Presents a systematic view of vibro-impact dynamics based on the nonlinear dynamics analysis Comprehensive understanding of any vibro-impact system is critically impeded by the lack of analytical tools viable for properly characterizing grazing bifurcation. The authors establish vibro-impact dynamics as a subset of the theory of discontinuous systems, thus enabling all vibro-impact systems to be explored and characterized for applications. Vibro-impact Dynamics presents an original theoretical way of analyzing the behavior of vibro-impact dynamics that can be extended to discontinuous dynamics. All topics are logically integrated to allow for vibro-impact dynamics, the central theme, to be presented. It provides a unified treatment on the topic with a sound theoretical base that is applicable to both continuous and discrete systems Vibro-impact Dynamics: <ul>
<li>Presents mapping dynamics to determine bifurcation and chaos in vibro-impact systems</li> <li>Offers two simple vibro-impact systems with comprehensive physical interpretation of complex motions</li> <li>Uses the theory for discontinuous dynamical systems on time-varying domains, to investigate the Fermi-oscillator</li> </ul>
Essential reading for graduate students, university professors, researchers and scientists in mechanical engineering.

Vibro-impact Dynamics

Science & Math

Guo, Yu

Luo, Albert C.J.

Physics

wiley

Exact analytical solutions to periodic motions in nonlinear dynamical systems are almost not possible. Since the 18th century, one has extensively used techniques such as perturbation methods to obtain approximate analytical solutions of periodic motions in nonlinear systems. However, the perturbation methods cannot provide the enough accuracy of analytical solutions of periodic motions in nonlinear dynamical systems. So the bifurcation trees of periodic motions to chaos cannot be achieved analytically. The author has developed an analytical technique that is more effective to achieve periodic motions and corresponding bifurcation trees to chaos analytically. Toward Analytical Chaos in Nonlinear Systems systematically presents a new approach to analytically determine periodic flows to chaos or quasi-periodic flows in nonlinear dynamical systems with/without time-delay. It covers the mathematical theory and includes two examples of nonlinear systems with/without time-delay in engineering and physics. From the analytical solutions, the routes from periodic motions to chaos are developed analytically rather than the incomplete numerical routes to chaos. The analytical techniques presented will provide a better understanding of regularity and complexity of periodic motions and chaos in nonlinear dynamical systems. Key features: <ul>
<li>Presents the mathematical theory of analytical solutions of periodic flows to chaos or quasieriodic flows in nonlinear dynamical systems</li> <li>Covers nonlinear dynamical systems and nonlinear vibration systems</li> <li>Presents accurate, analytical solutions of stable and unstable periodic flows for popular nonlinear systems</li> <li>Includes two complete sample systems</li> <li>Discusses time-delayed, nonlinear systems and time-delayed, nonlinear vibrational systems</li> <li>Includes real world examples</li> </ul>
Toward Analytical Chaos in Nonlinear Systems is a comprehensive reference for researchers and practitioners across engineering, mathematics and physics disciplines, and is also a useful source of information for graduate and senior undergraduate students in these areas.

Toward Analytical Chaos in Nonlinear Systems

Mathematics

Nonlinear problems are of interest to engineers, physicists and mathematicians and many other scientists because most systems are inherently nonlinear in nature. As nonlinear equations are difficult to solve, nonlinear systems are commonly approximated by linear equations. This works well up to some accuracy and some range for the input values, but some interesting phenomena such as chaos and singularities are hidden by linearization and perturbation analysis. It follows that some aspects of the behavior of a nonlinear system appear commonly to be chaotic, unpredictable or counterintuitive. Although such a chaotic behavior may resemble a random behavior, it is absolutely deterministic. Analytical Routes to Chaos in Nonlinear Engineering discusses analytical solutions of periodic motions to chaos or quasi-periodic motions in nonlinear dynamical systems in engineering and considers engineering applications, design, and control. It systematically discusses complex nonlinear phenomena in engineering nonlinear systems, including the periodically forced Duffing oscillator, nonlinear self-excited systems, nonlinear parametric systems and nonlinear rotor systems. Nonlinear models used in engineering are also presented and a brief history of the topic is provided. Key features: <ul>
<li>Considers engineering applications, design and control</li> <li>Presents analytical techniques to show how to find the periodic motions to chaos in nonlinear dynamical systems</li> <li>Systematically discusses complex nonlinear phenomena in engineering nonlinear systems</li> <li>Presents extensively used nonlinear models in engineering</li> </ul>
Analytical Routes to Chaos in Nonlinear Engineering is a practical reference for researchers and practitioners across engineering, mathematics and physics disciplines, and is also a useful source of information for graduate and senior undergraduate students in these areas.

Analytical Routes to Chaos in Nonlinear Engineering

Computers & Technology

Computer Science

Machine Tool Vibrations and Cutting Dynamics

“Machine Tool Vibrations and Cutting Dynamics” covers the fundamentals of cutting dynamics from the perspective of discontinuous systems theory. It shows the reader how to use coupling, interaction, and different cutting states to mitigate machining instability and enable better machine tool design. Among the topics discussed are; underlying dynamics of cutting and interruptions in cutting motions; the operation of the machine-tool systems over a broad range of operating conditions with minimal vibration and the need for high precision, high yield micro- and nano-machining.

Suh, C. Steve

Gegg, Brandon C.

Springer

Nonlinear and Complex Dynamics: Applications in Physical, Biological, and Financial Systems

Nonlinear Dynamics of Complex Systems describes chaos, fractal and stochasticities within celestial mechanics, financial systems and biochemical systems. Part I discusses methods and applications in celestial systems and new results in such areas as low energy impact dynamics, low-thrust planar trajectories to the moon and earth-to-halo transfers in the sun, earth and moon. Part II presents the dynamics of complex systems including bio-systems, neural systems, chemical systems and hydro-dynamical systems. Finally, Part III covers economic and financial systems including market uncertainty, inflation, economic activity and foreign competition and the role of nonlinear dynamics in each.

