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Resonance phenomena during nonlinear oscillations of solid bodies

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Literature Cited

  1. 1.

    V. I. Arnold, Conditions of Applicability and Estimation of Errors of the Method of Averaging for Systems which Pass through Resonances in the Process of Evolution, Dokl. AN SSSR,161, No. 1 (1956).

  2. 2.

    N. A. Artem'ev, Method of Determination of Characteristic Indices and Its Application to Two Problems of Celestial Mechanics, Izv. AN SSSR, Matematika,3, No. 2 (1944).

  3. 3.

    V. V. Beletskii, Motion of Artificial Satellite Relative to the Center of Mass [in Russian], Nauka, Moscow (1965).

  4. 4.

    N. N. Bogolyubov, On Some Statistical Methods in Mathematical Physics [in Russian], AN Ukr. SSR, Kiev (1945).

  5. 5.

    N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in The Theory of Nonlinear Oscillations [in Russian], Fizmatgiz, Moscow (1963).

  6. 6.

    V. V. Bolotin, On a Mechanical Model Describing Interaction of Parametric and Forced Oscillations, Report Moscow Energetics Inst., No. 32 (1959).

  7. 7.

    V. N. Borovenko, Rotational Motion of Space Crafts, Kosmicheskie issledovaniya,3, No. 3 (1965).

  8. 8.

    R. M. Borodina, On Nonstationary Processes in Dynamics of Free Solid Body in Transition from Regime of Rotation to Regime of Somersault, Proc. V Inter. Conference on Nonlinear Oscillations, Vol. III, Naukova dumka, Kiev (1970).

  9. 9.

    L. G. Boyarshina, Spatial Self-Oscillations of a Controlled Solid Body, Prikl. Mekhan.,8, No. 9 (1972).

  10. 10.

    J. V. Breakwell and R. Pringle Jr., Nonlinear Resonances Affecting the Stability of Gravitationally Stabilized Satellite, Express information, ser. Astronautics and rocket dynamics, No. 29 (1966).

  11. 11.

    K. G. Valeev, On Hazards of Combination Resonances, Prikl. mat. i mekh.,27, No. 6 (1963).

  12. 12.

    K. G. Valeev and R. F. Baniev, Methods of Investigation of Oscillations of Nonlinear Systems, Abstracts of papers presented at conference on problems of oscillations of mechanical systems, Naukova dumka, Kiev (1968).

  13. 13.

    K. G. Valeev and R. F. Ganiev, Investigation of Oscillations of Nonlinear Systems, Prikl. mat. i mekh.,33, No. 3 (1969).

  14. 14.

    K. G. Valeev and R. F. Ganiev, Integral Stability Criterion and its Application, Proc. V Inter. Conference on nonlinear oscillations, Vol. II, Naukova dumka, Kiev (1970).

  15. 15.

    R. F. Ganiev, Determination of Amplitudes in Oscillations of a Solid Body about the Center of Mass, Izv. AN SSSR, Mekhanika, No. 2 (1965).

  16. 16.

    R. F. Ganiev, Some Stability Problems in Nonlinear Oscillations of a Solid Body, in coll. Oscillations and Stability of Instruments, Machines, and Elements of Control System, Institute of Machine Construction, Moscow (1968).

  17. 17.

    R. F. Ganiev, On Characteristics of Spatial Instability of Motion of a Solid Body in Almost Periodic Interactions, Proc. Seminar on dynamics, Institute of Mechanics, AN Ukr. SSR (1969).

  18. 18.

    R. F. Ganiev, On Phase Portraits in Nonlinear Spatial Oscillations of a Solid Body, Proc. Seminar on Dynamics, Institute of Mechanics, AN Ukr. SSR (1969).

  19. 19.

    R. F. Ganiev and V. M. Vorob'ev, On Stability of Precessional Motion of a Gyroscope on Moveable Base, Prikl. Mekhan.,8, No. 10 (1972).

  20. 20.

    R. F. Ganiev and V. O. Kononenko, On Nonlinear Oscillations of a Solid Body Carrying a Rotating Rotor, Izv. AN SSSR, Mekhanika, No. 5 (1965).

  21. 21.

    R. F. Ganiev and V. O. Kononenko, Nonlinear Spatial Oscillations of a Solid Body on Elastic Supports, Proc. Seminar on Dynamics, Institute of Mechanics, AN Ukr. SSR (1967).

  22. 22.

    R. F. Ganiev and V. O. Kononenko, On Nonlinear Resonances in Spatial Oscillations of a Solid Body, Izv. AN SSSR, Mekhanika tverdogo tela, No. 4 (1967).

  23. 23.

    R. F. Ganiev and V. O. Konenko, Determination of Amplitudes in Spatial Oscillations of a Solid Body in the Case of Single-Frequency Resonances, Proc. Seminar on Dynamics, Institute of Mechanics, AN Ukr. SSR (1967).

  24. 24.

