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On the gyroscopic stabilization of conservative systems

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Abstract

We consider conservative systems with gyroscopic forces and prove theorems on stability and instability of equilibrium states for such systems. These theorems can be regarded as a generalization of the Kelvin theorem to nonlinear systems.

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References

  1. W. Thomson and P. Tait,Treatise on Natural Philosophy, Vol. 1, Clarendon Press, Oxford (1867).

    Google Scholar 

  2. N. G. Chetaev,Stability of Motion., Works on Analytical Mechanics [in Russian], Academy of Sciences of the USSR, Moscow(1962).

    Google Scholar 

  3. A. V. Karapetyan and V. V. Rumyantsev, “Stability of conservative and dissipative systems,” in:Results in Science and Technology.General Mechanics [in Russian], Vol. 6, VINITI (1983).

  4. V. V. Rumyantsev and S. P. Sosnitskii, “On the instability of equilibrium states of holonomic conservative systems,”Prikl. Mat.Mekh.,57, Issue 6, 144–166 (1993).

    MathSciNet  Google Scholar 

  5. D. R. Merkin,Gyroscopic Systems [in Russian], Nauka, Moscow 1974.

    Google Scholar 

  6. S. V. Bolotin and P. Negrini, “Asymptotic trajectories of gyroscopic systems,”Vestn. Most Univ., Ser. Mat. Mekh., No. 6, 66–75(1993).

    Google Scholar 

  7. V. V. Nemytskii and V. V. Stepanov,Qualitative Theory of Differential Equations [in Russian], Gostekhteoretizdat, Moscow-Leningrad 1949.

    Google Scholar 

  8. S. P. Sosnitskii, “On the stability of equilibrium state of natural systems,” in:Mathematical Simulation of Dynamical Processes inSystems of Bodies with Liquid [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1988), pp. 38–43.

    Google Scholar 

  9. R. Courant,Partial Differential Equations, Interscience, New York 1962.

    MATH  Google Scholar 

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Sosnyts’kyi, S.P. On the gyroscopic stabilization of conservative systems. Ukr Math J 48, 1592–1599 (1996). https://doi.org/10.1007/BF02377826

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  • DOI: https://doi.org/10.1007/BF02377826

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