i) Since a Lagrangian system is a point moving in its configuration space, it is natural to apply contact-impact rules using this point of view. More clearly, unilateral constraints define domains of the configuration space, and the point that represents the system strikes the boundaries of these domains (we already took this point of view in chapter 5, section 5.3). At the times of these “generalized” collisions, one needs additional informations to be able to calculate the post-impact values (recall that this is a basic fact of nonsmooth impact mechanics, see e.g. (4.25)): these may be named generalized restitution rules. Notice that this has to be considered exactly at the same level as the sweeping process formulation described in chapter 5: one provides a particular evolution problem, and tries to prove its theoretical coherence and practical usefulness if possible. In the same way as the sweeping process formulation extends purely inelastic impacts to complex systems, generalized restitution rules in the configuration space extend restitution rules for particles to more complex Lagrangian systems.
KeywordsConfiguration Space Generalize Impact Impact Time Unilateral Constraint Multiple Impact
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