The Coulomb law of friction and paradoxes of Painlev'e

The application of the Coulomb law has its own specifics related to the non-uniqueness of the solution of the dynamics problems. It was shown (1993), that the Painlev\'e paradoxes appear because of a priori assumptions on the character of motion and the character of the forces needed to induce this motion. The correct statement of the problem requires either to determine the forces by the given motion, or to determine the motion by the given forces [1, 2].
  1. Zhilin P.A., Zhilina O.P. On the Coulomb's laws of friction and the Painlev'e paradoxes // Mechanics and Control. Proc. of St. Petersburg State Technical University. 1993. N 446. P. 52-81. (In Russian).
  2. Wiercigroch M., Zhilin P.A. On the Painleve Paradoxes // “Nonlinear Oscillations in Mechanical Systems”: Proc. of the XXVII Summer Schools. St.-Petersburg. 2000. P. 1-22.