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Soviet Applied Mechanics

, Volume 11, Issue 8, pp 809–819 | Cite as

Dynamics of an absolutely rigid body with a single fixed point

  • B. N. Fradlin
  • V. M. Slyusarenko
Article
  • 33 Downloads

Keywords

Rigid Body Single Fixed Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature Cited

  1. 1.
    A. Anchev, “Stability of permanent rotations of a quasisymmetric gyrostat,” Prikl. Mat. Mekh.,28, No. 1 (1964).Google Scholar
  2. 2.
    A. Anchev, “Permanent rotations of a heavy gyrostat having a fixed point,” Prikl. Mat. Mekh.,31, No. 1 (1967).Google Scholar
  3. 3.
    G. G. Appel'rot, “The simplest cases of motion of the heavy nonsymmetric gyroscope of S. V. Kowalewski,” Matem. Sb.,27, No. 3 (1910).Google Scholar
  4. 4.
    G. G. Appel'rot, “Determination of classes of kinetically symmetric heavy gyroscopes capable of allowing simplified motions close to inertial or to some simplified motion of a Lagrange gyroscope,” Izv. Akad. Nauk SSSR, Ser. Fiz., No. 3 (1938).Google Scholar
  5. 5.
    G. G. Appel'rot, “Heavy gyroscopes that are not completely symmetric,” in: Motion of a Rigid Body about a Fixed Point [in Russian], Izd. Akad. Nauk SSSR, Moscow (1940).Google Scholar
  6. 6.
    Yu. A. Arkhangel'skii, “Unique integrals in the problem of the motion of a rigid body in a Newtonian force field,” Prikl. Mat. Mekh.,26, No. 3 (1962).Google Scholar
  7. 7.
    Yu. A. Arkhangel'skii, “A theorem of Poincaré referring to the problem of the motion of a rigid body in a Newtonian force field,” Prikl. Mat. Mekh.,26, No. 6 (1962).Google Scholar
  8. 8.
    Yu. A. Arkhangel'skii, “Algebraic integrals in the problem of the motion of a rigid body in a Newtonian force field,” Prikl. Mat. Mekh.,27, No. 1 (1963).Google Scholar
  9. 9.
    Yu. A. Arkhangel'skii, “Uniqueness of the general solution of the problem of the motion of a heavy rigid body in a Newtonian force field in one case,” Prikl. Mat. Mekh.,29, No. 3 (1965).Google Scholar
  10. 10.
    Yu. A. Arkhangel'skii, “Nonuniqueness of the general solution of the equations of motion of a rigid body about a fixed point in a Newtonian force field,” Vestn. Moskovsk. Gos. Univ., Mat. Mekh., No. 3 (1967).Google Scholar
  11. 11.
    V. V. Beletskii, “Some questions in the motion of a rigid body in a Newtonian force field,” Prikl. Mat. Mekh.,21, No. 6 (1957).Google Scholar
  12. 12.
    V. V. Beletskii, “Integrability of the equations of motion of a rigid body about a fixed point under the action of a central Newtonian force field,” Dokl. Akad. Nauk SSSR,113, No. 2 (1957).Google Scholar
  13. 13.
    V. V. Beletskii, “Libration of a satellite,” in: Artificial Earth Satellites [in Russian], No. 3, Izd. Akad. Nauk SSSR, Moscow (1959).Google Scholar
  14. 14.
    V. V. Beletskii, “A case of the motion of a rigid body about a fixed point in a Newtonian force field,” Prikl. Mat. Mekh.,27, No. 1 (1963).Google Scholar
  15. 15.
    V. V. Beletskii, “Some questions of the translational — rotational motion of a rigid body in a Newtonian force field,” in: Artificial Earth Satellites [in Russian], No. 16, Izd. Akad. Nauk SSSR, Moscow (1963).Google Scholar
  16. 16.
    A. D. Bilimovich, “Equations of motion for conservative systems with linear integrals,” Izd. Kievsk. Univ.,50, No. 10 (1910).Google Scholar
  17. 17.
    A. D. Bilimovich, “Equations of motion of a heavy rigid body about a fixed point,” Izd. Kievsk. Univ.,52, No. 9 (1912).Google Scholar
  18. 18.
