Mathematical modeling of a medium interaction onto rigid body and new two-parametric family of phase patterns

Mathematical model of a medium interaction onto a rigid body with the part of its interior surface as the cone is considered. The complete system of body motion equations which consists of dynamic and kinematic parts is presented. The dynamic part is formed by the independent three-order subsystem. New family of phase patterns on phase cylinder of quasi-velocities is found. This family consists of infinite set of topologically non-equivalent phase patterns. Furthermore, under the transition from one pattern type to another one, the reconstruction of topological type occurs by the degenerate way. Also the problem of key regime stability, i.e., rectilinear translational deceleration, is discussed.