Three-dimensional, one-point collision with friction

This paper deals with one-point collision with friction in three-dimensional, simple non-holonomic multibody systems. With Keller’s idea regarding the normal impulse as an independent variable during collision, and with Coulomb’s friction law, the system equations of motion reduce to five, coupled, nonlinear, first order differential equations. These equations have a singular point if sticking is reached, and their solution is ‘navigated’ through this singularity in a way leading to either sticking or sliding renewal in a uniquely defined direction. Here, two solutions are presented in connection with Newton’s, Poisson’s and Stronge’s classical collision hypotheses. One is based on numerical integration of the five equations. The other, significantly faster, replaces the integration by a recursive summation. In connection with a two-sled collision problem, close agreement between the two solutions is obtained with a few summation steps.