On Termination of Motion in Some Mechanical System with Coulomb Friction

We consider a mass particle moving on a horizontal plane. The particle is subjected to the Coulomb friction force and a central force with value proportional to the distance between the particle and the center. Such a central force can be modeled by a spring. The question is: does the particle stop for any initial conditions in a finite time? The answer «yes» is physically evident nevertheless an accurate proof turns out to be surprisingly complicated. It eventually comes to an asymptotic analysis of the solution in a neighborhood of the degenerate equilibrium in some smooth nonlinear system. In this paper we provide the formal proof. We also formulate some open problem.