Painleve paradox during oblique impact with friction

In analyses using non-smooth dynamics, oblique impact of rough bodies in an unsymmetrical configuration can result in self-locking or jam at the sliding contact if the coefficient of friction is sufficiently large: this has been termed, Painleve's paradox. In the range of configurations and coefficients of friction where Painleve's paradox occurs, analyses based on rigid body dynamics give results indicating that either there are multiple solutions or the solution is nonexistent. This conundrum has been resolved by considering that the contact has small normal and tangential compliance which is representative of deformability in a local region around the contact point. An analysis using a hybrid model which includes local compliance of the contact region has calculated the time-dependent changes in relative motion of colliding bodies for a range of incident angles of obliquity, tan(-1)[-V-1(0)/V-3(0)] where V-1(0)and V-3(0) are the incident tangential and normal relative velocities at the contact point, respectively. The paradox is shown to result from a negative relative acceleration of the contact points during an initial period of sliding - a negative acceleration that is inconsistent with the assumption of rigid-body contact. (C) 2011 Elsevier Masson SAS. All rights reserved.