Skip to main content
SpringerLink
Log in

Works on gyroscope theory in the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR

  • Published:
Ukrainian Mathematical Journal Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature cited

  1. A. Yu. Ishlinskii, Mechanics of Special Gyroscopic Systems [in Russian], Izd. AN UkrSSR, Kiev (1952).

    Google Scholar 

  2. A. Yu. Ishlinskii, “Mutual rotation of two stabilized platforms during rolling of a ship,” Priborostr., No. 2 (1944).

  3. A. Yu. Ishlinskii, “Geometry of two bi-Cardan systems,” Priborostr., No. 3 (1944).

  4. A. Yu. Ishlinskii, “Errors during the simultaneous operation of Cardan suspensions of different systems,” Priborostr., No. 1 (1945).

  5. A. Yu. Ishlinskii, “Two remarks on the theory of rocket motion,” Dokl. Akad. Nauk SSSR,53, No. 7 (1946).

  6. A. Yu. Ishlinskii, “Rolling and pitching and the change of course during rolling of the ship about an arbitrarily orientated axis,” Priborostr., Nos. 4–5 (1944).

  7. A. Yu. Ishlinskii, Mechanics of Gyroscopic Systems [in Russian], Izd. AN SSSR, Moscow (1963).

    Google Scholar 

  8. A. Yu. Ishlinskii (O. Yu. Ishlins'kyy), “Bending of a box-frame fixed at four points,” Prikl. Mekh.,3, No. 3 (1957).

  9. A. Yu. Ishlinskii (O. Yu. Ishlins'kyy), “Reference data on the deformation of elements of a Cardan suspension,” Prikl. Mekh.,3, No. 1, 105–108 (1957).

    Google Scholar 

  10. A. Yu. Ishlinskii (O. Yu. Ishlins'kyy), “Damping in highly-accelerated motion,” Prikl. Mekh.,3, No. 2 (1957).

  11. O. F. Boichuk (O. P. Boychuk), “Stability and self-oscillations of a nonlinear stabilization system,” Dokl. Akad. Nauk URSR, No. 10 (1964).

  12. V. A. Storozhenko, “Application of the energy method to the investigation of the motion of some oscillatory systems,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3 (1966).

  13. A. Yu. Ishlinskii, “Relative equilibrium of a physical pendulum with a moving point of support,” Prikl. Matem. Tekh.,20, No. 3 (1956).

  14. A. Yu. Ishlinskii, “On the theory of the gyrohorizoncompass,” Prikl. Matem. Mekh.,20, No. 4, 487–499 (1956).

    Google Scholar 

  15. A. Yu. Ishlinskii, “On the theory of the gyroscopic pendulum,” Prikl. Matem. Mekh.,21, No. 1 (1957).

  16. A. Yu. Ishlinskii, “Theory of the double-gyro vertical,” Prikl. Matem. Mekh.,21, No. 2, 175–183 (1957).

    Google Scholar 

  17. V. P. Vasilenko, V. N. Koshlyakov, and M. A. Shif, “On the theory of the corrected gyrohorizon compass,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5 (1967).

  18. O. F. Boichuk, “General scheme of calculating the errors of uncorrected inertial systems,” Prikl. Mekh.,16, No. 9 (1971).

  19. O. F. Boichuk, “Oscillations of the stabilized platform of an inertial navigation system,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 1 (1969).

  20. O. F. Boichuk and V. N. Kalinovich, “Theory of an inertial navigation system constructed on the basis of a gyrohorizon compass,” in: Mathematical Physics [in Russian], Part 8, Naukova Dumka, Kiev (1970).

    Google Scholar 

  21. V. A. Storozhenko (V. O. Storozhenko), “Investigation of the natural oscillations of an inertial vertical with a nonlinear correction,” Dokl. Akad. Nauk URSR, Ser. A, No. 5 (1967).

  22. V. A. Storozhenko and M. E. Temchenko, “Application of the theory of finite rotations to the problem of the autonomic determination of the locus coordinates of a moving body,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3 (1971).

  23. R. Grammel, The Gyroscope, Its Theory and Applications, Springer, Berlin (1950).

    Google Scholar 

  24. V. N. Koshlyakov, Theory of Gyrocompasses [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  25. V. P. Vasilenko and M. E. Temchenko, “Theory of a gyrocompass on a torsional suspension,” Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 1 (1966).

  26. V. P. Vasilenko, A. N. Kostritsa, and V. N. Koshlyakov, “Theory of a one-rotor corrected gyrocompass,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2 (1967).

  27. V. P. Vasilenko and S. M. Onishchenko, “On the theory of a corrected two-rotor gyrocompass,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4 (1971).

