Modeling Nonlinear Dynamics From Equations And Data With Applications To Solids Fluids And Controls
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Modeling Nonlinear Dynamics From Equations And Data With Applications To Solids Fluids And Controls
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Author : George Haller
language : en
Publisher: SIAM
Release Date : 2025-05-20
Modeling Nonlinear Dynamics From Equations And Data With Applications To Solids Fluids And Controls written by George Haller and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-20 with Computers categories.
This concise text presents an introduction to the emerging area of reducing complex nonlinear differential equations or time-resolved data sets to spectral submanifolds (SSMs). SSMs are ubiquitous low-dimensional attracting invariant manifolds that can be constructed systematically, building on the spectral properties of the linear part of a nonlinear system. The internal dynamics within SSMs then serve as exact, low-dimensional models with which the full system evolution synchronizes exponentially fast. SSM-based model reduction has a solid mathematical foundation and hence is guaranteed to deliver accurate and predictive reduced-order models under a precise set of assumptions. This book introduces the foundations of SSM theory to the novice reader; reviews recent extensions of classic SSM results for the advanced reader; and illustrates the power of SSM reduction on a large collection of equation- and data-driven applications in fluid mechanics, solid mechanics, and control. This book is intended for graduate students, postdocs, faculty, and industrial researchers working in model reduction for nonlinear physical systems arising in solid mechanics, fluid dynamics, and control theory. It is appropriate for courses on differential equations, modeling, dynamical systems, and data-driven modeling.
Modeling Nonlinear Dynamics From Equations And Data With Applications To Solids Fluids And Controls
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Author : George Haller
language : en
Publisher:
Release Date : 2025
Modeling Nonlinear Dynamics From Equations And Data With Applications To Solids Fluids And Controls written by George Haller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025 with Differential equations, Nonlinear categories.
"Introduces emerging area of reducing complex nonlinear differential equations to spectral submanifolds (SSMs) and illustrates the power of SSM reduction on large collection of applications"--
Chaos Near Resonance
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Author : G. Haller
language : en
Publisher: Springer
Release Date : 1999-10-01
Chaos Near Resonance written by G. Haller and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-01 with Mathematics categories.
A unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping. After a survey of the necessary background, the book develops a general finite dimensional theory of homoclinic jumping, illustrating it with examples. The main mechanism of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds. The results are applied to a variety of different problems, which include applications from beam oscillations, surface wave dynamics, nonlinear optics, atmospheric science and fluid mechanics.
University Of Michigan Official Publication
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Author : University of Michigan
language : en
Publisher: UM Libraries
Release Date : 1988
University Of Michigan Official Publication written by University of Michigan and has been published by UM Libraries this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Education, Higher categories.
Each number is the catalogue of a specific school or college of the University.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1995
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Aeronautics categories.
Differential Dynamical Systems Revised Edition
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Author : James D. Meiss
language : en
Publisher: SIAM
Release Date : 2017-01-24
Differential Dynamical Systems Revised Edition written by James D. Meiss and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-24 with Mathematics categories.
Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.
Dynamics And Fault Diagnosis Of Nonlinear Rotors And Impellers
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Author : Jiazhong Zhang
language : en
Publisher: Springer Nature
Release Date : 2022-04-28
Dynamics And Fault Diagnosis Of Nonlinear Rotors And Impellers written by Jiazhong Zhang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-28 with Technology & Engineering categories.
This contributed volume presents recent developments in nonlinear dynamics applied to engineering. Specifically, the authors address stability and bifurcation in large-scale, complex rotor dynamic systems; periodic motions and their bifurcations in nonlinear circuit systems, fault diagnosis of complex engineering systems with nonlinear approaches, singularities in fluid-machinery and bifurcation analysis, nonlinear behaviors in rotor dynamic system with multi-mistuned blades, mode localization induced by mistuning in impellers with periodical and cyclic symmetry, and nonlinear behaviors in fluid-structure interaction and their control. These new results will maximize reader understand on the recent progress in nonlinear dynamics applied to large-scale, engineering systems in general and nonlinear rotors and impellers in particular.
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 1948
Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1948 with Mechanics, Applied categories.
Siam Journal On Control And Optimization
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Author : Society for Industrial and Applied Mathematics
language : en
Publisher:
Release Date : 1996
Siam Journal On Control And Optimization written by Society for Industrial and Applied Mathematics and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Control theory categories.
Mathematics And Climate
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Author : Hans Kaper
language : en
Publisher: SIAM
Release Date : 2013-10-18
Mathematics And Climate written by Hans Kaper and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-18 with Science categories.
Mathematics and Climate is a timely textbook aimed at students and researchers in mathematics and statistics who are interested in current issues of climate science, as well as at climate scientists who wish to become familiar with qualitative and quantitative methods of mathematics and statistics. The authors emphasize conceptual models that capture important aspects of Earth's climate system and present the mathematical and statistical techniques that can be applied to their analysis. Topics from climate science include the Earth?s energy balance, temperature distribution, ocean circulation patterns such as El Ni?o?Southern Oscillation, ice caps and glaciation periods, the carbon cycle, and the biological pump. Among the mathematical and statistical techniques presented in the text are dynamical systems and bifurcation theory, Fourier analysis, conservation laws, regression analysis, and extreme value theory. The following features make Mathematics and Climate a valuable teaching resource: issues of current interest in climate science and sustainability are used to introduce the student to the methods of mathematics and statistics; the mathematical sophistication increases as the book progresses and topics can thus be selected according to interest and level of knowledge; each chapter ends with a set of exercises that reinforce or enhance the material presented in the chapter and stimulate critical thinking and communication skills; and the book contains an extensive list of references to the literature, a glossary of terms for the nontechnical reader, and a detailed index.