To the question of the shape of the spatial curve of the fastest descent in the conditions of its rotation

Abstract

Abstract The non-linear system of dynamic equations of the movement of the ball, sliding down on rotating with frequency ω on one-dimensional gutter of arbitrary form, is obtained. From the minimum sliding time. defined by the form of this curve. Taking into account the forces of dry and viscous friction, the results of the analytical and numerical solution of the received system of equations are presented.