SOME CLASSES OF PARTICULAR SOLUTIONS IN THE DYNAMICS OF A RIGID BODY INTERACTING WITH A MEDIUM

The plane-parallel motion of a rigid body in a resisting medium is studied in the cases of a jet or separation flow of the ambient medium [1, 2]. Earlier [3,4], for a linear mathematical model of the drag of the body, it was shown that the translational motions of the body are, as a rule, unstable. The investigation of possible oscillatory motions in the system requires taking into account nonlinear effects [5-7] and developing an analytic technique facilitating the global qualitative analysis. As was the case in [5-8], we investigate in the present paper the free dragged motion of the body. This case is the most important from the applied point of view. However, unlike [5-8], we obtain some analytical classes of particular solutions that correspond to stable and unstable singular points, which exist only under some additional conditions on the coefficients of the full nonlinear system of differential equations. In particular, a domain in the space of parameters is separated that goes to infinity and admits an (absolutely) structurally stable global phase portrait.