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Trudy Inst. Mat. i Mekh. UrO RAN, 2006, Volume 12, Number 1, Pages 25–47 (Mi timm132)  

This article is cited in 4 scientific papers (total in 4 papers)

On the fall of a heavy rigid body in an ideal fluid

A. V. Borisov, V. V. Kozlov, I. S. Mamaev


Abstract: We consider a problem about the motion of a heavy rigid body in an unbounded volume of an ideal irrotational incompressible fluid. This problem generalizes a classical Kirchhoff problem describing the inertial motion of a rigid body in a fluid. We study different special statements of the problem: the plane motion and the motion of an axially symmetric body. In the general case of motion of a rigid body, we study the stability of partial solutions and point out limiting behaviors of the motion when the time increases infinitely. Using numerical computations on the plane of initial conditions, we construct domains corresponding to different types of the asymptotic behavior. We establish the fractal nature of the boundary separating these domains.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2006, 12, suppl. 1, S24–S47

Bibliographic databases:

Document Type: Article
UDC: 531.3+532.5
Received: 25.11.2005

Citation: A. V. Borisov, V. V. Kozlov, I. S. Mamaev, “On the fall of a heavy rigid body in an ideal fluid”, Dynamical systems: modeling, optimization, and control, Trudy Inst. Mat. i Mekh. UrO RAN, 12, no. 1, 2006, 25–47; Proc. Steklov Inst. Math. (Suppl.), 12, suppl. 1 (2006), S24–S47

Citation in format AMSBIB
\Bibitem{BorKozMam06}
\by A.~V.~Borisov, V.~V.~Kozlov, I.~S.~Mamaev
\paper On the fall of a~heavy rigid body in an ideal fluid
\inbook Dynamical systems: modeling, optimization, and control
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2006
\vol 12
\issue 1
\pages 25--47
\mathnet{http://mi.mathnet.ru/timm132}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2246985}
\zmath{https://zbmath.org/?q=an:1119.70009}
\elib{http://elibrary.ru/item.asp?id=12040717}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2006
\vol 12
\issue , suppl. 1
\pages S24--S47
\crossref{https://doi.org/10.1134/S008154380605004X}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746894804}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Borisov A.V., Kozlov V.V., Mamaev I.S., “Asymptotic stability and associated problems of dynamics of falling rigid body”, Regul. Chaotic Dyn., 12:5 (2007), 531–565  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Borisov A.V., Mamayev I.S., “The dynamics of a Chaplygin sleigh”, J. Appl. Math. Mech., 73:2 (2009), 156–161  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. Kolomenskiy D., Schneider K., “Numerical simulations of falling leaves using a pseudo-spectral method with volume penalization”, Theor. Comput. Fluid Dyn., 24:1-4 (2010), 169–173  crossref  zmath  adsnasa  isi  elib  scopus
    4. S. P. Kuznetsov, “Dvizhenie padayuschei plastiny v zhidkosti: konechnomernye modeli i fenomeny slozhnoi nelineinoi dinamiki”, Nelineinaya dinam., 11:1 (2015), 3–49  mathnet  elib
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