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This the second volume of five from the 28th IMAC on Structural Dynamics and Renewable Energy, 2010, bringing together 17 chapters on Applications of Non-Linear Dynamics. It presents early findings from experimental and computational investigations on Non-Linear Dynamics including studies on Dynamics of a System of Coupled Oscillators with Geometrically Nonlinear Damping, Assigning the Nonlinear Distortions of a Two-input Single-output System, A Multi-harmonic Approach to Updating Locally Nonlinear Structures, A Block Rocking on a Seesawing Foundation, and Enhanced Order Reduction of Forced Nonlinear Systems Using New Ritz Vectors.

Dynamics -- Congresses. --- Dynamics. --- Nonlinear systems -- Congresses. --- Nonlinear systems. --- Structural dynamics --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Civil Engineering --- Engineering. --- Mathematical models. --- Statistical physics. --- Mechanics. --- Mechanics, Applied. --- Theoretical and Applied Mechanics. --- Nonlinear Dynamics. --- Mathematical Modeling and Industrial Mathematics. --- Mechanics, applied. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Models, Mathematical --- Simulation methods --- Physics --- Mathematical statistics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Statistical methods

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Recently, the subject of nonlinear control systems analysis has grown rapidly and this book provides a simple and self-contained presentation of stability and feedback stabilization methods, which enables the reader to learn and understand major techniques used in mathematical control theory. In particular: • the important techniques of proving global stability properties are presented closely linked with corresponding methods of nonlinear feedback stabilization; • a general framework of methods for proving stability is given, thus allowing the study of a wide class of nonlinear systems, including finite-dimensional systems described by ordinary differential equations, discrete-time systems, systems with delays and sampled-data systems; • approaches to the proof of classical global stability properties are extended to non-classical global stability properties such as non-uniform-in-time stability and input-to-output stability; and • new tools for stability analysis and control design of a wide class of nonlinear systems are introduced. The presentational emphasis of Stability and Stabilization of Nonlinear Systems is theoretical but the theory’s importance for concrete control problems is highlighted with a chapter specifically dedicated to applications and with numerous illustrative examples. Researchers working on nonlinear control theory will find this monograph of interest while graduate students of systems and control can also gain much insight and assistance from the methods and proofs detailed in this book.

Dynamics -- Congresses. --- Nonlinear control theory. --- Nonlinear systems -- Congresses. --- Nonlinear theories. --- Random dynamical systems. --- Stability. --- Stability -- Congresses. --- Nonlinear systems --- Stability --- System theory --- Economics, Mathematical --- Engineering --- Civil & Environmental Engineering --- Mechanical Engineering --- Engineering & Applied Sciences --- Mechanical Engineering - General --- Operations Research --- Nonlinear systems. --- Systems, Nonlinear --- Engineering. --- System theory. --- Statistical physics. --- Control engineering. --- Economic theory. --- Control. --- Systems Theory, Control. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Nonlinear Dynamics. --- Dynamics --- Mechanics --- Motion --- Vibration --- Benjamin-Feir instability --- Equilibrium --- Systems theory. --- Control and Systems Theory. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Economic theory --- Political economy --- Social sciences --- Economic man --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Physics --- Mathematical statistics --- Systems, Theory of --- Systems science --- Science --- Statistical methods --- Philosophy

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This volume contains the invited papers presented at the 9th International Conference "Dynamical Systems — Theory and Applications" held in Lódz, Poland, December 17-20, 2007, dealing with nonlinear dynamical systems. The conference brought together a large group of outstanding scientists and engineers, who deal with various problems of dynamics encountered both in engineering and in daily life. Topics covered include, among others, bifurcations and chaos in mechanical systems; control in dynamical systems; asymptotic methods in nonlinear dynamics; stability of dynamical systems; lumped and continuous systems vibrations; original numerical methods of vibration analysis; and man-machine interactions. Thus, the reader is given an overview of the most recent developments of dynamical systems and can follow the newest trends in this field of science. This book will be of interest to to pure and applied scientists working in the field of nonlinear dynamics.

Dynamics -- Congresses. --- Engineering. --- Nonlinear systems -- Congresses. --- Dynamics --- Nonlinear systems --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Civil Engineering --- Nonlinear control theory. --- Differential equations, Nonlinear. --- System analysis. --- Network theory --- Systems analysis --- Nonlinear differential equations --- Mathematical models. --- Statistical physics. --- Dynamical systems. --- Computational intelligence. --- Structural mechanics. --- Vibration. --- Dynamics. --- Vibration, Dynamical Systems, Control. --- Engineering, general. --- Mathematical Modeling and Industrial Mathematics. --- Structural Mechanics. --- Statistical Physics, Dynamical Systems and Complexity. --- Computational Intelligence. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Cycles --- Sound --- Architectural engineering --- Engineering, Architectural --- Structural mechanics --- Structures, Theory of --- Structural engineering --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Mathematical statistics --- Models, Mathematical --- Simulation methods --- Construction --- Industrial arts --- Technology --- Statistical methods --- Network analysis --- Network science --- System theory --- Mathematical optimization --- Nonlinear theories --- Control theory --- Mechanics. --- Mechanics, Applied. --- Solid Mechanics. --- Complex Systems. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Quantum theory

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This carefully edited book presents a focused debate on the mathematics and physics of chaos, nonlinearity and complexity in nature. It explores the role of non-extensive statistical mechanics in non-equilibrium thermodynamics, and presents an overview of the strong nonlinearity of chaos and complexity in natural systems that draws on the relevant mathematics from topology, measure-theory, inverse and ill-posed problems, set-valued analysis, and nonlinear functional analysis. It presents a self-contained scientific theory of complexity and complex systems as the steady state of non-equilibrium systems, denoting a homeostatic dynamic equilibrium between stabilizing order and destabilizing disorder.

Chaotic behavior in systems --- Nonlinear theories --- Dynamics --- Nonlinear systems. --- Systèmes non linéaires --- Mathematical models. --- Chaos --- Dynamique --- Modèles mathématiques --- Chaotic behavior in systems -- Congresses. --- Electronic books. -- local. --- Nonlinear systems -- Congresses. --- Nonlinear systems --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Civil Engineering --- Applied Mathematics --- Sciences - General --- Mathematical models --- Systems, Nonlinear --- Computer science. --- Computers. --- Artificial intelligence. --- Applied mathematics. --- Engineering mathematics. --- Statistical physics. --- Dynamical systems. --- Vibration. --- Dynamics. --- Computer Science. --- Theory of Computation. --- Appl.Mathematics/Computational Methods of Engineering. --- Statistical Physics, Dynamical Systems and Complexity. --- Artificial Intelligence (incl. Robotics). --- Applications of Mathematics. --- Vibration, Dynamical Systems, Control. --- System theory --- Information theory. --- Mathematics. --- Mathematical and Computational Engineering. --- Complex Systems. --- Artificial Intelligence. --- Cycles --- Mechanics --- Sound --- Math --- Science --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Engineering --- Engineering analysis --- Mathematical analysis --- Communication theory --- Communication --- Cybernetics --- Mathematics --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Physics --- Statics --- Mathematical statistics --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Calculators --- Cyberspace --- Statistical methods --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical physics --- Nonlinearity --- Complex systems