Simulation of rigid body motion in a resisting medium and analogies with vortex streets

Abstract

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.