    R. F. Ganiev and V. O. Kononenko, Nonlinear Problems of Spatial Stability of Flying Crafts, Abstracts of papers, III All Union Congress on theoretical and applied mechanics, Moscow (1968).

  25. 25.

    R. F. Ganiev and V. O. Kononenko, Nonlinear Oscillations of a Solid Body Carrying a Rotating Rotor, Izv. AN SSSR, Mashinovedenie, No. 3 (1968).

  26. 26.

    R. F. Ganiev and V. O. Kononenko, Nonlinear Spatial Oscillations of Artifical Earth's Satellite about Center of Mass, Izv. AN SSSR, Mekhanika tverdogo tela, No. 3 (1968).

  27. 27.

    R. F. Ganiev and V. O. Kononenko, On Interrelation of Translational and Rotational Oscillatory Motions of a Solid Body in Newtonian Force Field, Izv. AN SSSR, Mekhanika tverdogo tela, No. 4 (1971).

  28. 28.

    R. F. Ganiev, V. G. Kramarev and A. P. Kononov, On Measurement of Spatial Oscillations of a Solid Body, Prikl. Mekhan.,3, No. 12 (1967).

  29. 29.

    R. F. Ganiev and A. I. Lyutyi, On Drifts in Gyroscopic Systems in Resonance Conditions, Proc. Seminar on general mechanics, Institute of Mechanics, AN Ukr. SSR, Kiev, No. 5 (1971).

  30. 30.

    R. F. Ganiev and A. I. Lyutyi, On Stability of Gyroscope on Vibrating Base in Resonance Conditions, Prikl. Mekhan.,8, No. 11 (1972).

  31. 31.

    R. F. Ganiev, A. I. Lyutyi, and V. M. Vorob'ev, On Stability of Gyroscopic Systems in Resonance Conditions, Abstract of papers, conference on oscillations of mechanical systems, Kiev, Naukova dumka (1971).

  32. 32.

    R. F. Ganiev and K. V. Frolov, On a Typical Problem of Vibration Damping in Nonlinear Formulation, Izv. AN SSSR, Mashinovedenie, No. 4 (1965).

  33. 33.

    R. F. Ganiev and K. V. Frolov, Problem of Vibration Damping of Instruments and Machines in Nonlinear Formulation, Coll. Oscillations and Stability of Machines, Instruments, and Elements of Control System, AN SSSR, Moscow (1968).

  34. 34.

    V. A. Grobov and A. V. Kudinenko, Nonlinear Spatial Oscillations of Satellite about Center of Mass in its Motion in a Circular Orbit, Prikl. Mekhan.,4, No. 10 (1968).

  35. 35.

    D. M. Klimov, Effect of Moment of Rotor around the Axis on the Drift of a Gyroscope in Cardan Suspension Mounted on a Moveable Base, Izv. AN SSSR, OTN, Mekhanika i mashinostroenie, No. 5 (1962).

  36. 36.

    D. M. Klimov, Investigation of Systematical Drifts of Astatic Gyroscope in Cardan Suspension on Rocking Base, Izv. AN SSSR, OTN, Mekhanika i mashinostroenie, No. 5 (1963).

  37. 37.

    V. I. Klimchuk, Problem of Motion of Astatic Gyroscope in Cardan Suspension on Moveable Base, Prikl. Mekhan.,2, No. 2 (1966).

  38. 38.

    M. Z. Kolovskii, On Oscillations of a Solid Body on Nonlinear Elastic Shock Absorbers, Izv. AN SSSR, OTN, Mekhanika i mashinostroenie, No. 2 (1961).

  39. 39.

    V. O. Kononenko, On Oscillations of a Solid Body about Center of Mass, Izv. AN SSSR, OTN, Mekhanika i mashinostroenie, No. 4 (1963).

  40. 40.

    V. O. Kononenko, Spatial Nonlinear Oscillations of Solid Bodies, Prikl. Mekhan.,5, No. 2 (1969).

  41. 41.

    V. O. Kononenko and R. F. Ganiev, On Effect of Vibrating Base on Stability of Oscillations of a Solid Body, Prikl. Mekhan.,3, No. 7 (1967).

  42. 42.

    V. O. Kononenko and R. F. Ganiev, Nonlinear Spatial Oscillations of Solid and Elastic Bodies, Abstracts of papers, All Union Conference on problems of oscillations of mechanical systems, Kiev, Naukova dumka (1968).

  43. 43.

    V. O. Kononenko and R. F. Ganiev, Nonlinear Resonance Phenomena in Systems with Rotating Parts, Proc. Inter. Conference on nonlinear oscillations, Vol. III, Naukova dumka, Kiev (1970).

  44. 44.

    M. Ya. Kushul', Self-Oscillations of Rotors, AN SSSR, Moscow (1963).

  45. 45.

    M. Ya. Kushul' and G. I. Anikeev, On Stability of Torsional Oscillations of Nonsymmetric Solid Body on Elastic Couplings, Coll. Oscillations and Strength under Variable Stresses, Nauka, Moscow (1965).

