Doklady Physics

, Volume 53, Issue 10, pp 525–528 | Cite as

Explicit integration of one problem in nonholonomic mechanics

Mechanics

PACS numbers

02.30.Ik 45.20.dc 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. V. Borisov and Yu. N. Fedorov, Vestn. Mosk. Univ., Ser. Mat. Mech., No. 6, 793 (1995).Google Scholar
  2. 2.
    A. V. Borisov and I. S. Mamaev, Reg. Chaot. Dyn. 7(2), 177 (2002).MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    L. P. Eisenhart, Ann. Math. 35(2), 284 (1934).CrossRefMathSciNetGoogle Scholar
  4. 4.
    A. A. Kilin, Reg. Chaot. Dyn. 6(3), 291 (2001).MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    S. A. Chaplygin, To the Theory of Motion of Nonholonomic Systems. The Theorem of Reducing Factor, in Collected Works (OGIZ, Moscow, 1948), Vol. 1, pp. 15–25 [in Russian].Google Scholar
  6. 6.
    A. V. Borisov and I. S. Mamaev, Mat. Zametki 70, 793 (2001).MathSciNetGoogle Scholar
  7. 7.
    A. V. Borisov and I. S. Mamaev, Sib. Math. J. 48, 26 (2007) [Sib. Mat. Zh. 48 (1), 33 (2007)].CrossRefMathSciNetGoogle Scholar
  8. 8.
    S. A. Chaplygin, On a Ball Rolling over a Horizontal Plane, in Collected Works (OGIZ, Moscow, 1948), Vol. 1, pp. 76–101 [in Russian].Google Scholar
  9. 9.
    A. V. Borisov and I. S. Mamaev, Dynamics of Solid Body (Moscow-Izhevsk, 2001) [in Russian].Google Scholar
  10. 10.
    V. V. Kozlov, Usp. Mekh. 8(3), 85 (1985).Google Scholar
  11. 11.
    A. P. Markeev, Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela 21(1), 65 (1986).Google Scholar
  12. 12.
    M. P. Kharlamov, Topological Analysis of the Classical Integrable Problems of Solid Body Dynamics (Leningrad. Gos. Univ., Leningrad, 1988) [in Russian].Google Scholar
  13. 13.
    V. G. Marikhin and V. V. Sokolov, Theor. Math. Phys. 149, 1425 (2006) [Teor. Mat. Fiz. 149 (2), 147 (2006)].CrossRefMathSciNetGoogle Scholar
  14. 14.
    A. V. Borisov and I. S. Mamaev, Reg. Chaot. Dyn. 12(2), 153 (2007).CrossRefMathSciNetGoogle Scholar
  15. 15.
    V. A. Yaroshchuk, Vestn. Mosk. Univ., Ser. Mat. Mech., No. 6, 26 (1992).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  • A. V. Borisov
    • 1
  • I. S. Mamaev
    • 1
  • V. G. Marikhin
    • 2
  1. 1.Institute of Computer ScienceUdmurtian State UniversityIzhevsk, UdmurtiaRussia
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

Personalised recommendations