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Chaotic dynamics in the problem of the fall of a screw-shaped body in a fluid. (Russian. English summary) Zbl 1372.70016
Summary: This paper is concerned with the process of the free fall of a three-bladed screw in a fluid. The investigation is performed within the framework of theories of an ideal fluid and a viscous fluid. For the case of an ideal fluid the stability of uniformly accelerated rotations (the Steklov solutions) is studied. A phenomenological model of viscous forces and torques is derived for investigation of the motion in a viscous fluid. A chart of Lyapunov exponents and bifurcation diagrams are computed. It is shown that, depending on the system parameters, quasiperiodic and chaotic regimes of motion are possible. Transition to chaos occurs through cascade of period-doubling bifurcations.

MSC:
70E15 Free motion of a rigid body
65P30 Numerical bifurcation problems
76U05 General theory of rotating fluids
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