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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

**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.*

**From the Back Cover:**

This significantly enlarged and expanded second edition focuses on a class of nonsmooth hybrid dynamical systems, namely finite-dimensional mechanical systems subject to unilateral constraints. It contains a complete overview of the main problems in mathematics, mechanics, stability and control which are of interest in this field. The following topics are discussed in detail and are illustrated with examples:

· shock dynamics;

· multiple impacts;

· feedback control;

· Moreau's sweeping process; and

· complementarity formulations.

With a comprehensive bibliography of over a thousand references, *Nonsmooth Dynamics* is an indispensable source of information on impact phenomena and rigid-body dynamics.

Praise for the first edition:

The presentation is excellent in combining rigorous mathematics with a great number of examples ranging from simple mechanical systems to robotic systems allowing the reader to understand the basic concepts.

*Mathematical Abstracts*

It is written with clarity, contains the latest research results in the area of impact problems for rigid bodies and is recommended for both applied mathematicians and engineers.

*Mathematical Reviews*

Title: **Nonsmooth Mechanics**

Publisher: **Springer London Ltd**

Publication Date: **2012**

Binding: **Soft cover**

Book Condition: **New**

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**Book Description **Springer London Ltd, United Kingdom, 2012. Paperback. Book Condition: New. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. 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. 2nd ed. 1999. Softcover reprint of the original 2nd ed. 1999. Bookseller Inventory # LIE9781447111610

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**Book Description **Springer London Ltd, United Kingdom, 2012. Paperback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****.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. 2nd ed. 1999. Softcover reprint of the original 2nd ed. 1999. Bookseller Inventory # AAV9781447111610

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**Book Description **Springer London Ltd, 2012. PAP. Book Condition: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # LQ-9781447111610

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**Book Description **Springer London Ltd, United Kingdom, 2012. Paperback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****. 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. 2nd ed. 1999. Softcover reprint of the original 2nd ed. 1999. Bookseller Inventory # AAV9781447111610

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**Book Description **Springer, 2012. Paperback. Book Condition: Good. Ships with Tracking Number! INTERNATIONAL WORLDWIDE Shipping available. May not contain Access Codes or Supplements. Buy with confidence, excellent customer service! 2nd ed. 1999. Softcover reprint of the original 2nd ed. 1999. Bookseller Inventory # 1447111613

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**Book Description **Springer. Paperback. Book Condition: New. Paperback. 552 pages. Dimensions: 9.2in. x 6.1in. x 1.3in.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 systems 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 systems state space. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Bookseller Inventory # 9781447111610

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