Skip to main content
SpringerLink
Log in

On stability of motion of a symmetric body placed on a vibrating base

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We consider the problem of stabilization of a symmetric solid body rotating about a fixed point and show that its unstable states can be stabilized by vertical vibration.

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. N. N. Bogolyubov, “Theory of perturbations in nonlinear mechanics,”Sb. Tr. Inst. Stroit. Mekh. Ukr. SSR,14, 9–34 (1950).

    Google Scholar 

  2. P. L. Kapitsa, “Dynamical stability of a pendulum with oscillating suspension,”Zh. Eksp. Teor. Fiz.,21, No. 5, 588–597 (1951).

    Google Scholar 

  3. V. N. Chelomei, “On the possibility of improving the characteristics of stability of elastic systems by vibrations,”Dokl. Akad. Nauk SSSR,110, No. 3, 345–347 (1956).

    Google Scholar 

  4. T. G. Strizhak,Averaging Method in the Problems of Mechanics [in Russian], Vyshcha Shkola, Kiev-Donetsk (1982).

    Google Scholar 

  5. A. Erdélyi, “Über die kleinen Schwingungen eines Pendels mit oszilierenden Aufhängepunkt,”Z. Angew. Math. Mech.,14, 235–247 (1934).

    Google Scholar 

  6. Ya. G. Panovko and I. I. Gubanova,Stability and Oscillations of Elastic Systems [in Russian], Nauka, Moscow (1987).

    Google Scholar 

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

    Google Scholar 

  8. B. V. Bulgakov,Applied Theory of Gyroscopes [in Russian], Moscow University, Moscow (1976).

    Google Scholar 

  9. V. N. Koshlyakov,Problems of the Dynamics of Solid Body and Applied Theory of Gyroscopes. Analytic Methods [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  10. N. G. Chetaev,Stability of Motion [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  11. R. Bellman,Stability Theory of Differential Equations, McGraw-Hill, New York (1953).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    V. N. Koshlyakov

Authors
  1. V. N. Koshlyakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 12, pp. 1661–1666, December, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koshlyakov, V.N. On stability of motion of a symmetric body placed on a vibrating base. Ukr Math J 47, 1898–1904 (1995). https://doi.org/10.1007/BF01060963

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01060963

Keywords

Search

Navigation