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A Variational Approach to Nonsmooth Dynamics : Applications in Unilateral Mechanics and Electronics / by Samir Adly.
Springer Nature - Springer Mathematics and Statistics eBooks 2017 English International Available online
View online- Format:
- Book
- Author/Creator:
- Adly, Samir., Author.
- Series:
- SpringerBriefs in Mathematics, 2191-8198
- Language:
- English
- Subjects (All):
- Calculus of variations.
- System theory.
- Automatic control.
- Vibration.
- Dynamics.
- Physics.
- Calculus of Variations and Optimal Control; Optimization.
- Systems Theory, Control.
- Control and Systems Theory.
- Vibration, Dynamical Systems, Control.
- Applications of Graph Theory and Complex Networks.
- Local Subjects:
- Calculus of Variations and Optimal Control; Optimization.
- Systems Theory, Control.
- Control and Systems Theory.
- Vibration, Dynamical Systems, Control.
- Applications of Graph Theory and Complex Networks.
- Physical Description:
- 1 online resource (168 pages) : illustrations (some clor).
- Edition:
- 1st ed. 2017.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2017.
- Summary:
- This brief examines mathematical models in nonsmooth mechanics and nonregular electrical circuits, including evolution variational inequalities, complementarity systems, differential inclusions, second-order dynamics, Lur'e systems and Moreau's sweeping process. The field of nonsmooth dynamics is of great interest to mathematicians, mechanicians, automatic controllers and engineers. The present volume acknowledges this transversality and provides a multidisciplinary view as it outlines fundamental results in nonsmooth dynamics and explains how to use them to study various problems in engineering. In particular, the author explores the question of how to redefine the notion of dynamical systems in light of modern variational and nonsmooth analysis. With the aim of bridging between the communities of applied mathematicians, engineers and researchers in control theory and nonlinear systems, this brief outlines both relevant mathematical proofs and models in unilateral mechanics and electronics.
- Contents:
- 1 Mathematical Background
- 2 Nonsmooth Dynamics: An Overview
- 3 Stability Analysis of First-order Nonsmooth Dynamics
- 4 Stability Analysis of Second-order Nonsmooth Dynamics
- 5 Nonsmooth Lur’e Dynamical Systems
- 6 Moreau’s Sweeping Processes
- Historical vignettes
- References
- Index.
- Notes:
- Includes bibliographical references and index.
- ISBN:
- 3-319-68658-5
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