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Doklady Physics

, Volume 61, Issue 1, pp 32–36 | Cite as

Free and controlled motion of a body with a moving internal mass through a fluid in the presence of circulation around the body

  • E. V. Vetchanin
  • A. A. Kilin
Mechanics

Abstract

The free and controlled motion of an arbitrary two-dimensional body with a moving internal mass and constant circulation around the body in an ideal fluid is studied. Bifurcation analysis of the free motion is performed (under the condition of a fixed internal mass). It is shown that the body can be moved to a given point by varying the position of the internal mass. Some problems related to the presence of a nonzero drift of the body with a fixed internal mass are noted.

Keywords

Phase Portrait Bifurcation Diagram Control Motion Free Motion DOKLADY Physic 
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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References

  1. 1.
    G. Kirchhoff and K. Hensel, Vorlesungen’ ber mathematische Physik. Mechanik (BG Teubner, Leipzig, 1874).Google Scholar
  2. 2.
    H. Lamb, Hydrodynamics (Dover, New York, 1945).Google Scholar
  3. 3.
    S. A. Chaplygin, Tr. Tsentr. Aerogidrodinam. Inst., No. 19, 300 (1926).Google Scholar
  4. 4.
    V. A. Steklov, Soobshch. Khar’k. Matem. Obshch. 2, 209 (1891).Google Scholar
  5. 5.
    A. V. Borisov, V. V. Kozlov, and I. S. Mamaev, Regul. Chaotic Dyn. 12, 531 (2007).CrossRefADSMathSciNetzbMATHGoogle Scholar
  6. 6.
    A. V. Borisov and I. S. Mamaev, Chaos 16, 013118 (2006).CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    J. Vankerschaver, E. Kanso, and J. E. Marsden, Regul. Chaotic Dyn. 15, 606 (2010).CrossRefADSMathSciNetzbMATHGoogle Scholar
  8. 8.
    V. V. Kozlov and S. M. Ramodanov, J. Appl. Math. Mech. (Engl. Transl.) 65, 579 (2001).CrossRefMathSciNetGoogle Scholar
  9. 9.
    V. V. Kozlov and D. A. Onishchenko, J. Appl. Math. Mech. (Engl. Transl.) 67, 553 (2003).CrossRefMathSciNetGoogle Scholar
  10. 10.
    A. A. Kilin, S. M. Ramodanov, and V. A. Tenenev, Nonlinear Dyn. Mob. Robot. 2, 115 (2014).Google Scholar
  11. 11.
    S. M. Ramodanov, V. A. Tenenev, and D. V. Treschev, Regul. Chaotic Dyn. 17, 547 (2012).CrossRefADSMathSciNetzbMATHGoogle Scholar
  12. 12.
    S. Childress, S. E. Spagnolie, and T. Tokieda, J. Fluid Mech. 669, 527 (2011).CrossRefADSMathSciNetzbMATHGoogle Scholar
  13. 13.
    E. V. Vetchanin, I. S. Mamaev, and V. A. Tenenev, Regul. Chaotic Dyn. 18, 100 (2013).CrossRefADSMathSciNetzbMATHGoogle Scholar
  14. 14.
    B. Bonnard, C. R. Acad. Sci. Paris, S’r. 1 292, 535 (1981).MathSciNetzbMATHGoogle Scholar
  15. 15.
    A. V. Borisov, A. A. Kilin, and I. S. Mamaev, Regul. Chaotic Dyn. 17, 258 (2012).CrossRefADSMathSciNetzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Kalashnikov Izhevsk State Technical UniversityIzhevsk, UdmurtiaRussia
  2. 2.Udmurt State UniversityIzhevsk, UdmurtiaRussia
  3. 3.Steklov Mathematical InstituteMoscowRussia

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