Static friction indeterminacy problems and modeling of stick-slip phenomenon in discrete dynamic systems

The paper presents a new method of modeling of the friction action in discrete dynamic systems in cases of undetermined distribution of static friction forces. This method is based on the Gauss Principle and the piecewise linear $ \luz(\ldots)$ and $ \tar(\ldots)$ projections with their original mathematical apparatus. The derived variable-structure model of a two-body system with three frictional contacts describes the stick-slip phenomenon in detail. The model has an analytical form applicable to standard (without iterations) computational procedures.