The Painlevé paradoxes and the dynamics of a brake shoe

Abstract Using experience gained in studies of the celebrated Painleve-Klein example [1, 2], a mathematical model of a brake shoe is constructed that avoids the Painleve paradoxes. A qualitative analysis of this model (using, in particular, the method of point mappings) has enabled the nature of the possible motions of a brake shoe to be ascertained, and has enabled self-excited oscillations to be observed which may be attributed to dry friction with a characteristic curve, no part of which is descending. As far as is known, this is the first record of this phenomenon, quite normal for automatic control systems, in simple mechanical systems (without servoconstraints).