Stability of Rectilinear Motion of a Cone Rotating Around the Axis of Symmetry

Resumo

The effect of constant friction on the stability of the rectilinear motion of a cone rotating around the axis of symmetry is considered. It is assumed that the lateral surface of the cone is seamlessly streamlined and that normal stresses and friction act on this surface, which are determined by the method of local interaction. Normal contact stresses are assumed to be proportional to the square of the normal velocity component, and friction is assumed to be constant modulo and acting in the direction of the inverse projection of the velocity vector onto the tangent plane. For frozen velocities of the center of mass and angular velocity of rotation around the axis of symmetry, asymptotic stability criteria are obtained in the form of a system of two inequalities that does not contain integrals. The effect of friction on the stability of the rectilinear motion of a homogeneous cone is studied in detail.