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On the fall of a heavy rigid body in an ideal fluid. (English) Zbl 1119.70009
Maksimov, V. I. (ed.), Dynamical systems: modeling, optimization, and control. Transl. from the Russian. Moscow: Maik Nauka/Interperiodica, Pleiades Publishing/distrib. by Springer. Proc. Steklov Inst. Math. 2006, Suppl. 1, S24-S47 (2006); translation from Tr. Inst. Mat. Mekh. 12, No. 1, 25-47 (2006).
Summary: 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.
For the entire collection see [Zbl 1116.37003].

MSC:
70E99 Dynamics of a rigid body and of multibody systems
70E50 Stability problems in rigid body dynamics
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