On the Structure of Multiple Impact Systems

Multibody systems including impacts with friction possess a rich dynamical structure, mainly due to their non-smooth and therefore highly nonlinear characteristics together with the variety of multiple contact possibilities. Existing theories describe such situations efficiently and correctly as has been proven by many practical applications. It can be shown, that even in large multibody systems with many possible impacts very seldom two or more impacts occur at exactly the same time, usually impacts are separated from each other. From this it makes sense to consider in more detail the structure of one impact alone and to investigate the functional dependencies with respect to the initial magnitudes, namely normal and tangential relative velocities and normal and tangential impulses before an impact. This paper describes the theory and gives examples.