On a mechanical lens

Alexander P. Ivanov^a, Nadezhda N. Erdakova<sup>b

a</sup> Moscow Institute of Physics and Technology, Institutskii per., 9, Dolgoprudny, Moscow Region, 141700, Russia
^b Udmurt State University, Laboratory of Nonlinear Analysis and the Design of New Types of Vehicles, Universitetskaya st. 1, Izhevsk, 426034, Russia

Abstract: The problem of dynamics of heavy uniform ball moving on the fixed rough plane under its own inertia and forces of dry friction is considered. Assuming that friction coefficient is variable, the switching curve for change the value of friction coefficient is constructed. Using this curve to change the value of friction coefficient we have shown that the bundle of equal balls starting from one interval with equal linear and angular velocities should gather at one point.

Keywords: dry friction, variable friction coefficient, ball's dynamics.

UDC: 531.37

MSC: 70E18; 70F40

Received: 30.07.2012
Revised: 15.08.2012