Stability of the Vertical Descent of a Heavy Finned Body in a Resisting Medium

Abstract

The free descent of a finned body in a resisting medium is studied. Fins are installed in such a way that there exists the regime of translational descent with constant speed. Earlier, the descent of a heavy body in the autorotation mode was studied. It arises when the pitch angles of all fins are equal to each other. For descent with autorotation, the general properties and tendencies of motion are described depending on the initial conditions and parameters. In the current paper, the descent of a body is discussed for the case when fins have equal absolute values of the pitch angles, but the signs of these angles alternate. The asymptotic stability of translational descent with constant speed is studied for such fin orientation. Domains of stability are constructed in the plane of the following parameters: pitch angle of the fins and displacement of the center of mass. Fins represented either by circular or rectangular blades are discussed. The domains of stability are compared with that for the autorotation mode. Trajectories of the center of mass are constructed. Varied types of such trajectories are obtained when the parameters of the model correspond to the case of unstable translation descent with constant speed.