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Differential Equations

, Volume 44, Issue 8, pp 1064–1071 | Cite as

On the instability of equilibria of conservative systems under typical degenerations

  • V. V. Kozlov
Ordinary Differential Equations

Abstract

We study systems of differential equations admitting first integrals with degenerate critical points. We find conditions for the instability of equilibria for the cases in which the first integral loses the minimum property. Results of general nature are used in the proof of the impossibility of gyroscopic stabilization of equilibria in conservative mechanical systems under simple typical bifurcations.

Keywords

Quadratic Form Full System Conservative System Trivial Equilibrium Nontrivial Equilibrium 
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References

  1. 1.
    Kozlov, V.V., Prikl. Mat. Mekh., 1992, vol. 56, no. 6, pp. 900–906.MathSciNetGoogle Scholar
  2. 2.
    Kozlov, V.V. and Karapetyan, A.A., Differ. Uravn., 2005, vol. 41, no. 2, pp. 186–192.MathSciNetGoogle Scholar
  3. 3.
    Poston, T. and Stewart, I., Catastrophe Theory and Its Applications, London: Pitman, 1978. Translated under the title Teoriya katastrof i ee prilozheniya, Moscow: Mir, 1980.zbMATHGoogle Scholar
  4. 4.
    Chetaev, N.G., Ustoichivost’ dvizheniya (Stability of Motion), Moscow: Gostekhizdat, 1955.Google Scholar
  5. 5.
    Koiter, W., Proc. Kon. ned. acad. wet., 1965, vol. 68, no. 3, pp. 107–113.zbMATHMathSciNetGoogle Scholar
  6. 6.
    Kozlov, V.V., Prikl. Mat. Mekh., 1986, vol. 50, no. 6, pp. 928–937.MathSciNetGoogle Scholar

Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  • V. V. Kozlov
    • 1
  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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