Fundamentals of Theory of Friction

The monograph is devoted to the systematic statement of the main methods of analysis of the mechanical systems with friction. It’s a compilation of known and original results covering all phases of the problem solving: the description of friction with a glance to kinematic and dynamic characteristics, the formulation of equations of motion in a standard form, the study of the properties of these equations’ solution. The possibility of the application of general principles of mechanics to frictional systems is discussed; the idea of dynamic matching of friction law with the system configuration is stated and grounded. Much consideration is given to the qualitative investigation of dynamics including the stability analysis of the classification of the bifurcations of the equilibrium positions and of the periodic motions. The author presents the detailed exposition of the specific features of systems with friction including so called paradoxes of Painleve and Gellette and new paradoxes related to the specification of the state of unilateral constraints with friction. The book is intended to specialists in the field of theoretical mechanics and nonsmooth dynamics, as well as to advanced students and postgraduate students.