    V. V. Vagner, “Geometrical interpretation of the motion of nonholonomic mechanical systems,” in: Proceedings of a Seminar on Vector and Tensor Analysis [in Russian], No. 5, Gostekhizdat, Moscow-Leningrad (1941).Google Scholar
  19. 19.
    P. V. Voronets, “Equations of motion of a rigid body rolling without slippage over a fixed prime,” Izv. Kievsk. Univ.,43, No. 1 (1903).Google Scholar
  20. 20.
    Ya. L. Geronimus, Outlines on the Works of Korifeev in Russian Mechanics [in Russian], GITTL, Moscow (1952).Google Scholar
  21. 21.
    V. V. Golubev, Lectures on the Integration of the Equations of Motion of a Heavy Rigid Body about a Fixed Point [in Russian], Gostekhizdat, Moscow (1953).Google Scholar
  22. 22.
    G. V. Gorr, “Motion of a rigid body in a Newtonian force field,” in: Mechanics of Solids [in Russian], No. 1, Naukova Dumka, Kiev (1969).Google Scholar
  23. 23.
    G. V. Gorr, “Investigation of the motion of a rigid body having a fixed point in a potential force field,” in: Mechanics of Solids [in Russian], No. 1, Naukova Dumka, Kiev (1969).Google Scholar
  24. 24.
    G. V. Gorr, “Motion of a heavy rigid body in the Goryachev-Chaplygin case,” Prikl. Mat. Mekh.,34, No. 6 (1970).Google Scholar
  25. 25.
    G. V. Gorr, “Motion of a body with cavities filled with a liquid in a potential force field,” in: Mechanics of Solids [in Russian], No. 2, Naukova Dumka, Kiev (1970).Google Scholar
  26. 26.
    G. V. Gorr, “The moving hodograph of the vector of the angular velocity in the solution of D. N. Goryachev,” in: Mechanics of Solids [in Russian], No. 3, Naukova Dumka, Kiev (1971).Google Scholar
  27. 27.
    G. V. Gorr and P. M. Burlaka, “Investigation of a particular solution of the problem of the motion of a rigid body having a fixed point in a central Newtonian force field,” in: Mechanics of Solids [in Russian], No. 3, Naukova Dumka, Kiev (1971).Google Scholar
  28. 28.
    G. V. Gorr and A. A. Ilyukhin, “Conditions constraining the parameters in a particular solution of the problem of the motion of a body filled with a liquid,” in: Mathematical Physics [in Russian], No. 5, Naukova Dumka, Kiev (1968).Google Scholar
  29. 29.
    G. V. Gorr, A. A. Ilyukhin, and V. K. Kuz'menko, “The solution of N. Kowalewski of the equations of motion of a body having a fixed point,” in: Mathematical Physics [in Russian], No. 5, Naukova Dumka, Kiev (1968).Google Scholar
  30. 30.
    G. V. Gorr and A. Ya. Savchenko, “A case of the motion of a heavy rigid body in the solution of S. V. Kowalewski,” in: Mechanics of Solids [in Russian], No. 2, Naukova Dumka, Kiev (1970).Google Scholar
  31. 31.
    G. V. Gorr and A. Ya. Savchenko, “A periodic motion in the solution of S. V. Kowalewski,” in: Mechanics of Solids [in Russian], No. 3, Naukova Dumka, Kiev (1971).Google Scholar
  32. 32.
    D. N. Goryachev, “New partial solution in the problem of the motion of a heavy rigid body about a fixed point,” Tr. Otd. Fiz. Nauk Obshch. Lyubitelei Estestvoznaniya,10, No. 1 (1899).Google Scholar
  33. 33.
    D. N. Goryachev, “Motion of a heavy rigid body about a fixed point for the case A=B=4C,” Matem. Sb.,21, No. 3 (1900).Google Scholar
  34. 34.
    D. N. Goryachev, Some General Integrals in the Problem of the Motion of a Rigid Body [in Russian], Varshava (1910).Google Scholar
  35. 35.
    D. N. Goryachev, “New cases of the motion of a rigid body about a fixed point,” Izv. Varshavsk. Univ.,3 (1915).Google Scholar
  36. 36.
    D. N. Goryachev, “New cases of the integrability of the dynamic Euler equations,” Izv. Varshavsk. Univ.,3 (1916).Google Scholar
  37. 37.
