Chaotic dynamics in the problem of the fall of a screw-shaped body in a fluid

V. A. Tenenev ; E. V. Vetchanin ; L. Ilaletdinov

Russian journal of nonlinear dynamics, Tome 12 (2016) no. 1, pp. 99-120.

Résumé

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 bifucation 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.

Détail

Keywords: ideal fluid, motion of a rigid body, dynamical system, stability of motion, chart of Lyapunov exponents.
Mots-clés : viscous fluid, bifurcations

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