Spatiotemporal singular transformation in dynamical systems with impacts and its use in obtaining generalized solution of painleve problem

This work consider classical problems of motion in system with dry friction, known as the Painleve problem. This problem takes place in the presence of collisions of a rod with a flat surface, and the use of the classical mechanics method runs into difficulties due to the impulsive nature of the interaction force that does not lend itself to exact calculations. The methodology suggested by the authors in recent years permits approximating a family of solutions corresponding to a large value of the stiffness coefficient of the obstacle