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Nonsmooth Mechanics

Brogliato, Bernard

Published by Springer London Ltd
ISBN 10: 1447111613 / ISBN 13: 9781447111610
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Bibliographic Details


Title: Nonsmooth Mechanics

Publisher: Springer London Ltd

Binding: Soft cover

Book Condition: New

Description:

2012. 2nd ed. 1999. Softcover reprint of the original 2n. Paperback. Series: Communications and Control Engineering. Num Pages: 552 pages, biography. BIC Classification: TGB; TGM; TJF. Category: (P) Professional & Vocational. Dimension: 233 x 156 x 31. Weight in Grams: 802. . . . . . Books ship from the US and Ireland. Bookseller Inventory # V9781447111610

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Synopsis: Thank you for opening the second edition of this monograph, which is devoted to the study of a class of nonsmooth dynamical systems of the general form: ::i; = g(x,u) (0. 1) f(x, t) 2: 0 where x E JRn is the system's state vector, u E JRm is the vector of inputs, and the function f (-, . ) represents a unilateral constraint that is imposed on the state. More precisely, we shall restrict ourselves to a subclass of such systems, namely mechanical systems subject to unilateral constraints on the position, whose dynamical equations may be in a first instance written as: ii= g(q,q,u) (0. 2) f(q, t) 2: 0 where q E JRn is the vector of generalized coordinates of the system and u is an in­ put (or controller) that generally involves a state feedback loop, i. e. u= u(q, q, t, z), with z= Z(z, q, q, t) when the controller is a dynamic state feedback. Mechanical systems composed of rigid bodies interacting fall into this subclass. A general prop­ erty of systems as in (0. 1) and (0. 2) is that their solutions are nonsmooth (with respect to time): Nonsmoothness arises primarily from the occurence of impacts (or collisions, or percussions) in the dynamical behaviour, when the trajectories attain the surface f(x, t) = O. They are necessary to keep the trajectories within the subspace = {x : f(x, t) 2: O} of the system's state space.

Product Description:

This significantly enlarged and expanded second edition, focuses on nonsmooth finite dimensional mechanical systems, subject to unilateral constraints. It contains a complete overview of the main problems in the areas of mathematics, mechanics, stability and control, which are of interest in this field. The following topics are discussed in detail and are illustrated with examples: Short dynamics; Multiple impacts; Feedback control; Moreau's sweeping process; Complimentary formulations. With a comprehensive bibliography of over a thousand references, this book is an indispensable source of information on the subject treated.

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