Titlebook: Nonsmooth Mechanics; Models, Dynamics and Bernard Brogliato Book 19992nd edition Springer-Verlag London 1999 Control.Control Theory.Impact.

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Bernard Brogliato PhDriginal phrase reportedly meant it as a sarcastic snipe, a criticism of those who would bulldoze their way across the frontier with the self-serving intent to acquire and exploit vast new land tracts for their own private control and profit.

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Distributional model of impacts,thout mentioning constraints. Then unilateral constraints are presented without speaking of contact forces. Emphasis is put on measure differential equations (MDEs), and on the difference between several types of MDEs and those which represent the dynamics of mechanical systems with unilateral const

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Approximating problems,vantage of providing an attractive framework of impact dynamics. Note however that bodies that collide do possess a certain compliance, so that the collision duration is strictly positive (.) and local deformations occur near the point of impact. Actually global (vibrational) deformations are also c

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Variational principles,erive extensions to basic tools of classical mechanics, e.g.. the . and the . in the case of impacts phenomena. From the rigid body assumption, it can be shown that the theorems of the linear and angular momenta can be easily retrieved (see chapter 4), and that they do not depend on the chosen frame

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Two bodies colliding,ooth dynamics and the unilateral constraints is not complete, since one needs the knowledge of the behaviour of the system on the constraints surface to investigate global motion. In fact, the behaviour at the impact is generally modeled by a set of coefficients (not necessarily constant) that relat

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Multiconstraint nonsmooth dynamics,iculties encountered when several constraints are present. Some simple examples are used to introduce the problem. Then we present a general method, the so-called ., that consists of a particular way of writing the dynamical equations of systems with unilateral constraints, through specific measure

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Stability of nonsmooth dynamical systems,tence, uniqueness, continuous dependence on initial conditions and parameters. Roughly, we have seen that those dynamical systems are represented by measure differential equations (MDEs). We have also discussed the differences between dynamical equations of systems with unilateral constraints and MD

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