    V. V. Dobronravov, Fundamentals of the Dynamics of Nonholonomic Systems [in Russian], Vysshaya Shkola, Moscow (1970).Google Scholar
  38. 38.
    A. I. Dokshevich, “Reduction of the equations of a problem on the rotation of a heavy rigid body about a fixed point to a system of two equations and to a single equation,” in: Investigations in Analytical Mechanics [in Russian], Nauka, Tashkent (1965).Google Scholar
  39. 39.
    A. I. Dokshevich, “A form of the equations of motion of a heavy rigid body about a fixed point,” Izv. Akad. Nauk UzbSSR, Ser. Tekh. Nauk, No. 3 (1965).Google Scholar
  40. 40.
    A. I. Dokshevich, “A particular solution of the problem of the rotation of a heavy rigid body about a fixed point,” Dokl. Akad. Nauk SSSR,167, No. 6 (1966).Google Scholar
  41. 41.
    A. I. Dokshevich, “Integrable cases of the problem of the motion of a heavy rigid body about a fixed point,” Prikl. Mekh.,4, No. 11 (1968).Google Scholar
  42. 42.
    A. I. Dokshevich, “New particular solution of the problem of the motion of a heavy rigid body about a fixed point,” in: Mechanics of Solids [in Russian], No. 2, Naukova Dumka, Kiev (1970).Google Scholar
  43. 43.
    E. I. Zabelina, “Motion of a rigid body about a fixed point in the presence of a nonholonomic constraint,” Tr. Donetsk. Industr. Univ.,20, No. 1 (1957).Google Scholar
  44. 44.
    A. M. Kovalev, “Motion of a body for the case of L. N. Sretenskii,” Prikl. Mat. Mekh.,32, No. 3 (1968).Google Scholar
  45. 45.
    A. M. Kovalev, “Steady-state solutions of differential equations of motion of a body having a fixed point,” in: Mathematical Physics [in Russian], No. 5, Naukova Dumka, Kiev (1968).Google Scholar
  46. 46.
    A. M. Kovalev, “A moving hodograph of the angular velocity in the Hess solution of the problem of the motion of a body having a fixed point, Prikl. Mat. Mekh.,32, No. 6 (1968).Google Scholar
  47. 47.
    A. M. Kovalev, “Motion of a body for the Hess case,” in: Mechanics of Solids [in Russian], No. 1, Naukova Dumka, Kiev (1969).Google Scholar
  48. 48.
    A. M. Kovalev, “Kinematic interpretation of the motion of a body in the Hess solution,” Prikl. Mat. Mekh.,34, No. 3 (1970).Google Scholar
  49. 49.
    A. M. Kovalev, “A moving hodograph of the angular velocity in the solution of L. N. Sretenskii of the problem of the motion of a gyrostat,” in: Mechanics of Solids [in Russian], No. 2, Naukova Dumka, Kiev (1970).Google Scholar
  50. 50.
    A. M. Kovalev, “Kinematic interpretation of the motion of a body in the case of L. N. Sretenskii,” in: Mechanics of Solids [in Russian], No. 2, Naukova Dumka, Kiev (1970).Google Scholar
  51. 51.
    L. M. Kovaleva, “Geometrical investigation of a motion of a rigid body having a fixed point,” in: Mechanics of Solids [in Russian], No. 3, Naukova Dumka, Kiev (1971).Google Scholar
  52. 52.
    L. M. Kovaleva, “New solutions of the problem of the motion of a gyrostat in a central Newtonian force field,” in: Mechanics of Solids [in Russian], No. 4, Naukova Dumka, Kiev (1972).Google Scholar
  53. 53.
    G. V. Kolosov, Some Change in the Origin of the Hamiltonian as Applied to the Solution of Questions in the Mechanics of Solids [in Russian], St. Petersburg (1903).Google Scholar
  54. 54.
    B. I. Konosevich and E. V. Pozdnyakovich, “Two particular solutions of the problem of the motion of a body having a fixed point,” Prikl. Mat. Mekh.,32, No. 3 (1968).Google Scholar
  55. 55.
    B. I. Konosevich and E. V. Pozdnyakovich, “Motion of a rigid body having a fixed point for two particular cases of integrability of the Euler-Poisson equations,” in: Mechanics of Solids [in Russian], No. 2, Naukova Dumka, Kiev (1970).Google Scholar
  56. 56.