Baleanu, Dumitru

Machado, José António Tenreiro

Reference

Regularity and Complexity in Dynamical Systems describes periodic and chaotic behaviors in dynamical systems, including continuous, discrete, impulsive, discontinuous, and switching systems. In traditional analysis, the periodic and chaotic behaviors in continuous, nonlinear dynamical systems were extensively discussed even if unsolved. In recent years, there has been an increasing amount of interest in periodic and chaotic behaviors in discontinuous dynamical systems because such dynamical systems are prevalent in engineering. Usually, the smoothening of discontinuous dynamical system is adopted in order to use the theory of continuous dynamical systems. However, such technique cannot provide suitable results in such discontinuous systems. In this book, an alternative way is presented to discuss the periodic and chaotic behaviors in discontinuous dynamical systems.

Regularity and Complexity in Dynamical Systems

Exploring periodic and chaotic behaviors in discontinuous dynamical systems, including impulsive, discontinuous, and switching systems, this book offers new concepts in discontinuous systems and the smoothening of discontinuity misleading dynamical behaviors.

Regularity and Complexity in Dynamical Systems (Nonlinear Systems and Complexity, 1)

This book examines nonlinear dynamics - chaos, fractals and stochasticities - in such diverse settings as celestial mechanics including impact dynamics, financial systems including inflation and biochemical systems, such as neural and hydro-dynamic systems.

Machado, José António Tenreiro Tenreiro

The inherent complex dynamics of a parametrically excited pendulum is of great interest in nonlinear dynamics, which can help one better understand the complex world. Even though the parametrically excited pendulum is one of the simplest nonlinear systems, until now, complex motions in such a parametric pendulum cannot be achieved. In this book, the bifurcation dynamics of periodic motions to chaos in a damped, parametrically excited pendulum is discussed. Complete bifurcation trees of periodic motions to chaos in the parametrically excited pendulum include: <ul> <li>period-1 motion (static equilibriums) to chaos, and</li> <li>period- motions to chaos ( = 1, 2, ---, 6, 8, ---, 12).</li> </ul> The aforesaid bifurcation trees of periodic motions to chaos coexist in the same parameter ranges, which are very difficult to determine through traditional analysis. Harmonic frequency-amplitude characteristics of such bifurcation trees are also presented to show motion complexity and nonlinearity in such a parametrically excited pendulum system. The non-travelable and travelable periodic motions on the bifurcation trees are discovered. Through the bifurcation trees of travelable and non-travelable periodic motions, the travelable and non-travelable chaos in the parametrically excited pendulum can be achieved. Based on the traditional analysis, one cannot achieve the adequate solutions presented herein for periodic motions to chaos in the parametrically excited pendulum. The results in this book may cause one rethinking how to determine motion complexity in nonlinear dynamical systems.

Bifurcation Dynamics of a Damped Parametric Pendulum (Synthesis Lectures on Mechanical Engineering, 22)

Morgan & Claypool Publishers

The Brusselator is a mathematical model for autocatalytic reaction, which was proposed by Ilya Prigogine and his collaborators at the Université Libre de Bruxelles. The dynamics of the Brusselator gives an oscillating reaction mechanism for an autocatalytic, oscillating chemical reaction. The Brusselator is a slow-fast oscillating chemical reaction system. The traditional analytical methods cannot provide analytical solutions of such slow-fast oscillating reaction, and numerical simulations cannot provide a full picture of periodic evolutions in the Brusselator. In this book, the generalized harmonic balance methods are employed for analytical solutions of periodic evolutions of the Brusselator with a harmonic diffusion. The bifurcation tree of period-1 motion to chaos of the Brusselator is presented through frequency-amplitude characteristics, which be measured in frequency domains. Two main results presented in this book are: <ul> <li>analytical routes of periodical evolutions to chaos and</li> <li>independent period-(2&#119897; + 1) evolution to chaos.</li> </ul> This book gives a better understanding of periodic evolutions to chaos in the slow-fast varying Brusselator system, and the bifurcation tree of period-1 evolution to chaos is clearly demonstrated, which can help one understand routes of periodic evolutions to chaos in chemical reaction oscillators. The slow-fast varying systems extensively exist in biological systems and disease dynamical systems. The methodology presented in this book can be used to investigate the slow-fast varying oscillating motions in biological systems and disease dynamical systems for a better understanding of how infectious diseases spread.

Towards Analytical Chaotic Evolutions in Brusselators (Synthesis Lectures on Materials and Optics)

Guo, Siyu

Morgan Claypool

See the best price to sell, buy, or rent books by Luo, Albert C.J.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Luo, Albert C.J.

See the best price to sell, buy, or rent books by Luo, Albert C.J.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Vibro-impact Dynamics

Toward Analytical Chaos in Nonlinear Systems

Analytical Routes to Chaos in Nonlinear Engineering

Machine Tool Vibrations and Cutting Dynamics

Nonlinear and Complex Dynamics: Applications in Physical, Biological, and Financial Systems

Regularity and Complexity in Dynamical Systems

Regularity and Complexity in Dynamical Systems (Nonlinear Systems and Complexity, 1)

Nonlinear and Complex Dynamics: Applications in Physical, Biological, and Financial Systems

Bifurcation Dynamics of a Damped Parametric Pendulum (Synthesis Lectures on Mechanical Engineering, 22)

Towards Analytical Chaotic Evolutions in Brusselators (Synthesis Lectures on Materials and Optics)