  28. V. P. Vasilenko and A. P. Yanishevskii, “The small-parameter method in gyrocompass theory,” Ukr. Matem. Zh.,32, No. 1 (1971).

  29. A. N. Polishchuk, “Stability of one-rotor corrected gyrocompasses,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 6 (1970).

  30. S. M. Onishchenko, “Use of the averaging method in applied gyrocompass theory,” Prikl. Mekh.,5, No. 5, 89–93 (1969).

    Google Scholar 

  31. S. M. Onishchenko, “Nonasymptotic stability of the unperturbed motion of two-rotor gyrocompasses,” Prikl. Mekh., 6, No. 1 (1970).

    Google Scholar 

  32. S. M. Onishchenko and S. P. SosnitsKii, “Reduceability of the equations of motion of two-rotor gyrocompasses to canonical form,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5 (1970).

  33. S. M. Onishchenko, “Stability of gyrocompasses to circulation, ” Dokl. Akad. Nauk URSR, Ser. A, No. 3 (1967).

  34. S. M. Onishchenko, “Stability of a nonspatial gyroscope in a finite time-interval,” Dokl. Akad. Nauk URSR, Ser. A, No. 2, 138–141 (1969).

    Google Scholar 

  35. S. P. Sosnitskii, “Combination resonance of a two-rotor gyrocompass,” Prikl. Mekh.,7, No. 3, 125–129 (1970).

    Google Scholar 

  36. S. P. Sosnitskii, “Investigation of the stability of the gyrohorizon compass,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3 (1971).

  37. A. Yu. Ishlinskii, “Theory of compound systems of gyroscopic stabilization,” Prikl. Matem. Mekh., 22, No. 3 (1958).

  38. A. Yu. Ishlinskii, “Equations of the precessional theory of gyroscopes in the form of the equations of motion of the pole in the phase plane,” Prikl. Matem. Mekh.,23, No. 5, 801–809 (1959).

    Google Scholar 

  39. A. Yu. Ishlinskii, “Mechanical analog of a gyroscopic stabilizer with elastic pliancy of its elements,” Dokl. Akad. Nauk SSSR,161, No. 6 (1965).

  40. O. F. Boichuk (O. P. Boychuk) and M. E. Temchenko, “Theory of a triaxial gyroscopic stabilizer,” Avtomatika, No. 3, 11–23 (1959).

    Google Scholar 

  41. O. F. Boichuk (O. P. Boychuk) and M. E. Temchenko, “Means of eliminating ballistic deviations of a triaxial gyroscopic stabilizer,” Avtomatika, No. 2, 44–52 (1961).

    Google Scholar 

  42. O. F. Boichuk (O. P. Boychuk), “Precessional theory of a Kinematically imperfect gyroscopic stabilizer,” Visnyk Kyyivs'k. Derzh. Univ.,2, No. 5 (1962).

  43. A. Yu. Ishlinskii, “Equations of the problem of determining the position of a moving object by means of gyroscopes and accelerometers,” Prikl. Matem. Mekh.,21, No. 6 (1957).

  44. A. Yu. Ishlinskii, “Autonomic determination of the position of a moving object by means of a spatial gyrocompass, directional gyroscope and integrating device,” Prikl. Matem. Mekh.,23, No. 1, 58–63 (1959).

    Google Scholar 

  45. O. F. Boichuk, “Question of the autonomic determination of coordinates,” Prikl. Mekh.,2, No. 4 (1966).

  46. O. F. Boichuk and V. N. Kalinovich (O. P. Boychuk and V. M. Kalynovych), “Errors of an inertial navigation system with a gyrohorizon compass and directional gyroscope,” Dokl. Akad. Nauk URSR, Ser. A, No. 11 (1969).

  47. O. F. Boichuk (O. P. Boychuk), “Method of equivalent rotations in the kinematics of inertial. systems,” Dokl. Akad. Nauk URSR, Ser. A, No. 7 (1972).

  48. O. F. Boichuk (O. P. Boychuk), “Errors of a system of autonomic determination of the coordinates of a moving object with dry friction in the accelerometers,” Dokl. Akad. Nauk URSR, Ser. A, No. 7 (1970).

  49. V. N. Kalinovich (V. M. Kalynovych), “Modifications of an inertial navigation system consisting of gyrohorizon compass, directional gyroscope and computing-solving unit,” Dokl. Akad. Nauk URSR, No. 5 (1962).

  50. V. N. Kalinovich (V. M. Kalynovych), “Effect of nonorthogonality of the accelerometers on the operation of an inertial navigation system,” Dokl. Akad. Nauk URSR, Ser. A, No. 9 (1968).

