Characteristic features of the high-velocity motion of bodies in dense media

The characteristic features of the high-velocity motion of conical and pyramidal bodies are investigated when the force acting on their surface is described by a local interaction model. It is assumed that the pressure on the body surface is represented by a binomial formula that is quadratic in the velocity. Three friction models are used to represent the tangential stresses: constant friction, friction that is proportional to the pressure and mixed friction. Analytical solutions of problems of the plane inertial motion of slender bodies with a base contour in the form of a circle, a rhombus or a star consisting of four cycles are constructed for an unseparated flow past the bodies and small perturbations imposed on the parameters of the linear motion at the initial instant of time. A criterion for the stability of the motion is found that enables the perturbed motion of the body to be determined when the medium parameters and the velocity, mass and shape of the body are known. The analytical results are validated by a numerical solution of the Cauchy problem for a system of equations of motion obtained without simplifying assumptions.