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Di erential Equations, Vol. 37, No. 3, 2001, pp. 367{376. Translated from Di erentsial'nye Uravneniya, Vol. 37, No. 3, 2001, pp. 343{351. Original Russian Text Copyright c 2001 by Matrosov. ORDINARY DIFFERENTIAL EQUATIONS Solvability of the Equations of Motion of a Mechanical System with Dry Friction I. V. Matrosov Moscow State University, Moscow, Russia Received March 17, 2000 INTRODUCTION We consider the equations of motion of a mechanical system containing kinematic pairs with dry friction forces. By the Coulomb law, these forces are proportional to the absolute values of normal reactions [1, 2]. The rst attempt to construct a theory of such systems was made by Painleve[3]. He showed that the equations of motion of such a system may not have a solution in the classical sense even outside the surfaces of discontinuity of the right-hand side. Analytic dynamics of systems with dry friction was later developed in [4{6] under the assumption that the solution exists. The existence of a right-sided solution was proved in [7] for the case in which each friction force depends only on one generalized velocity and one normal reaction, but, in this approach, one has to nd the normal reactions. In the present paper,
Differential Equations – Springer Journals
Published: Oct 17, 2004
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