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.
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
\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
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2246985}
\zmath{https://zbmath.org/?q=an:1119.70009}
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2006
\vol 12
\issue , suppl. 1
\pages S24--S47
\crossref{https://doi.org/10.1134/S008154380605004X}
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This publication is cited in the following 5 articles:
S. P. Kuznetsov, “Dvizhenie padayuschei plastiny v zhidkosti: konechnomernye modeli i fenomeny slozhnoi nelineinoi dinamiki”, Nelineinaya dinam., 11:1 (2015), 3–49
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
Borisov A.V., Mamayev I.S., “The dynamics of a Chaplygin sleigh”, J. Appl. Math. Mech., 73:2 (2009), 156–161
Dmitry Kolomenskiy, Kai Schneider, Iutam Bookseries, 20, 150 Years of Vortex Dynamics, 2009, 185
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
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