Integrable nonholonomic systems on Lie groups

  • A. P. Veselov
  • L. E. Veselova


Nonholonomic System Integrable Nonholonomic System 
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Literature cited

  1. 1.
    S. A. Chaplygin, “Rolling of a ball on a horizontal plane,” Mat. Sb.,24, No. 1, 139–168 (1903).Google Scholar
  2. 2.
    E. I. Kharlamova, “Rolling of a ball on an inclined plane,” Prikl. Mat. Mekh.,22, No. 4, 504–509 (1958).Google Scholar
  3. 3.
    V. V. Kozlov, “Integration of the equations of nonholonomic mechanics,” Usp. Mekh.,8, No. 3, 85–107 (1985).Google Scholar
  4. 4.
    A. P. Markeev, “Integrability of the problem of rolling of a ball from a multiply connected cavity filled with a fluid,” Mekh. Tverd. Tela, No. 3, 3–15 (1985).Google Scholar
  5. 5.
    A. P. Veselov, “Geodesic flows on Lie groups with nonholonomic constraint,” Usp. Mat. Nauk,40, No. 5 (1985).Google Scholar
  6. 6.
    A. P. Veselov and L. E. Veselova, “Flows on Lie groups with nonholonomic constraint and integrable nonhamiltonian systems,” Funkts. Anal. Prilozhen.,20, No. 4, 65–66 (1986).Google Scholar
  7. 7.
    L. E. Veselova, “New cases of integrability of the equations of motion of a rigid body in the presence of a nonholonomic constraint,” in: Geometry, Differential Equations, and Mechanics [in Russian], Moscow State Univ. (1986), pp. 64–68.Google Scholar
  8. 8.
    L. E. Veselova, “Integrability and analytic properties of solutions in some problems of dynamics of a rigid body,” Author's Abstract of Dissertation, Moscow State Univ. (1986).Google Scholar
  9. 9.
    V. I. Arnol'd, Mathematical Methods of Classical Mechanics [in Russian], Nauka, Moscow (1974).Google Scholar
  10. 10.
    D. B. Fuks, Cohomology of Infinite-dimensional Lie Algebras [in Russian], Nauka, Moscow (1974).Google Scholar
  11. 11.
    V. V. Golubev, Lectures on Integration of the Equations of Motion of a Heavy Rigid Body Near a Fixed Point [in Russian], Gostekhizdat, Moscow (1953).Google Scholar
  12. 12.
    G. K. Suslov, Theoretical Mechanics [in Russian], Gostekhizdat, Moscow (1946).Google Scholar
  13. 13.
    V. V. Kozlov, “Invariant measures of Euler-Poincaré equations on Lie algebras,” Funkts. Anal. Prilozhen.,22, No. 1, 69–71 (1988).Google Scholar
  14. 14.
    C. Neumann, “De probleme quodam mechanico, quod and priman Integralium ultraelliptocorum classem revocatum,” J. Reine Angew. Math.,56, 46–63 (1859).Google Scholar
  15. 15.
    V. V. Beletskii, Motion of a Satellite with Respect to the Center of Mass in a Gravitational Field [in Russian], Moscow State Univ. (1975).Google Scholar
  16. 16.
    A. N. Kolmogorov, “Dynamical systems with integral invariant on the torus,” Dokl. Akad. Nauk SSSR,93, No. 5, 763–766 (1953).Google Scholar
  17. 17.
    A. P. Veselov, “Change of time in integrable systems,” Vestn. Mosk. Gos. Univ., Ser. Mat., 25–29 (1987).Google Scholar
  18. 18.
    S. A. Chaplygin, Studies on the Dynamics of Nonholonomic Systems [in Russian], Gostekhizdat, Moscow-Leningrad (1949).Google Scholar

Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • A. P. Veselov
    • 1
  • L. E. Veselova
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityUSSR

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