Two Dimensional Self Independent Variable Cubic Nonlinear Systems
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Two Dimensional Self Independent Variable Cubic Nonlinear Systems
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Author : Albert C. J. Luo
language : en
Publisher: Springer Nature
Release Date : 2024-11-07
Two Dimensional Self Independent Variable Cubic Nonlinear Systems written by Albert C. J. Luo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-07 with Science categories.
This book, the third of 15 related monographs, presents systematically a theory of self-independent cubic nonlinear systems. Here, at least one vector field is self-cubic, and the other vector field can be constant, self-linear, self-quadratic, or self-cubic. For constant vector fields in this book, the dynamical systems possess 1-dimensional flows, such as source, sink and saddle flows, plus third-order source and sink flows. For self-linear and self-cubic systems discussed, the dynamical systems possess source, sink and saddle equilibriums, saddle-source and saddle-sink, third-order sink and source (i.e, (3rd SI:SI)-sink and (3rdSO:SO)-source) and third-order source (i.e., (3rd SO:SI)-saddle, (3rd SI, SO)-saddle) . For self-quadratic and self-cubic systems, in addition to the first and third-order sink, source and saddles plus saddle-source and saddle-sink, there are (3:2)-saddle-sink and (3:2) saddle-source and double-saddles. For the two self-cubic systems, (3:3)-source, sink and saddles exist. Finally, the author describes that homoclinic orbits without centers can be formed, and the corresponding homoclinic networks of source, sink and saddles exists. Readers will learn new concepts, theory, phenomena, and analytic techniques, including Constant and crossing-cubic systems Crossing-linear and crossing-cubic systems Crossing-quadratic and crossing-cubic systems Crossing-cubic and crossing-cubic systems Appearing and switching bifurcations Third-order centers and saddles Parabola-saddles and inflection-saddles Homoclinic-orbit network with centers Appearing bifurcations
Two Dimensional Single Variable Cubic Nonlinear Systems Vol Ii
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Author : Albert C. J. Luo
language : en
Publisher: Springer Nature
Release Date : 2024-11-19
Two Dimensional Single Variable Cubic Nonlinear Systems Vol Ii written by Albert C. J. Luo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-19 with Science categories.
This book, the second of 15 related monographs, presents systematically a theory of cubic nonlinear systems with single-variable vector fields. The cubic vector fields are of crossing-variables, which are discussed as the second part. The 1-dimensional flow singularity and bifurcations are discussed in such cubic systems. The appearing and switching bifurcations of the 1-dimensional flows in such 2-diemnsional cubic systems are for the first time to be presented. Third-order parabola flows are presented, and the upper and lower saddle flows are also presented. The infinite-equilibriums are the switching bifurcations for the first and third-order parabola flows, and inflection flows with the first source and sink flows, and the upper and lower-saddle flows. The appearing bifurcations in such cubic systems includes inflection flows and third-order parabola flows, upper and lower-saddle flows. Readers will learn new concepts, theory, phenomena, and analytic techniques, including Constant and crossing-cubic systems Crossing-linear and crossing-cubic systems Crossing-quadratic and crossing-cubic systems Crossing-cubic and crossing-cubic systems Appearing and switching bifurcations Third-order centers and saddles Parabola-saddles and inflection-saddles Homoclinic-orbit network with centers Appearing bifurcations
Limit Cycles And Homoclinic Networks In Two Dimensional Polynomial Systems
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Author : Albert C. J. Luo
language : en
Publisher: Springer Nature
Release Date : 2025-04-17
Limit Cycles And Homoclinic Networks In Two Dimensional Polynomial Systems written by Albert C. J. Luo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-17 with Mathematics categories.
This book is a monograph about limit cycles and homoclinic networks in polynomial systems. The study of dynamical behaviors of polynomial dynamical systems was stimulated by Hilbert’s sixteenth problem in 1900. Many scientists have tried to work on Hilbert's sixteenth problem, but no significant results have been achieved yet. In this book, the properties of equilibriums in planar polynomial dynamical systems are studied. The corresponding first integral manifolds are determined. The homoclinic networks of saddles and centers (or limit cycles) in crossing-univariate polynomial systems are discussed, and the corresponding bifurcation theory is developed. The corresponding first integral manifolds are polynomial functions. The maximum numbers of centers and saddles in homoclinic networks are obtained, and the maximum numbers of sinks, sources, and saddles in homoclinic networks without centers are obtained as well. Such studies are to achieve global dynamics of planar polynomial dynamical systems, which can help one study global behaviors in nonlinear dynamical systems in physics, chemical reaction dynamics, engineering dynamics, and so on. This book is a reference for graduate students and researchers in the field of dynamical systems and control in mathematics, mechanical, and electrical engineering.
Mathematics For Mechanical Engineers
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Author : Frank Kreith
language : en
Publisher: CRC Press
Release Date : 2022-03-30
Mathematics For Mechanical Engineers written by Frank Kreith and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-30 with Technology & Engineering categories.
