However, they are only an approximation to a full elastic model requiring complex systems of partial differential equations.
[3] In the same decade, Franck Génot and Bernard Brogliato, published an explanation of the paradox from a more mechanical point of view, introducing the GB-points (or manifolds).
Another situation (different from the first one) is that the trajectories may attain a zone in the phase space, where the linear complementarity problem (LCP) that gives the contact force, has no solution.
[6] Following the discovery of Genot and Brogliato, Hogan, Cheesman and their coworkers made an in-depth analysis of the Painleve paradox in dimension 3.
[8][9] It is noteworthy that J. J. Moreau has shown in his seminal paper[10] through numerical simulation with his time-stepping scheme (afterwards called Moreau's scheme) that Painlevé paradoxes can be simulated with suitable time-stepping methods, for the above reasons given later by Génot and Brogliato.