Soviet Applied Mechanics

, Volume 21, Issue 11, pp 1117–1123 | Cite as

Qualitative analysis of independent systems with first integrals

  • N. N. Kozhukhovskii


Qualitative Analysis Independent System 
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Literature Cited

  1. 1.
    E. A. Barbashin and N. N. Krasovskii, “Stability of motion as a whole,” Dokl. Akad. Nauk SSSR,86, No. 3, 453–456 (1952).Google Scholar
  2. 2.
    V. D. Irtegov, “Steady motions of a Kovalevskii gyroscope,” in: Methods of Lyapunov Functions in the Dynamics of Nonlinear Systems [in Russian], Novosibirsk, Nauka (1983), pp. 128–149.Google Scholar
  3. 3.
    A. V. Karapetyan and V. V. Rumyantsev, “Stability of conservative and dissipative systems,” Itogi Nauki Tekh. Obshch. Mekh.,6, 3–128 (1983).Google Scholar
  4. 4.
    V. V. Kozlov, “Integrability and nonintegrability in Hamiltonian mechanics,” Usp. Mat. Nauk,38, No. 1 (229), 3–67 (1983).Google Scholar
  5. 5.
    A. M. Lyapunov, “Constant screw motions of a solid in a liquid,” in: Collected Works [in Russian], Vol. 1, Izd. AN SSSR, Moscow (1954), pp. 276–379.Google Scholar
  6. 6.
    A. A. Martynyuk, “Averaging method and the comparison principle in the engineering theory of the stability of motion,” Prikl. Mekh.,7, No. 9, 64–69 (1971).Google Scholar
  7. 7.
    A. A. Martynyuk and R. Gutovskii, Integral Inequalities and Stability of Motion [in Russian], Nauk. Dumka, Kiev (1979).Google Scholar
  8. 8.
    A. A. Martynyuk and N. N. Kozhukhovskii, “Stability of equilibrium positions of Hamiltonian systems,” Prikl. Mekh.,16, No. 12, 83–89 (1980).Google Scholar
  9. 9.
    A. A. Martynyuk and N. N. Kozhukhovskii, “Comparison method in the problem of the practical stability of systems with first integrals,” Preprint, Inst. Mat., Akad. Nauk Ukr. SSR, Kiev, No. 81. 19 (1981).Google Scholar
  10. 10.
    Yu. I. Neimark and N. A. Fufaev, “Stability of steady motions of holonomic and nonholonomic systems,” Prikl. Mat. Mekh.,30, No. 2, 236–242 (1966).Google Scholar
  11. 11.
    P. K. Rashevskii, Riemannian Geometry and Tensor Analysis [in Russian], Nauka, Moscow (1964).Google Scholar
  12. 12.
    V. N. Rubanovskii and S. Ya. Stepanov, “Routh theorem and Chetaev method of constructing a Lyapunov function from integrals of equations of motion,” Prikl. Mat. Mekh.,33, No. 5, 904–912 (1969).Google Scholar
  13. 13.
    V. N. Rubanovskii, “Bifurcation and stability of steady motions of systems with first integrals,” Zadachi Issled. Ustoichivosti Stabilizatsii Dvizhenya, No. 1, 121–200 (1975).Google Scholar
  14. 14.
    V. V. Rumyantsev, “Stability of steady motions,” Prikl. Mat. Mekh.,33, No. 5, 923–933 (1966).Google Scholar
  15. 15.
    V. V. Rumyantsev, Stability of Steady Motions of Satellites [in Russian], Izd. AN SSSR, Moscow (1967).Google Scholar
  16. 16.
    V. V. Rumyantsev, “Stability of steady motions,” Prikl. Mat. Mekh.,32, No. 3, 504–508 (1968).Google Scholar
  17. 17.
    N. Rush, P. Abbots, and M. Lowe, Direct Lyapunov Method in the Theory of Stability [Russian translation], Mir, Moscow (1980).Google Scholar
  18. 18.
    A. Ya. Savchenko, Stability of Steady Motions of Mechanical Systems [in Russian], Naukova Dumka, Kiev (1977).Google Scholar
  19. 19.
    G. M. Fikhtengol'ts, Principles of Mathematical Analysis, Vol. 1, Gostekhizdat, Moscow (1955).Google Scholar
  20. 20.
    N. G. Chetaev, Stability of Motion. Studies in Analytical Mechanics [in Russian], Izd. AN SSSR, Moscow (1962).Google Scholar
  21. 21.
    A. N. Chudnenko, Stability of Steady Motions of Hamiltonian Systems with Application to Rigid-Body Dynamics, Author's Abstract of Physical-Mathematical Sciences, Candidate Dissertation, Moscow (1980), 21 pp.Google Scholar
  22. 22.
    M. V. Berry, “Regular and irregular motion,” in: Topics in Nonlinear Dynamics, Amer. Inst. Phys., New York (1978), pp. 16–120.Google Scholar
  23. 23.
    P. Brumer, “Intermolecular energy transfer: Theories for onset of statistical behavior,” Adv. Chem. Eng.,47, 201–237 (1982).Google Scholar
  24. 24.
    M. Henon and C. Heiles, “The applicability of the third integral of motion: some numerical experiments,” Astron. J.,69, No. 1, 73–79 (1964).Google Scholar
  25. 25.
    H. Kabakow, “A perturbation procedure for weakly coupled oscillators,” Int. J. Non-Linear Mech.,7, No. 1, 125–137 (1972).Google Scholar
  26. 26.
    C. Risito, “Metodi per lo studio della stabilita di sistemi con integrali primi noti,” Ann. Mat. Purra Ad Appl.,107, No. 4, 49–94 (1975).Google Scholar
  27. 27.
    E. J. Routh, The Advanced Part of a Treatise on the Dynamics of Rigid Bodies, MacMillan and Co., London (1884).Google Scholar
  28. 28.
    E. J. Routh, A. Treatise on the Stability of a Given State of Motion, MacMillan and Co., London (1887).Google Scholar

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© Plenum Publishing Corporation 1986

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  • N. N. Kozhukhovskii

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