On the motion of a heavy rigid body in an ideal fluid with circulation

Chaos

Volumn 16, Issue 1, 2006, Pages

  Borisov, Alexey V ^a   Mamaev, Ivan S ^a  

^a UDMURT STATE UNIVERSITY   (Russian Federation)

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[No Author keywords available]

Indexed keywords

EID: 33645661221     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2166530     Document Type: Article

References (26)

1. S. A. Chaplygin, " On the effect of a plane-parallel air flow on a cylindrical wing moving in it, " Complete Works (Leningrad: Izd. Akad. Nauk SSSR, 1933), Vol. 3, pp. 3-64.
2. N. E. Zhukovski, " On light elongated bodies that fall in the air while rotating around the longitudinal axis: I " (Glav. Red. Aviats. Lit., 1937), Vol. 5, pp. 72-80.
3. N. E. Zhukovski, " On birds' hovering, " Complete Works (Moscow-Leningrad: Glav. Red. Aviats. Lit., 1937), Vol. 5, pp. 7-35.
4. S. A. Chaplygin, " On heavy body falling in an incompressible fluid, "Complete Works (Leningrad: Izd. Akad. Nauk SSSR, 1933), Vol. 1, pp. 133-150.
5. D. N. Goryachev, " On the motion of a heavy rigid body in a fluid, " Izv. Imper. Ob-va (Mosk. Imper. Univ., 1893), Vol. 78, No. 2, pp. 59-61.
6. V. A. Steklov, On the Motion of a Rigid Body in a Fluid (Uch. Zap. Harkov. Univ., Kharkov, 1893), 234 pp.
7. V. V. Kozlov, " On a heavy rigid body falling in an ideal fluid, " Izv. Akad. Nauk SSSR, Mekh. tv. tela, No. 5, pp. 10-17 (1989).
8. M. V. Deryabin, " On asymptotics of the solution of Chaplygin equation., " Regular Chaotic Dyn. 3, 93 (1998).
9. S. M. Ramodanov, " Asymptotic solutions of the Chaplygin equations., " Vestn. Mosk. Univ., Ser. 1: Mat., Mekh., 93 (1995).
10. M. V. Deryabin and V. V. Kozlov, " On the effect of abruptly rising of a heavy solid body in a fluid, " Izv. Akad. Nauk SSSR, Mekh. tv. tela, No. 1 pp. 68-74 (2002).
11. V. V. Kozlov, " On the stability of equilibrium positions in a nonstationary force field, " PMM, Vol. 55, No. 1, pp. 12-19.
12. A. V. Borisov and I. S. Mamaev, Rigid Body Dynamics (SPC Regular and Chaotic Dynamics, Izhevsk, 2001).
13. V. V. Kozlov, " On the problem of a heavy rigid body falling in a resistant medium., " Vestn. Mosk. Univ., Ser. 1: Mat., Mekh., 79-86 (1990).
14. A. Belmonte, H. Eisenberg, and E. Moses, " From flutter to tumble: inertial drag and Froude similarity in falling paper., " Phys. Rev. Lett. 81, 345 (1998).
15. Y. Tanabe and K. Kaneko, " Behavior of a falling paper., " Phys. Rev. Lett. 73, 1372 (1994).
16. S. B. Feild, M. Klaus, M. G. Moore, and F. Nori, " Chaotic dynamics of falling disks., " Nature (London) 388, 252 (1997).
17. U. Pesavento and Z. J. Wang, " Falling Paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation., " Phys. Rev. Lett. 93, 144 (2004).
18. L. Mahadevan, N. S. Ryu, and A. D. T. Samuel, " Tumbling cards., " Phys. Fluids 11, 1 (1999).
19. J. C. Maxwell, " On a particular case of the descent of a heavy body in a resisting medium, " Camb. Dublin Math. J. Vol. 9, pp. 115-118 (1853).
20. V. V. Kozlov, " On a heavy cylindrical body falling in a fluid, " Izv. RAN, Mekh. tv. tela No. 4, 113-117 (1993).
21. H. Lamb, Hydrodynamics (OGIZ, Gostekhizdat, 1947) (in Russian); H. Lamb, Hydrodynamics, 6th ed. (Dover, New York, 1945).
22. H. Lamb, Hydrodynamics (OGIZ, Gostekhizdat, 1947) (in Russian); H. Lamb, Hydrodynamics, 6th ed. (Dover, New York, 1945).
23. P. Capodanno, " Sur la ráduction des equations du mouvement d'un profil pesant dans une fluide., " Rev. Roum. Math. Pures Appl. 32, 763 (1987).
24. G. Couchet, " Sur un cas d'integration par quadratures du mouvement d'un profil au sein d'un fluide parfait incompressible en mouvement irrotational., " Acad. Sci., Paris, C. R. 258, 1722 (1964).
25. V. V. Kozlov, Symmetry, Topology and Resonances in Hamiltonian Mechanics (Springer-Verlag, Berlin, 1996).
26. S. M. Ramodanov, " The effect of circulation on the fall of a heavy rigid body, " Izv. RAN, Mekh. tv. tela No. 5, pp. 19-24 (1996).