## Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry FrictionThis book is devoted to the sndy of some clifferentia.l inclusions motivated by Mechanics and of existcnce rcsults for the dynamics of systems with inelastic shocks, with or without friction. This ensures a certain unity of subject, techniques and applications, at the price of not including some earlier works [Mon 1-4] . In the introductory Chapter 0, sevcral essentia.l mathematical tools (either recent or recently rediscoven~d) are presented. l\1ainly they concern functions of bouncled variation defincd in real interva.ls ( deriva.tion of Stieltjcs measures, compactness results. convergencrc in tlw sense of graphs) a.ncl geometrical inequa.lities. In Chapters 1 and 2, Ivforea.u' s swecpiug process is considcred; this is a first-order differential inclusion (1) where the right-ha.nd siele is tla:' outw |

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### Contents

Sweeping Processes by Convex Scts with Noncmpty Interior | 45 |

Chapter 3 | 77 |

Chapter 4 | 113 |

Copyright | |

2 other sections not shown

### Other editions - View all

Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry ... Monteiro Marques No preview available - 1993 |

Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry ... Monteiro Marques No preview available - 2013 |

### Common terms and phrases

absolutely continuous apply approximants arbitrary assume assumption ball Banach space belongs bounded variation Chapter choose closed convex Cn(t compact condition cone consider constant constraint contained continuous function convergence converges uniformly convex set defined definition denote differential inclusion dist ensure equals equation equivalent estimate example existence fact finite fixed formulation friction function function of bounded given gives Hence Hilbert space holds implies inequality initial value instance integral interval Lemma limit Lipschitz-continuous lower semicontinuous measure Moreau Moreover motion multifunction neighbourhood nonempty interior norm normal Notice obtain particular pointwisely positive problem projection Proof Proposition prove rcbv function Remark respect result right-continuous satisfies selection sense sequence shocks shown similar solution subsequence subsets sweeping process Theorem un(t unique ut(t write zero