Since Poincaré's early work on the nonlinear dynamics of the n-body problem in celestial mechanics, the twentieth century has seen an explosion of interest in nonlinear systems. Lorenz's study of a deterministic, third-order system of weather dynamics showed that this system demonstrated a random-like behavior called chaos. Through numerical simulations made possible by modern computers, and through experiments with physical systems, the presence of chaos has been discovered in many dynamical systems. The phenomenon of chaos has, in turn, spurred a great revival of interest in nonlinear dynamics.

Applied Nonlinear Dynamics provides a coherent and unified treatment of analytical, computational, and experimental methods and concepts of nonlinear dynamics. Analytical approaches based on perturbation methods and dynamical systems theory are presented and illustrated through applications to a wide range of nonlinear systems. Geometrical concepts, such as Poincaré maps, are also treated at length. A thorough discussion of stability and local and global bifurcation analyses for systems of differential equations and algebraic equations is conducted with the aid of examples and illustrations. Continuation methods for fixed points and periodic solutions and homotopy methods for determining fixed points are detailed. Bifurcations of fixed points, limit cycles, tori, and chaos are discussed. The fascinating phenomenon of chaos is explored, and the many routes to chaos are treated at length. Methods of controlling bifurcations and chaos are described. Numerical methods and tools to characterize motions are examined in detail. Poincaré sections, Fourier spectra, polyspectra, autocorrelation functions, Lyapunov exponents, and dimension calculations are presented as analytical and experimental tools for analyzing the motion of nonlinear systems.

This book contains numerous worked-out examples that illustrate the new concepts of nonlinear dynamics. Moreover, it contains many exercises that can be used both to reinforce concepts discussed in the chapters and to assess the progress of students. Students who thoroughly cover this book will be well prepared to make significant contributions in research efforts.

Unlike most other texts, which emphasize either classical methods, experiments and physics, geometrical methods, computational methods, or applied mathematics, Applied Nonlinear Dynamics blends these approaches to provide a unified treatment of nonlinear dynamics. Further, it presents mathematical concepts in a manner comprehensible to engineers and applied scientists. The synthesis of analytical, experimental, and numerical methods and the inclusion of many exercises and worked-out examples will make this the textbook of choice for classroom teaching. Moreover, the inclusion of an extensive and up-to-date bibliography will make it an invaluable text for professional reference.

In this introductory treatment Ali Nayfeh presents different concepts from dynamical systems theory and nonlinear dynamics in a rigorous yet plan way. He systematically introduces models and techniques and states the relevant ranges of validity and applicability. The reader is provided with a clear operational framework for consciously use rather than focused on the underlying mathematical apparatus. The exposition is largely by means of examples, dealt with up to their final outcome. For most of the examples, the results obtained with the method of normal forms are equivalent to those obtained with other perturbation methods, such as the method of multiple scales and the method of averaging. The previous edition had a remarkable success by researchers from all over the world working in the area of nonlinear dynamics and their applications in engineering. Additions to this new edition concern major topics of current interest. In particular, the author added three new chapters dedicated to Maps, Bifurcations of Continuous Systems, and Retarded Systems. In particular the latter has become of major importance in several applications, both in mechanics and in different areas. Accessible to engineers and applied scientist involved with nonlinear dynamics and their applications in a wide variety of fields. It is assumed that readers have a knowledge of basic calculus as well as the elementary properties of ordinary-differential equations.

The Joint Institute for Aeronautics and Acoustics at Stanford University was established in October 1973 to provide an academic environment for long-term cooperative research between Stanford and NASA Ames Research Center. Since its establishment, the Institute has conducted theoretical and experimental work in the areas of aerodynamics, acoustics, fluid mechanics, flight dynamics, guidance and control, and human factors. This research has involved Stanford faculty, research associates, graduate students, and many distinguished visitors in collaborative efforts with the research staff of NASA Ames Research Center. The occasion of the Institute's tenth anniversary was used to reflect back on where that research has brought us, and to consider where our endeavors should be directed next. Thus, an International Symposium was held to review recent advances in the fields relevant to the activities of the Institute and to discuss the areas of research to be undertaken in the future. This anniversary was also chosen as an opportunity to honor one of the Institute's founders and its director, Professor Krishnamurty Karamcheti. It has been his crea tive inspiration that has provided the ideal research environment at the Joint Institute."