    G. N. Kosmodem'yanskaya, “Motion of a body about a fixed point in the presence of a nonholonomic constraint,” in: Mechanics of Cosmic Flight [in Russian], Mashinostroenie, Moscow (1969).Google Scholar
  57. 57.
    L. V. Kudryashova and L. A. Stepanova, “Exact solutions of a problem on the motion in a potential force field of a rigid body having a fixed point,” in: Mechanics of Solids [in Russian], No. 5, Naukova Dumka, Kiev (1973).Google Scholar
  58. 58.
    L. V. Kudryashova and L. A. Stepanova, “Exact solutions of the equations of motion of a heavy rigid body with a fixed point,” in: History and Method of Natural Sciences [in Russian], No. 14, Izd. MGU (1973).Google Scholar
  59. 59.
    L. V. Kudryashova and L. A. Stepanova, “Some studies devoted to the problem of the motion of a rigid body with a nonholonomic constraint,” in: History and Method of Natural Sciences [in Russian], No. 14, Izd. MGU (1973).Google Scholar
  60. 60.
    N. I. Mertsalov, “Problem of the motion of a rigid body having a fixed point, for A=B=4C and for an area integral not equal to zero,” Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, No. 5 (1946).Google Scholar
  61. 61.
    G. V. Mozalevskaya, “Investigation of a moving hodograph in a solution of the problem of the motion of a gyrostat,” in: Mechanics of Solids [in Russian], No. 1, Naukova Dumka, Kiev (1969).Google Scholar
  62. 62.
    G. V. Mozalevskaya, “Particular solution of the problem of the motion of a heavy gyrostat,” in: Mechanics of Solids [in Russian], No. 2, Naukova Dumka, Kiev (1970).Google Scholar
  63. 63.
    G. V. Mozalevskaya, “Investigation of a particular solution of a problem of the motion of a heavy gyrostat,” in: Mechanics of Solids [in Russian], No. 2, Naukova Dumka, Kiev (1970).Google Scholar
  64. 64.
    G. V. Mozalevskaya, “Fixed hodograph of the angular velocity in a solution of the problem of the motion of a gyrostat,” in: Mechanics of Solids [in Russian], No. 3, Naukova Dumka, Kiev (1971).Google Scholar
  65. 65.
    G. V. Mozalevskaya, “Investigation of a solution of the problem of the motion of a heavy gyrostat,” in: Mechanics of Solids [in Russian], No. 3, Naukova Dumka, Kiev (1971).Google Scholar
  66. 66.
    G. V. Mozalevskaya, “Solutions with a linear invariant relation of the problem of the motion of a gyrostat satisfied by a nonholonomic constraint,” in: Mechanics of Solids [in Russian], No. 3, Naukova Dumka, Kiev (1971).Google Scholar
  67. 67.
    G. V. Mozalevskaya, “Dependence on time of the fundamental variables in a symmetric solution of the problem of the motion of a body having a fixed point,” in: Mechanics of Solids [in Russian], No. 4, Naukova Dumka, Kiev (1972).Google Scholar
  68. 68.
    P. Ya. Polubarinova-Kochina, “Single-valued solutions and algebraic integrals of the problem of the rotation of a heavy rigid body about a fixed point,” in: Motion of a Rigid Body about a Fixed Point [in Russian], Izd. Akad. Nauk SSSR, Moscow-Leningrad (1940).Google Scholar
  69. 69.
    V. V. Rumyantsev, “Stability of permanent rotations of a heavy rigid body,” Prikl. Mat. Mekh.,20, No. 1 (1956).Google Scholar
  70. 70.
    V. V. Rumyantsev, “Stability of the motion of a gyrostat,” Prikl. Mat. Mekh.,25, No. 1 (1961).Google Scholar
  71. 71.
    G. N. Savin, T. V. Putyata, and B. N. Fradlin, Outlines in the Development of Some Fundamental Problems in Mechanics [in Russian], Naukova Dumka, Kiev (1964).Google Scholar
  72. 72.
    L. N. Sretenskii, “The works of S. A. Chaplygin on theoretical mechanics,” in: Collected Works of S. A. Chaplygin [in Russian], Vol. 3, Gostekhizdat, Moscow (1950).Google Scholar
  73. 73.
