On the problem of free deceleration of a rigid body with the cone front part in a resisting medium

The author constructs the nonlinear mathematical model of the planar interaction of a medium to the rigid body having the circular convex as the front part of its external shape. We make the multi-parametric analysis of dynamic equations of the body motion. We obtain new family of the phase patterns on the phase cylinder of quasi-velocities. This family consists of the infinite set of topologically nonequivalent phase patterns. We also obtain the sufficient conditions of important regime stability, i.e. the rectilinear translational deceleration, and also the conditions of existence of auto-oscillations in the system considered.