Skip to main content
SpringerLink
Log in

Stability analysis of gyroscopic systems with integral correction

  • Published:
International Applied Mechanics Aims and scope

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

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. A. Agafonov, “Stability and motion stabilization of nonconservative mechanical systems,” J. Math. Sci., 112, No. 5, 4419–4497 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  2. V. V. Bolotin, Nonconservative Problems in the Theory of Elastic Stability [in Russian], Fizmatgiz, Moscow (1961).

    Google Scholar 

  3. B. V. Bulgakov, Applied Theory of Gyroscopes [in Russian], Izd. Mosk. Univ., Moscow (1976).

    Google Scholar 

  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. V. N. Koshlyakov, “Structural transformations of nonconservative systems,” Prikl. Mat. Mekh., 64, No. 6, 933–941 (2000).

    MATH  MathSciNet  Google Scholar 

  6. A. M. Lyapunov, The General Problem of the Stability of Motion, Taylor & Francis, London (1992).

    MATH  Google Scholar 

  7. D. R. Merkin, An Introduction to the Theory of Stability of Motion [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  8. I. I. Metelitsyn, “On gyroscopic stabilization,” Dokl. AN SSSR, 86, No. 1, 31–34 (1952).

    Google Scholar 

  9. Yu. I. Neimark, “On the distribution of roots of polynomials,” Dokl. AN SSSR, 58, No. 3, 357–360 (1947).

    MathSciNet  Google Scholar 

  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).

  11. N. G. Chetaev, Stability of Motion: Studies on Analytic Mechanics [in Russian], Izd. AN SSSR, Moscow (1962).

    Google Scholar 

  12. E. I. Jury, “Innor’s approach to some problems of system theory,” IEEE Trans. Autom. Contr., AC-16, No. 3, 233–240 (1971).

    Article  Google Scholar 

  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. A. A. Martynyuk and A. C. Khoroshun, “On parametric asymptotic stability of large-scale systems,” Int. Appl. Måch., 44, No. 5, 565–574 (2008).

    Article  Google Scholar 

  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).

    Article  Google Scholar 

  16. P. S. Müller, Stabilität und Matrizen, Springer, Berlin–New York (1977).

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkovskaya St., Kyiv, Ukraine, 01601

    V. A. Storozhenko

Authors
  1. V. A. Storozhenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. A. Storozhenko.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 45, No. 11, pp. 122–132, November 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Storozhenko, V.A. Stability analysis of gyroscopic systems with integral correction. Int Appl Mech 45, 1248–1256 (2009). https://doi.org/10.1007/s10778-010-0266-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-010-0266-8

Keywords

Search

Navigation