    L. N. Sretenskii, “Some cases of integrability of the equations of motion of a gyrostat,” Dokl. Akad. Nauk SSSR,149, No. 2 (1963).Google Scholar
  74. 74.
    L. N. Sretenskii, “Some cases of the motion of a heavy rigid body with a gyroscope,” Vestn. Moskovsk. Gos. Univ., No. 3 (1963).Google Scholar
  75. 75.
    L. A. Stepanova, “The words of D. N. Goryachev on the dynamics of a rigid body,” in: Mechanics of Solids [in Russian], No. 1, Naukova Dumka, Kiev (1969).Google Scholar
  76. 76.
    L. A. Stepanova, “History of the solution of W. Hess of the problem of the motion of a body having fixed point,” in: Mechanics of Solids [in Russian], No. 2, Naukova Dumka, Kiev (1970).Google Scholar
  77. 77.
    L. A. Stepanova, “Some generalizations of the invariant Hess relation,” in: Mechanics of Solids [in Russian], No. 2, Naukova Dumka, Kiev (1970).Google Scholar
  78. 78.
    G. K. Suslov, Theoretical Mechanics [in Russian], Gostekhizdat, Moscow-Leningrad (1946).Google Scholar
  79. 79.
    É. M. Tyumenova, “The problem of the nonholonomic motion of a rigid body about a point fastened to a rotating platform,” in: Scientific Proceedings of Tashkent State University [in Russian], No. 422 (1972).Google Scholar
  80. 80.
    E. I. Kharlamova-Zabelina, “Rapid rotation of a rigid body about a fixed point in the presence of a nonholonomic constraint,” Vestn. Moskovsk. Gos. Univ., Mat. Mekh., No. 6 (1957).Google Scholar
  81. 81.
    E. I. Kharlamova, “A particular case of integrability of the Euler — Poisson equations,” Dokl. Akad. Nauk SSSR,125, No. 5 (1959).Google Scholar
  82. 82.
    E. I. Kharlamova, “Motion of a rigid body about a fixed point in a central Newtonian force field,” Izv. Sibirsk. Otd. Akad. Nauk SSSR, Otd. Tekh. Nauk, No. 6 (1959).Google Scholar
  83. 83.
    E. I. Kharlamova, “A particular solution of the Euler — Poisson equations,” Prikl. Mat. Mekh.,23, No. 4 (1959).Google Scholar
  84. 84.
    E. I. Kharlamova, “New solution of the problem of motion in a Newtonian force field of a body having a cavity filled with a liquid,” Dokl. akad. Nauk SSSR,157, No. 3 (1964).Google Scholar
  85. 85.
    E. I. Kharlamova, “Some solutions of the problem of the motion of a body having a fixed point,” Prikl. Mat. Mekh.,29, No. 4 (1965).Google Scholar
  86. 86.
    E. I. Kharlamova, “Reduction of the problem of the motion of a heavy rigid body having a fixed point to a single equation. New particular solution of this problem,” Prikl. Mat. Mekh.,30, No. 4 (1966).Google Scholar
  87. 87.
    E. I. Kharlamova, “Kinematic interpretation of a motion of a body having a fixed point,” Prikl. Mat. Mekh.,32, No. 2 (1968).Google Scholar
  88. 88.
    E. I. Kharlamova, “Canonical equations of motion of a body having a fixed point,” in: Mechanics of Solids [in Russian], No. 1, Naukova Dumka, Kiev (1969).Google Scholar
  89. 89.
    E. I. Kharlamova, “A linear invariant relation for the equations of motion of a body having a fixed point,” in: Mechanics of Solids [in Russian], No. 1, Naukova Dumka, Kiev (1969).Google Scholar
  90. 90.
    E. I. Kharlamova, “Reduction of the problem of the motion of a body having a fixed point to a single differential equation” in: Mechanics of Solids, [in Russian], No. 1, Naukova Dumka, Kiev (1969).Google Scholar
  91. 91.
    E. I. Kharlamova, “A quadratic invariant relation for the equations of motion of a body having a fixed point,” in: Mechanics of Solids [in Russian], No. 2, Naukova Dumka, Kiev (1970).Google Scholar
  92. 92.
    E. I. Kharlamova, “A motion of a body having a fixed point,” in: Mechanics of Solids [in Russian], No. 2, Naukova Dumka, Kiev (1970).Google Scholar
  93. 93.
