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Mechanics of Solids

, Volume 53, Issue 3, pp 262–270 | Cite as

On Stationary Motions of a Rigid Body under the Partial Hess Integral Existence

  • M. A. NovikovEmail author
Article
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Abstract

In the article, the Routh–Lyapunov method distinguishes stationary motions of a rigid body in the case of the existence of a partial Hess integral. In addition to already known, new families of stationary movements have been obtained.

Keywords

stationary motion partial integral bundle of integrals stationarity solution 

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References

  1. 1.
    E. J. Routh, A Treatise on the Stability of a Given State of Motion, Particulary Steadly Motion (McMillan, London, 1877).Google Scholar
  2. 2.
    E. J. Routh, The Advanced Part of a Treatiseon the Dynamics of a System of Rigid Bodies (McMillan, london, 1884).Google Scholar
  3. 3.
    A. M. Lyapunov, “On Permanent Helical Motions of a Solid in a Liquid,” in Collected Works, Vol. 1 (Izd. AN SSSR,Moscow. 1954), pp. 276–319 [in Russian].Google Scholar
  4. 4.
    P. A. Kuz’min, “Stationary Motions of a Solid Body and Their Stability in the Central Field of an Agglomeration,” in Proceedings of the Inter-University Conference on the Applied Theory of the Stability of Motions and Analytical Mechanics (Kazan, 1964), pp. 93–98 [in Russian].Google Scholar
  5. 5.
    V. D. Irtegov, “The StationaryMotion of a Balanced Solid and Their Stability in the Central Field of Forces,” Trudy Kazan. Aviats. Inst. No. 83, 3–15 (1964).Google Scholar
  6. 6.
    A. V. Karapetyan and V. V. Rumyantsev, “Stability of Conservative and Disspative Systems,” in Results of Science and Technology. General Mechanics, Vol. 6 (VINITI,Moscow, 1983), pp. 1–132 [in Russian].Google Scholar
  7. 7.
    A. V. Karapetyan and V. N. Rubanovsky, “On the Stability of Stationary Motions of Non-Conservative Mechanical Systems,” Prikl. Mat. Mekh. 50 (1), 43–49 (1986) [J. Appl.Math. Mech. (Engl. Transl.) 50 (1), 30–35 (1986)]Google Scholar
  8. 8.
    A. V. Karapetyan and V. N. Rubanovsky, “On the Modification of the Routh Theorem on the Stability of Stationary Motions of Systems with First Integrals,” in Collection of Scientific and Methodical Articles on Theoretical Mechanics, Issue 17 (Vyssh. Shkola,Moscow, 1986), pp. 91–99 [in Russian].Google Scholar
  9. 9.
    A. V. Karapetyan, Stability of Stationary Movements (Editorial,Moscow, 1998).Google Scholar
  10. 10.
    V. V. Golubev, Lectures on the Integration of the Equations of Motion of a Heavy Rigid Body near a Fixed Point (NITs “Regular. Khaotich. Din.,”Moscow, 2002) [in Russian].Google Scholar
  11. 11.
    V.D. Irtegov, InvariantManifolds of StationaryMotions and Their Stability (Nauka, Novosibirsk, 1985) [in Russian].Google Scholar

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© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Matrosov Institute for System Dynamics and Control TheorySiberian Branch of the Russian Academy of SciencesIrkutskRussia

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