Rough Balanced Collisions

In multibody systems, balanced collisions—in which the sliding velocity would not change if friction was negligible—are a generalization of central collisions. For them Newton’s and Poisson’s rules are energetically consistent, but even though they are applied an “all linear solution” does not exist if the sliding varies its direction and does not stop. The properties of these collisions are reviewed, the hodographs of the sliding velocity are calculated and used to develop a systematic method to integrate the equations of motion that relies on a single integration from which the remaining unknowns are calculated by means of algebric expressions.