    E. I. Kharlamova, “Motion based on the inertia of a gyrostat satisfying a nonholonomic constraint,” in: Mechanics of Solids [in Russian], No. 3, Naukoya Dumka, Kiev (1971).Google Scholar
  94. 94.
    E. I. Kharlamova, “Polynomial solutions of an integrodifferential equation of the problem of the motion of a rigid body having a fixed point under Lagrange conditions” in: Mechanics of Solids [in Russian], No. 3, Naukova Dumka, Kiev (1971).Google Scholar
  95. 95.
    E. I. Kharlamova, “An algebraic invariant relation for the integrodifferential equation of the problem of the motion of a rigid body having a fixed point under the Hess conditions,” in: Mechanics of Solids [in Russian], No. 3, Naukova Dumka, Kiev (1971.Google Scholar
  96. 96.
    E. I. Kharlamova, “Existence conditions for the algebraic invariant relations for the equations of motion of a rigid body,” in: Mechanics of Solids [in Russian], No. 3, Naukova, Dumka, Kiev (1971).Google Scholar
  97. 97.
    E. I. Kharlamova, “Exponential solutions of the integrodifferential equation of the problem of the motion of a body having a fixed point,” in: Mechanics of Solids [in Russian], No. 3, Naukova Dumka, Kiev (1971).Google Scholar
  98. 98.
    E. I. Kharlamova and L. M. Kovaleva, “Equations of motions of a gyrostat in a Newtonian force field,” in: Mechanics of Solids [in Russian], No. 4, Naukova Dumka, Kiev (1972).Google Scholar
  99. 99.
    E. I. Kharlamova and G. V. Mozalevskaya, “Investigation of the solution of V. A. Steklov for the equations of motion of a body having a fixed point,” in: Mathematical Physics [in Russian], No. 5, Naukova Dumka, Kiev (1968).Google Scholar
  100. 100.
    E. I. Kharlamova and P. V. Kharlamov, “A new case of integrability for the equations of motion of a heavy rigid body having a fixed point,” Dokl. Akad. Nauk SSSR,188, No. 4 (1969).Google Scholar
  101. 101.
    E. I. Kharlamova and P. V. Kharlamov, “A new particular solution of the differential equations of motion of a body having a fixed point under the conditions of S. V. Kowalewski,” Dokl. Akad. Nauk SSSR,189, No. 5 (1969).Google Scholar
  102. 102.
    P. V. Kharlamov, “Linear integrals of theequations of motion of a heavy rigid body about a fixed point,” Dokl. Akad. Nauk SSSR,143, No. 4 (1962).Google Scholar
  103. 103.
    P. V. Kharlamov, “Equations of motion of a heavy rigid body having a fixed point,” Prikl. Mat. Mekh.,27, No. 4 (1963).Google Scholar
  104. 104.
    P. V. Kharlamov, “A case of the integrability of the equations of motion of a heavy rigid body having a cavity filled with a liquid,” Dokl. Akad. Nauk SSSR,150, No. 4 (1963).Google Scholar
  105. 105.
    P. V. Kharlamov, “Two particular cases of the solution of the problem of the motion of a body having a fixed point,” Dokl. Akad. Nauk SSSR,154, No. 2 (1964).Google Scholar
  106. 106.
    P. V. Kharlamov, “Kinematic interpretation of the motion of a body having a fixed point,” Prikl. Mat. Mekh.,28, No. 3 (1964).Google Scholar
  107. 107.
    P. V. Kharlamov, “Kinematic interpretation of a solution of the problem of the motion of a body having a fixed point,” Dokl. Akad. Nauk SSSR,158, No. 5 (1964).Google Scholar
  108. 108.
    P. V. Kharlamov, “Equations of motion of a gyrostat,” in: Proceedings of an Intercollegiate Conference on the Applied Theory and Stability of Motion and Analytical Mechanics, Kazan', 1962, [in Russian], Izd. Kazansk. Aviats. Inst. (1964).Google Scholar
  109. 109.
    P. V. Kharlamov, “A solution of the problem of the motion of a body having a fixed point,” Prikl. Mat. Mekh.,28, No. 1 (1964).Google Scholar
  110. 110.
    P. V. Kharlamov, Lectures on the Dynamics of a Rigid Body [in Russian], Izd. Novosibirsk. Gos. Univ. (1965).Google Scholar
  111. 111.
