Advertisement

Doklady Mathematics

, Volume 90, Issue 2, pp 631–634 | Cite as

Nonintegrability and obstructions to the hamiltonianization of a nonholonomic Chaplygin top

  • I. A. Bizyaev
Mathematical Physics

Keywords

Invariant Measure DOKLADY Mathematic Rotation Number Invariant Torus Hamiltonian Vector Field 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. V. Borisov, I. S. Mamaev, and I. A. Bizyaev, Regul. Chaotic Dyn. 18(3), 277–328 (2013).CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    A. V. Bolsinov, A. V. Borisov, and I. S. Mamaev, Regul. Chaotic Dyn. 17(6), 571–579 (2012).CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    A. V. Borisov and I. S. Mamaev, Regul. Chaotic Dyn 13(5), 443–490 (2008).CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    I. A. Bizyaev and A. V. Tsiganov, J. Phys. A: Math. Theor. 46(8), 1–11 (2013).CrossRefMathSciNetGoogle Scholar
  5. 5.
    S. A. Chaplygin, Regul. Chaotic Dyn 7(2), 131–148 (2002).CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    V. V. Kozlov, Usp. Mekh. 8(3), 85–107 (1985).Google Scholar
  7. 7.
    V. V. Kozlov, Proc. Steklov Inst. Math. 256, 188–205 (2007).CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    V. V. Kozlov, J. Appl. Math. Mech. 51(4), 420–426 (1987).CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    A. V. Borisov, I. S. Mamaev, and A. V. Tsyganov, Math. Notes 95(3), 308–315 (2014).CrossRefGoogle Scholar
  10. 10.
    J. Shen, D. A. Schneider, and A. M. Bloch, in Proceedings of the 42th IEEE Conference on Decision and Control, Maui, 2013 (Maui, 2013), Vol. 53, 4369–4374.Google Scholar
  11. 11.
    J. Shen, D. A. Schneider, and A. M. Bloch, Intern. J. Robust Nonlinear Control 18(9), 905–945 (2008).CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    P. Lynch and M. D. Bustamante, J. Phys. A: Math. Theor. 42, 425203 (2009).CrossRefMathSciNetGoogle Scholar
  13. 13.
    A. V. Borisov and I. S. Mamaev, Regul. Chaotic Dyn. 7(2), 177–200 (2002).CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    K. M. Ehlers and J. Koiler, in Proceedings of IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence, Moscow, Russia, 2006 (Springer, Dordrecth, 2006).Google Scholar
  15. 15.
    A. O. Kazakov, Regul. Chaotic Dyn. 18(5), 508–520 (2013).CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Udmurt State UniversityIzhevskRussia

Personalised recommendations