  46. 46.

    P. W. Likins and G. M. Wrout, Limits of Vibrations of Parametrically Resonant Satellites, Raketnaya tekhnika i kosmonavtika,7, No. 4 (1964).

  47. 47.

    Ya. L. Lunts, On Motion of a Gyroscope in Cardan Suspension Mounted on Mobile Platform, Izv. vuzov, Ser. Priborostroenie,3, No. 4 (1960).

  48. 48.

    Ya. L. Lunts, On Systematic Drifts of Gyrostabilizer in Presence of Oscillations of the Base, Izv. vuzov, Ser. Priborostroenie,7, No. 4 (1964).

  49. 49.

    Ya. L. Lunts and V. S. Slepkov, Determination of Systematic Drifts of Biaxial Gyrostabilizer in Oscillations of Gyroscopes along Axes of Precession, Izv. vuzov, Ser. Priborostroenie,11, No. 3 (1968).

  50. 50.

    A. M. Lyapunov, General Problem of Stability of Motion [in Russian], Gostekhizdat, Moscow (1950).

  51. 51.

    I. G. Malkin, Some Problems of the Theory of Nonlinear Oscillations [in Russian], GITTL, Moscow (1956).

  52. 52.

    I. G. Malkin, Theory of Stability of Motion [in Russian], Fizmatgiz, Moscow (1966).

  53. 53.

    A. P. Markeev, Stability of Stationary Rotation of Satellite on Elliptic Orbit, Kosmicheskie issledovaniya,5, No. 4 (1967).

  54. 54.

    A. P. Markeev, On Rotational Motion of Dynamically Symmetric Satellite in Elliptic Orbit, Kosmicheskie issledovaniya,5, No. 4 (1967).

  55. 55.

    A. P. Markeev, Resonance Effects and Stability of Stationary Rotations of a Satellite, Kosmicheskie issledovaniya,5, 3 (1967).

  56. 56.

    A. P. Markeev, On Stability of Canonical System with Two Degrees of Freedom in Presence of Resonance, Prikl. mat. i mekh.,32, No. 4 (1968).

  57. 57.

    J. A. Morrison, Stationary Resonance Motions of Pitch Controlled Satellite, Rocket Engineering and Cosmonautics,7, No. 6 (1968).

  58. 58.

    L. Pust, Effect of Nonlinear Characteristics of Springs on Oscillation of Bases of Machines, Proc. II All Union Conference on basic problems of theory of machines and mechanisms, Mashgiz, Moscow (1960).

  59. 59.

    A. P. Torzhevskii, Fast Rotation of Satellite around Center of Masses in Resonance Regime, Kosmicheskie issledovaniya,6, No. 1 (1968).

  60. 60.

    A. P. Torzhevskii, Motion of Turning Satellite under Action of Gravitational and Magnetic Moments, Abstracts of III All-Union conference on theoretical and applied mechanics, Moscow (1968).

  61. 61.

    D. L. Hitzl, Nonlinear oscillations of Orientation of a Satellite near Resonance, Rocket technology and cosmonautics,7, No. 6 (1969).

  62. 62.

    S. N. Shimanov, Problem of Searching Characteristic Indices of a System of Linear Differential Equations with Periodic Coefficients, Dokl. AN SSSR,109, No. 6 (1956).

  63. 63.

    S. N. Shimanov, On Search of Characteristic Indices of Systems of Linear Differential Equations with Periodic Coefficients, Prikl. mat. i mekh.,22, No. 3 (1958).

  64. 64.

    Delp Debra, Satellite Stability and Natural Frequencies in a Circular Orbit, J. of the Ast. Soc.,8, No. 1 (1961).

  65. 65.

    T. R. Kane, Altitude Stability of Earth-pointing Satellites, AIAA Journal,3, No. 4 (1965).

  66. 66.

    L. Meirovitch and F. B. Wallace, Altitude Instability Regions of a Spinning Unsymmetrical Satellite in a Circular Orbit, J. of the Aeronautical Sciences,16, No. 3 (1967).

  67. 67.

    G. Schmiedt and F. Weidenhammer, Instabilitaten gedampfter rheolinearer Swingungen, Math. Nachrichten,23, No. 4-5 (1961).

  68. 68.

    F. B. Wallace and L. Meirovitch, Altitude Instability Regions of a Spinning Symmetric Satellite in an Elliptic Orbit, Journal of the Aerospace Sciences Meeting, New York (1967).

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Additional information

Institute of Mechanics of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 8, No. 12, pp. 45–70, December, 1972.

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Ganiev, R.F. Resonance phenomena during nonlinear oscillations of solid bodies. Soviet Applied Mechanics 8, 1324–1344 (1972). https://doi.org/10.1007/BF00883530

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Keywords

  • Solid Body
  • Nonlinear Oscillation
  • Resonance Phenomenon