    P. V. Kharlamov, “Polynomial solutions of the equations of motion of a body having a fixed point,” Prikl. Mat. Mekh.,29, No. 1 (1965).Google Scholar
  112. 112.
    P. V. Kharlamov, “Uniform rotations of a body having a fixed point,” Prikl Mat. Mekh.,29, No. 2 (1965).Google Scholar
  113. 113.
    P. V. Kharlamov, “A gyrostat with a nonholonomic constraint,” in: Mechanics of Solids [in Russian], No. 3, Naukova Dumka, Kiev (1971).Google Scholar
  114. 114.
    P. V. Kharlamov, “A case of the integrability of the equations of motion of a rigid body having a fixed point,” in: Mechanics of Solids [in Russian], No. 3, Naukova Dumka, Kiev (1971).Google Scholar
  115. 115.
    P. V. Kharlamov and L. M. Kovaleva, “A new solution of the problem of the motion of a heavy gyrostat,” in: Mechanics of Solids [in Russian], No. 2, Naukova Dumka, Kiev (1970).Google Scholar
  116. 116.
    P. V. Kharlamov and G. V. Mozalevskaya, “Investigation of a moving hodograph of the angular velocity in a symmetric solution of the problem of the motion of a body having a fixed point,” in: Mechanics of Solids [in Russian], No. 4, Naukova Dumka, Kiev (1972).Google Scholar
  117. 117.
    P. V. Kharlamov and G. V. Mozalevskaya, “Geometrical interpretation of certain motions of the gyroscope of S. V. Kowalewski,” in: Mechanics of Solids [in Russian], No. 5, Naukova Dumka, Kiev (1973).Google Scholar
  118. 118.
    P. V. Kharlamov and E. I. Kharlamova, “A solution of the problem of the motion of a gyrostat satisfying a nonholonomic constraint,” in: Mechanics of Solids [in Russian], No. 3, Naukova Dumka, Kiev (1971).Google Scholar
  119. 119.
    S. A. Chaplygin, “A new case of rotation of a rigid body supported at a single point,” in: Collected Works [in Russian], Vol. 1 Gostekhizdat, Moscow (1948).Google Scholar
  120. 120.
    S. A. Chaplygin, “A new particular solution of the problem of the rotation of a heavy rigid body about a fixed point,” in: Collected Works [in Russian], Vol. 1, Gostekhizdat, Moscow (1948).Google Scholar
  121. 121.
    L. Alfieri, “Risoluzione di un problema compredente quelle di Staude,” Univ. Roma. Ist. Nax. Alta. Mat. Rend. Mat. Appl.,12, (1954).Google Scholar
  122. 122.
    E. Bentsik, “Su di in tipo di precessioni reglari per un corpo rigido asimmetrico soggetts afforze Newtoniona,” Rend. Seminario Mat. Padova,41, (1968).Google Scholar
  123. 123.
    P. Burgatti, “Dimonstrazione della non esistenna d'integrali (oltre i noti) nel problema del moto d'un corpo pesante intorno a un punto fisso,” Rend. Circ. Mat. Palermo,29 (1910).Google Scholar
  124. 124.
    P. Burgatti, “Sugl'integrali primi dell'equazioni del moto d'un corpo pesante intorno a un punto fisso,” Ann. Mat. Pura Appl.,12 (1906).Google Scholar
  125. 125.
    T. M. Cherry, “On Poincaré's theorem of the nonexistence of uniform integrals of dynamical equations,” Proc. Cambridge Philos. Soc.,22 (1924).Google Scholar
  126. 126.
    J. Drach, “Sur le mouvement d'un solide pesante qui a un point fixé (determinacion du groupe de rationalité de l'equation differentielle du probleme)”, C. R. Acad. Sci. Paris,179 (1929).Google Scholar
  127. 127.
    A. Gray, A Treatise on Gyrostatics and Rotational Motion, Macmillan, London (1918).Google Scholar
  128. 128.
    G. Grioli, “Esistenza e determinazione delle precessioni regolari dinamicamente possibili per un solido pesante asimmetrico,” Ann. Math. Pure Appl., Ser. 4,24, Nos. 3–4 (1947).Google Scholar
  129. 129.
    G. Hamel, “Über den algemeinen schweren Krelsel,” Z. Angew Math. Mech.,5–6 (1947).Google Scholar
  130. 130.
