Motion of a rigid body with frontal cone in a resistive medium: Qualitative analysis and integrability

We consider a mathematical model of the plane-parallel action of a medium on a rigid body whose surface contains a cone-shaped being part. A complete system of equations of motion under in the quasi-stationary case is presented. A new family of phase portraits on the phase cylinder of quasi-velocity is obtained. Also, we consider a mathematical model of the influence of the medium on an axisymmetric body whose surface contains a cone-shaped part. We examine the stability with respect to a part of variables of the key mode, namely, the spatial rectilinear translational deceleration of the body. The problem of integrability is discussed.