Mathematics for Mechanical Engineers gives mechanical engineers convenient access to the essential problem solving tools that they use each day. It covers applications employed in many different facets of mechanical engineering, from basic through advanced, to ensure that you will easily find answers you need in this handy guide. For the engineer venturing out of familiar territory, the chapters cover fundamentals like physical constants, derivatives, integrals, Fourier transforms, Bessel functions, and Legendre functions. For the experts, it includes thorough sections on the more advanced topics of partial differential equations, approximation methods, and numerical methods, often used in applications. The guide reviews statistics for analyzing engineering data and making inferences, so professionals can extract useful information even with the presence of randomness and uncertainty. The convenient Mathematics for Mechanical Engineers is an indispensable summary of mathematics processes needed by engineers.
The Engineering Handbook
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Author : Richard C Dorf
language : en
Publisher: CRC Press
Release Date : 2018-10-03
The Engineering Handbook written by Richard C Dorf and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Technology & Engineering categories.
First published in 1995, The Engineering Handbook quickly became the definitive engineering reference. Although it remains a bestseller, the many advances realized in traditional engineering fields along with the emergence and rapid growth of fields such as biomedical engineering, computer engineering, and nanotechnology mean that the time has come to bring this standard-setting reference up to date. New in the Second Edition 19 completely new chapters addressing important topics in bioinstrumentation, control systems, nanotechnology, image and signal processing, electronics, environmental systems, structural systems 131 chapters fully revised and updated Expanded lists of engineering associations and societies The Engineering Handbook, Second Edition is designed to enlighten experts in areas outside their own specialties, to refresh the knowledge of mature practitioners, and to educate engineering novices. Whether you work in industry, government, or academia, this is simply the best, most useful engineering reference you can have in your personal, office, or institutional library.
Solitons And Particles
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Author : Giulio Soliani
language : en
Publisher: World Scientific
Release Date : 1984-12-01
Solitons And Particles written by Giulio Soliani and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-01 with Science categories.
This is the most up-to-date book on solitons and is divided into two parts. Part 1: Detailed introductory lectures on different aspects of solitons plus lectures on the mathematical aspects on this subject. Part 2: Is a collection of reprints on mathematical theories of solitons, solitons in field theory, solitons as particles and their properties, especially topological and physical properties. This book is aimed at a wide audience of physicists and mathematicians. It is an ideal reference book for young researchers and graduate students.
Harmonic Oscillators And Two By Two Matrices In Symmetry Problems In Physics
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Author : Young Suh Kim
language : en
Publisher: MDPI
Release Date : 2018-07-09
Harmonic Oscillators And Two By Two Matrices In Symmetry Problems In Physics written by Young Suh Kim and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-09 with Mathematics categories.
This book is a printed edition of the Special Issue "Harmonic Oscillators In Modern Physics" that was published in Symmetry
Analytical Properties Of Nonlinear Partial Differential Equations
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Author : Alexei Cheviakov
language : en
Publisher: Springer Nature
Release Date : 2024-03-22
Analytical Properties Of Nonlinear Partial Differential Equations written by Alexei Cheviakov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-22 with Mathematics categories.
Nonlinear partial differential equations (PDE) are at the core of mathematical modeling. In the past decades and recent years, multiple analytical methods to study various aspects of the mathematical structure of nonlinear PDEs have been developed. Those aspects include C- and S-integrability, Lagrangian and Hamiltonian formulations, equivalence transformations, local and nonlocal symmetries, conservation laws, and more. Modern computational approaches and symbolic software can be employed to systematically derive and use such properties, and where possible, construct exact and approximate solutions of nonlinear equations. This book contains a consistent overview of multiple properties of nonlinear PDEs, their relations, computation algorithms, and a uniformly presented set of examples of application of these methods to specific PDEs. Examples include both well known nonlinear PDEs and less famous systems that arise in the context of shallow water waves and far beyond. The book will beof interest to researchers and graduate students in applied mathematics, physics, and engineering, and can be used as a basis for research, study, reference, and applications.
Waves And Structures In Nonlinear Nondispersive Media
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Author : Sergey Nikolaevich Gurbatov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-03-23
Waves And Structures In Nonlinear Nondispersive Media written by Sergey Nikolaevich Gurbatov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-23 with Science categories.
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is the Full member of Russian Academy of Sciences, the head of Department at Moscow University and Professor at BTH (Sweden). Dr. Saichev A.I. is the Professor at the Faculty of Radiophysics of Nizhny Novgorod State University, Professor of ETH Zürich.
The Crc Handbook Of Mechanical Engineering Second Edition
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Author :
language : en
Publisher: CRC Press
Release Date : 1998-03-24
The Crc Handbook Of Mechanical Engineering Second Edition written by and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-03-24 with Technology & Engineering categories.
During the past 20 years, the field of mechanical engineering has undergone enormous changes. These changes have been driven by many factors, including: the development of computer technology worldwide competition in industry improvements in the flow of information satellite communication real time monitoring increased energy efficiency robotics automatic control increased sensitivity to environmental impacts of human activities advances in design and manufacturing methods These developments have put more stress on mechanical engineering education, making it increasingly difficult to cover all the topics that a professional engineer will need in his or her career. As a result of these developments, there has been a growing need for a handbook that can serve the professional community by providing relevant background and current information in the field of mechanical engineering. The CRC Handbook of Mechanical Engineering serves the needs of the professional engineer as a resource of information into the next century.