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 Fr>kFN, where k is the friction coefficient. Differential equations of motion on a rough surface (g, tp, z) = 0 point M of weight g in cylindrical coordinates 1 g, 2 (z axis is directed vertically downwards) - see. article.