Simulation of rigid body motion in a resisting medium and analogies with vortex streets
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The author returns to constructing the nonlinear mathematical model of a plane-parallel impact of a medium on a rigid body with allowance for the dependence of the arm of force on the reduced angular velocity of the body (a kind of Strouhal number). In this case, the arm of the force is also a function of the angle of attack. As was shown by the processing of the experimental data on the motion of homogeneous circular cylinders in water, these circumstances should be taken into account in the simulation. The analysis of a plane model of the interaction of a rigid body with a medium revealed new cases of the complete integrability in elementary functions, which made it possible to find qualitative analogies between the motion of free bodies in a resisting medium and vibrations of partly fixed bodies in a flow of an oncoming medium. Phase patterns obtained in the analysis of the nonlinear model of the impact of the medium are compared with real Karman’s vortex streets.
Keywordsrigid body resisting medium jet flow complete integrability
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- 2.M. V. Shamolin, Methods for the Analysis of Dynamical Systems with Variable Dissipation in Rigid Body Dynamics (Ekzamen, Moscow, 2007) [in Russian].Google Scholar
- 5.M. I. Gurevich, Theory of Jets of an Ideal Liquid (Nauka, Moscow, 1979) [in Russian].Google Scholar
- 6.S. A. Chaplygin, Selected Works (Nauka, Moscow, 1976) [in Russian].Google Scholar
- 7.S. A. Chaplygin, “About motion of heavy bodies in an incompressible liquid,” in Complete Collection of Works (Akad. Nauk SSSR, Leningrad, 1933), Vol. 1, pp. 133–135 [in Russian].Google Scholar
- 12.M. V. Shamolin, “Introduction to problem on braking of a body in a resisting medium and new two-parametric family of phase portraits,” Mosc. Univ. Mech. Bull. 41(4), 1–9 (1996).Google Scholar
- 15.D. Arrowsmith and C. Place, Ordinary Differential Equations. A Qualitative Approach. With Applications (Springer, London, 1983).Google Scholar
- 16.A. Poincare, On Curves Defined by a Differential Equation (OGIZ, Moscow, Leningrad, 1947) [in Russian].Google Scholar
- 17.L. Prandtl, Führer durch die Strömungslehre: Grundlagen und Phänomene (Herbert Oertel, Berlin, 1944).Google Scholar
- 20.N. E. Kochin, “On non-stability of vortex chains,” Dokl. Akad. Nauk SSSR 24, 748–751 (1939).Google Scholar