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On structural transformations of equations of perturbed motion for a certain class of dynamical systems

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Ukrainian Mathematical Journal Aims and scope

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Abstract

We consider a general method for structural transformations of one class of dynamical systems with gyroscopic forces, which enables us to remove gyroscopic terms from the original equations of perturbed motion. Without changing the qualitative properties of these equations, this method simplifies their investigation.

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References

  1. N. N. Bogolyubov, On Some Statistical Methods in Mathematical Physics [in Russian], Academy of Sciences of the Ukrainian SSR, Kiev (1945).

    Google Scholar 

  2. N. N. Bogolyubov and Yu. A. Mitropol’skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).

    MATH  Google Scholar 

  3. E. A. Grebennikov, Averaging Method in Applied Problems [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  4. V. F. Zhuravlev and D. M. Klimov, Applied Methods in Oscillation Theory [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  5. H. G. Chetaev, Stability of Motion [in Russian], Nauka, Moscow (1955).

    Google Scholar 

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

    Google Scholar 

  7. B. V. Bulgakov, “On normal coordinates,” Prikl. Mat. Mekh., 10, Issue 2, 273–290 (1946).

    MATH  MathSciNet  Google Scholar 

  8. Yu. A. Mitropol’skii, Problems of the Asymptotic Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1964).

    Google Scholar 

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

    MATH  Google Scholar 

  10. V. A. Yakubovich and V. M. Starzhinskii, Parametric Resonance in Linear Systems [in Russian], Nauka, Moscow (1987).

    MATH  Google Scholar 

  11. V. N. Koshlyakov, “On stability of motion of a symmetric body placed on a vibrating base,” Ukr. Mat. Zh., 47, No. 12, 1661–1666 (1995).

    Article  MATH  MathSciNet  Google Scholar 

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Authors
  1. V. N. Koshlyakov
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Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 4, pp. 535–539, April, 1997.

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Koshlyakov, V.N. On structural transformations of equations of perturbed motion for a certain class of dynamical systems. Ukr Math J 49, 590–594 (1997). https://doi.org/10.1007/BF02487322

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  • DOI: https://doi.org/10.1007/BF02487322

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