On the movement of a heavy point along a rough helical surface with a vertical axis

Abstract

Let FT and Fn be the absolute values ​​of the tangent and normal to the surface components of the weight force acting on a point. A point placed on a surface without an initial velocity” remains in equilibrium in the presence of friction if Fr~kFN> and begins to move if Ft ⩾ kFn, where k is the friction coefficient. Differential equations of motion on a rough surface (r, φ, z) = 0 point M of weight g in cylindrical coordinates r, φ, z (z axis is directed vertically downwards) - see. article.