Sthenic incompatibilities in rigid bodies motion

When a rigid body slides with friction on a surface, hopping motion is observed: this is an everyday phenomenon. In rigid bodies mechanics, this phenomenon appears when it is no longer possible to compute the reaction contact forces. The difficulty is overcome by a motion theory involving velocity discontinuities. Velocity discontinuities may result either from an obstacle which makes impossible to compute the acceleration: this is a cinematic incompatibility or from the impossibility to compute the reaction forces: this is a sthenic incompatibility. We describe two examples: the Klein and Painlevé sthenic incompatibilities. Springer 2006.