    E. Husson, “Sur un theoreme de M. Poincaré relativement au mouvement d'un solide pesant autour d'un point fixé,” C. R. Acad. Sci. Paris,141 (1905).Google Scholar
  131. 131.
    E. Husson, “Recherches des integrales algebriques dans le mouvement d'un corps solide pesant autour d'un point fixé,” C. R. Acad. Sci., Paris,141 (1905).Google Scholar
  132. 132.
    E. Husson, “Sur un theoreme de M. Poincaré, relativement au mouvement d'un solide pesant,” Acta Math.,31 (1908).Google Scholar
  133. 133.
    F. Klein and A. Sommerfeld, Über die Theorie des Kreisels, Leipzig (1923); 2nd ed., Berlin (1965).Google Scholar
  134. 134.
    N. Kowalewski, “Eine neue partikuläre losung der differenzial-gleichungen der bewegung eines schweren starren körpers um einen festen punkt.,” Math. Ann.,65 (1908).Google Scholar
  135. 135.
    O. Lazzarino, “Sull'equivalenza fra la equazioni differenziali de Hess — Schiff e quelle de Euler —Poisson nella teoria dei giroscopi asimmetrici pesanti,” Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat.,28 (1919).Google Scholar
  136. 136.
    E. Leimanis, The General Problem of the Motion of Coupled Rigid Bodies about a Fixed Point, Springer-Verlag, New York (1965).Google Scholar
  137. 137.
    T. Levi-Civita, “Sur la resolution qualitative du probleme restreint des trois corps,” Acta Math.,30 (1906).Google Scholar
  138. 138.
    M. Manarini, “Sopra un teorema de Staude — van der Woude relative al moto di un corpo pesante intorno ad un punto fisso,” Atti R. Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat.,14 (1931).Google Scholar
  139. 139.
    M. Manarini, “Alcune notevoli proprieta del centro d'inezia relative alle rotazioni permanenti nella dinamica del corpo rigido con un punto fisso,” Boll. Unione Mat. Ital.,3 (1948).Google Scholar
  140. 140.
    A. Mayer, “Symmetrische lösung der aufgabe, die rotatione eines starren körpers dessen winkelgeschwindigkeiten bereits gefunden wurden, volständig zu bestimmen,” Ber. Verh. Königl. Sächs. Ges. Wiss. Leipzig, Math.-Phys. Kl.,54 (1902).Google Scholar
  141. 141.
    C. W. Oseen, “Über eine in der theorie des Kreisels auftretende famile von flächen sechsten grades,” Arkiv. Mat. Astron. Fys.,6, No. 28 (1910);7 No. 28 (1912).Google Scholar
  142. 142.
    F. Quatela, “Extensione di una dimostrazione del Bargatti nel problems del giroscopic pesante,” Giorn. Mat. Battaglini,67 (1929).Google Scholar
  143. 143.
    F. Sbrana, “Un osservarione sul moto di un solido pesante attorno ad un punto,” Boll. Unione Mat. Ital.,13 (1934).Google Scholar
  144. 144.
    P. Stäckel, “Ausgezeichnete bewegungen des schweren unsymmetrischen kreisels,” Math. Ann,65 (1908).Google Scholar
  145. 145.
    P. Stäckel, “Ausgezeichnete kreiselbewegungen,” I. Deutschen Math. Verein.,18 (1909).Google Scholar
  146. 146.
    P. Stäckel, “Die reduzierten differenzialgleichungender bewegung des schweren unsymmetrischen kreisels,” Math. Ann.,67 (1909).Google Scholar
  147. 147.
    P. Stäckel, “Elementaren dynamik der punkt-susteme und starren körper,” Enc. der Math., Wiss.,4 (1908).Google Scholar
  148. 148.
    C. Totaro, “Ompossibillita problema delle precessioni generalizzate regolari ellittiche per un solido pesante asimmetrico,”41 (1968) Journal title omitted in Russian original. — Publisher.Google Scholar
  149. 149.
    W. Woude, “Über die staudeschen kreiselbewegungen,” Math. Zeit.,16 (1923).Google Scholar

Copyright information

© Plenum Publishing Corporation 1975

Authors and Affiliations

  • B. N. Fradlin
  • V. M. Slyusarenko

There are no affiliations available

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