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One of the drawbacks of classical hydraulic system models consists in the fact, that the simulation programs couple the hydraulic components by compressible joints. Since the compressibility of oil is very small, we get stiff differential equations. To avoid these difficulties stiff elastic couplings can be replaced by unilateral constraints. Examples for hydraulic components with unilateral behavior are check valves, cylinders with stop limits and fluid volumes, in which cavitation can occur. The resulting complementarity equations can be solved with a standard Lemke algorithm. Compared to conventional methods, this leads to a significant reduction of computing times.

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.

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