On the movement of support points along a helical line on a rough surface (On the theory of a spiral separator)

Abstract

Generalizing the Catalan problem about the motion of a point rotating on a polished surface, the author searches for surfaces that allow the motion of a point rotating in a spiral with a vertical axis in the presence of friction, and explores the nature of the stability of the motion of a point of rotation on a spiral located on a rough helical surface with a vertical axis, and also the influence on this movement of the resistance of the environment, depending on the speed, and the rotation of the surface around the aerodynamic propellers.