Abstract

Using a full rigid body model, Painlevé (1895) found that inconsistency (no solution) or indeterminacy (non-unique solution) can occur in analyses of oblique impact for rigid bodies colliding against a contact surface with a large coefficient of friction. This dynamic phenomenon is called Painlevé paradox. Mainly, this talk focuses on explaining the cause of Painlevé paradox and describing how to resolve the problem. The assumptions of a rigid body model and their contribution to the Painlevé paradox are explained thoroughly from 3 aspects including constraint conditions, governing equations and physics behaviour. The Painlevé paradox can be resolved by considering the compliance of the contact region between the colliding bodies. Based on a hybrid analytical model, a unique solution is obtained for the case of Painlevé paradox. The dynamic properties of this paradox are investigated further. Theoretical analysis indicates that, other than a case of β32=0, Painlevé paradox only occurs in a region of Linear Complementarity Problem (LCP) identical to the jam (self-locking) region of oblique impact. Irrespective of the initial value of tangential relative velocity, the jam process always goes through three periods: sliding, stick, and terminal (reverse) sliding.