Nonsmooth Mechanics: Models, Dynamics and Control (Communications and Control Engineering) - Hardcover

Brogliato, Bernard

Hardcover

ISBN 10: 1852331437 ISBN 13: 9781852331436

Publisher: Springer, 1999

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.

About this title

Product Description:

Nonsmooth Mechanics Focuses on a class of nonsmooth hybrid dynamical systems, namely finite-dimensional mechanical systems subject to unilateral constraints. This book contains overview of the main problems in mathematics, mechanics, stability and control. It discusses such topics as: shock dynamics; multiple impacts; feedback control; and, Moreau's sweeping process.

Review:

From reviews for the first edition:

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 1998f (Reviewer: P.D. Panagiotopoulos)

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 (Reviewer: H. Troger)

About this edition

• Publisher: Springer
• Publication date: 1999
• ISBN 10: 1852331437
• ISBN 13: 9781852331436
• Binding: Hardcover
• Edition number: 2
• Number of pages: 552