Nonsmooth Mechanics by Bernard Brogliato

Author:Bernard Brogliato
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

5.5.5.2 Sticking Contact

Let us now assume that the contact is established with and is in a sticking mode (and ). As for the foregoing system, our objective is to use the acceleration Coulomb’s law to determine the conditions for stick/slip transitions with , or such that sticking persists with . Additional conditions are and (for if the constraint is deactivated and ). If one wants to study the conditions under which contact persists then one adds , which forces a particular mode of the contact LCP (we call it the normal/tangential stick/stick mode). But if one admits that the system may detach from the constraint then and the contact LCP holds.

The normal/tangential stick/stick mode implies that , and using the dynamical equation one finds , . The constraint of the friction cone then implies that , hence . In such a case .

One has , with , , , where the first equation in (5.162) has been used. When Coulomb’s law in acceleration states that . Therefore, the stick/slip transition may occur if and only if the following generalized equation :

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