The Complexity of a Basic Impact Mapping for Rigid Bodies with Impacts and Friction

We consider two impact mappings, the Brach impact mapping and an energetic impact mapping, for rigid-body mechanisms with impacts and friction. The two impact mappings represent the opposite end of the spectrum from basic to advanced impact mappings. Both impact mappings are briefly derived and described. For the Brach impact mapping we will introduce the concept of impulse ratio and discuss how the kinetic energy changes during an impact as the impulse ratio is varied. This analysis is used to further extend the Brach impact mapping to cover situations that were previously omitted. Finally, we make comparisons between the two impact mappings and show how the Painlevé paradox appears in the two impact mappings. The conclusion of the comparisons is that while the basic impact mapping seems easy to implement in a computer simulator it may in the end be more complex and also introduce unnecessary complications that are completely artificial.