The present text reflects developments in the literature on nonlinear systems, while retaining a reader-friendly presentation. It has been developed from problems on nonlinear differential equations given over several years in the nonlinear dynamics team  at the Mechanical Department of Babol Noshirvani University of Technology.  A large variety of applied processes in both linear and nonlinear forms for important nonlinear differential equations are covered, enabling readers to  solve  problems without needing  to refer to other sources.  An introduction to  systems in the context of nonlinear differential equations is provided and is suitable for courses of varying emphasis. The chapters  are designed to be self-contained so readers can easily navigate to the material of interest.  Emphasis is given to direct applications of the subject matter, and will therefore be of particular  interest  to students of engineering, mathematics and the natural sciences.  The most recent analytic methods and developments are included and  over 300 references are given. In addition to discussing  linear and nonlinear problems, demonstrated solutions  are provided.

Nonlinear Equations: Analytical Methods and Applications

Science & Math

Ganji, Davood Domairry

Kachapi, Seyed Habibollah Hashemi

Mathematics

Cambridge International Science Publishing

<p>Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems. <br>There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between theory and practice, fundamentals and advanced subjects, and generality and specialization. <br>None of the books in this area have completely studied and analyzed nonlinear equation in dynamical and vibratory systems using the latest analytical and numerical methods, so that the user can solve the problems without the need of studying too many different references. Thereby in this book, by the use of the latest analytic, numeric laboratorial methods and using more than 300 references like books, papers and the researches done by the authors and by considering almost all possible processes and situation, new theories has been proposed to encounter applied problems in engineering and applied sciences. In this way, the user (bachelor’s, master’s and PhD students, university teachers and even in research centers in different fields of mechanical, civil, aerospace, electrical, chemical, applied mathematics, physics, and etc.) can encounter such systems confidently. In the different chapters of the book, not only are the linear and especially nonlinear problems with oscillatory form broadly discussed, but also applied examples are practically solved by the proposed methodology.</p>

Dynamics and Vibrations: Progress in Nonlinear Analysis (Solid Mechanics and Its Applications, 202)

Physics

Springer

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