008).CrossRefGoogle Scholar
  15. 15.
    A. A. Martynyuk and V. I. Slyn’ko, “On stability of moving autonomous mechanical systems under uncertainty,” Int. Appl. Måch., 44, No. 2, 217–227 (2008).CrossRefGoogle Scholar
  16. 16.
    P. S. Müller, Stabilität und Matrizen, Springer, Berlin–New York (1977).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Institute of MathematicsNational Academy of Sciences of UkraineKyivUkraine01601

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