  51. V. N. Kalinovich (V. M. Kalynovych), “Errors in an autonomic determination system due to free oscillations of the platform,” Dokl. Akad. Nauk URSR, No. 11 (1963).

  52. V. N. Kalinovich (V. M. Kalynovych), “Finding the first integral of the equations of inertial navigation,” Dokl. Akad. Nauk URSR, Ser. A, No. 8 (1968).

  53. V. N. Kalinovich (V. M. Kalynovych), “Effect of dry friction in the axle bearings of the casings of the gyroscopes of a gyrohorizon compass on the nature of its motion and on the accuracy of autonomic determination,” Dokl. Akad. Nauk URSR, No. 6, 735–739 (1960).

    Google Scholar 

  54. V. N. Kalinovich (V. M. Kalynovych), “Equations of an inertial navigation system with the platform orientated in a geographical system of coordinates,” Dokl. Akad. Nauk URSR, No. 1 (1966).

  55. V. N. Koshlyakov, “Use of the Rodriguez-Hamilton and Cayley-Klein parameters in applied gyroscope theory,” Prikl. Matem. Mekh.,29, No. 4, 863–867 (1965).

    Google Scholar 

  56. V. P. Vasilenko, V. N. Kalinovich, and V. N. Koshlyakov, “Structure of a gyrocompass inertial system,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4 (1969).

  57. V. N. Koshlyakov, Yu. B. Lyusin, M. E. Temchenko, I. Sh. Shul'man, and V. A. Storozhenko, “Stability of the solutions of the system of differential equations of the problem of the autonomic determination of the coordinates of a moving object,” Dokl. Akad. Nauk SSSR,179, No. 1 (1968).

  58. V. A. Storozhenko (V. O. Storozhenko), “Effect of the zone of insensitivity of the moment sensor on the operation of a uniaxial system of autonomic determination of the position of a moving object,” Dokl. Akad. Nauk URSR, No. 7 (1964).

  59. V. A. Storozhenko (V. O. Storozhenko), “Effect of viscous friction on the stability of an inertial vertical,” Dokl. Akad. Nauk URSR, Ser. A, No. 2 (1967).

  60. V. A. Storozhenko, “Autocompensation of dry friction in accelerometers by means of forced rotation,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3 (1971).

  61. V. A. Storozhenko and M. E. Temchenko, “Problem of the autonomic determination of the position of a moving object in the polar regions,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5 (1971).

  62. O. F. Boichuk (O. P. Boychuk).“Solution of the equations of the errors of autonomic determination of coordinates,” Dokl. Akad. Nauk URSR, Ser. A, No. 10 (1968).

  63. V. N. Kalinovich (V. M. Kalynovych), “Errors of autonomic determination due to inaccurate introduction of the initial conditions for the coordinates,” Dokl. Akad, Nauk URSR, Ser. A, No. 6 (1969).

  64. V. N. Kalinovich (V. M. Kalynovych), “Geometrical method of determining the errors of an inertial navigation system,” Dokl. Akad. Nauk URSR, Ser. A, No. 12, 1112–1115 (1969).

    Google Scholar 

  65. V. A. Storozhenko and M. E. Temchenko, “Errors in the operation of an inertial navigation system due to incorrect feed of the initial conditions into the computing-solving unit,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4 (1967).

  66. V. A. Storozhenko (V. O. Storozhenko) and M. E. Temchenko, “Determination of the trajectory of an object using the computing-solving unit of an inertial navigation system with incorrect initial conditions,” Dokl. Akad. Nauk URSR, Ser. A, No. 10 (1967).

  67. D. M. Klimov, “Integration of the kinematic equations of an inertial navigation system,” Izv. VUZ, Priborostr.,11, No. 7 (1968).

  68. A. Yu. Ishlinskii, “Geometrical consideration of the stability of the solution of the fundamental initial navigation problem,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3 (1968).

  69. A. Yu. Ishlinskii, Inertial Control of Ballistic Rockets [in Russian], Nauka, Moscow (1968).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Ukraine

    Yu. A. Mitropol'skii, V. N. Koshlyakov, O. F. Boichuk, V. N. Kalinovich, V. A. Storozhenko & M. E. Temchenko

Authors
  1. Yu. A. Mitropol'skii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. N. Koshlyakov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. O. F. Boichuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. V. N. Kalinovich
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. V. A. Storozhenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M. E. Temchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 25, No. 6, pp. 747–760, November–December, 1973.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mitropol'skii, Y.A., Koshlyakov, V.N., Boichuk, O.F. et al. Works on gyroscope theory in the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR. Ukr Math J 25, 618–629 (1973). https://doi.org/10.1007/BF01090794

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01090794

Search

Navigation