There are a number of reasons for producing this edition of Simili tude and Approximation Theory. The methodologies developed remain important in many areas of technical work. No other equivalent work has appeared in the two decades since the publication of the first edition. The materials still provide an important increase in understanding for first-year graduate students in engineering and for workers in research and development at an equivalent level. In addition, consulting experiences in a number of industries indi cate that many technical workers in research and development lack knowledge of the methodologies given in this work. This lack makes the work of planning and controlling computations and experiments less efficient in many cases. It also implies that the coordinated grasp of the phenomena (which is so critical to effective research and develop ment work) will be less than it might be. The materials covered in this work focus on the relationship between mathematical models and the physical reality such models are intended v vi Preface to the Springer Edition to portray. Understanding these relationships remains a key factor in simplifying and generalizing correlations, predictions, test programs, and computations. Moreover, as many teachers of engineering know, this kind of understanding is typically harder for students to develop than an understanding of either the mathematics or the physics alone.

Similitude and Modeling describes the theoretical aspects and application of similitude method using mathematical apparatus. This book is organized into two parts encompassing 13 chapters, and begins with an introduction to a simple technological problem in similitude modeling. The first part deals with the concept, physical fundamentals, dimensional analysis, and approximate and partial modeling of similitude. This part explores also the preparation and evaluation of similitude experiments, as well as the general types of similitude invariants. The second part highlights the application areas of similitude modeling, including heat conduction and diffusion, fluid dynamics, elastic deformation, and chemical reactions. This book will prove useful to plant and design engineers.

This book contains the proceedings of a colloquium held in Monte Verit from September 9-13, 1991. Special care has been taken to devote adequate space to the scientific discussions, which claimed about half of the time available. Scientists from all over the world presented their views on the importance of kinematic properties, topology and fractal geometry, and on the dynamic behaviour of turbulent flows. They debated the importance of coherent structures and the possibility to incorporate these in the statistical theory of turbulence, as well as their significance for the reduction of the degrees of freedom and the prospective of dynamical systems and chaos approaches to the problem of turbulence. Also under discussion was the relevance of these new approaches to the study of the instability and the origin of turbulence, and the importance of numerical and physical experiments in improving the understanding of turbulence.

Fluid mechanics is a core component of many undergraduate engineering courses. It is essential for both students and lecturers to have a comprehensive, highly illustrated textbook, full of exercises, problems and practical applications to guide them through their study and teaching. Engineering Fluid Mechanics By William P. Grabel is that book The ISE version of this comprehensive text is especially priced for the student market and is an essential textbook for undergraduates (particularly those on mechanical and civil engineering courses) designed to emphasis the physical aspects of fluid mechanics and to develop the analytical skills and attitudes of the engineering student. Example problems follow most of the theory to ensure that students easily grasp the calculations, step by step processes outline the procedure used, so as to improve the students' problem solving skills. An Appendix is included to present some of the more general considerations involved in the design process. The author also links fluid mechanics to other core engineering courses an undergraduate must take (heat transfer, thermodynamics, mechanics of materials, statistics and dynamics) wherever possible, to build on previously learned knowledge.

This textbook provides a concise introduction to the mathematical theory of fluid motion with the underlying physics. Different branches of fluid mechanics are developed from general to specific topics. At the end of each chapter carefully designed problems are assigned as homework, for which selected fully worked-out solutions are provided. This book can be used for self-study, as well as in conjunction with a course in fluid mechanics.

This book considers methods of approximate analysis of mechanical, elec tromechanical, and other systems described by ordinary differential equa tions. Modern mathematical modeling of sophisticated mechanical systems consists of several stages: first, construction of a mechanical model, and then writing appropriate equations and their analytical or numerical ex amination. Usually, this procedure is repeated several times. Even if an initial model correctly reflects the main properties of a phenomenon, it de scribes, as a rule, many unnecessary details that make equations of motion too complicated. As experience and experimental data are accumulated, the researcher considers simpler models and simplifies the equations. Thus some terms are discarded, the order of the equations is lowered, and so on. This process requires time, experimentation, and the researcher's intu ition. A good example of such a semi-experimental way of simplifying is a gyroscopic precession equation. Formal mathematical proofs of its admis sibility appeared some several decades after its successful introduction in engineering calculations. Applied mathematics now has at its disposal many methods of approxi mate analysis of differential equations. Application of these methods could shorten and formalize the procedure of simplifying the equations and, thus, of constructing approximate motion models. Wide application of the methods into practice is hindered by the fol lowing. 1. Descriptions of various approximate methods are scattered over the mathematical literature. The researcher, as a rule, does not know what method is most suitable for a specific case. 2.

Asymptotic Methods for Engineers is based on the authors’ many years of practical experience in the application of asymptotic methods to solve engineering problems. This book is devoted to modern asymptotic methods (AM), which is widely used in engineering, applied sciences, physics, and applied mathematics. Avoiding complex formal calculations and justifications, the book’s main goal is to describe the main ideas and algorithms. Moreover, not only is there a presentation of the main AM, but there is also a focus on demonstrating their unity and inseparable connection with the methods of summation and asymptotic interpolation. The book will be useful for students and researchers from applied mathematics and physics and of interest to doctoral and graduate students, university and industry professors from various branches of engineering (mechanical, civil, electro-mechanical, etc.).

Modern Vibrations Primer provides practicing mechanical engineers with guidance through the computer-based problem solving process. The book illustrates methods for reducing complex engineering problems to manageable, analytical models. It is the first vibrations guide written with a contemporary approach for integration with computers. Ideal for self-study, each chapter contains a helpful exposition that emphasizes practical application and builds in complexity as it progresses. Chapters address discrete topics, creating an outstanding reference tool. The lecture-like format is easy to read. The primer first promotes a fundamental understanding, then advances further to problem solving, design prediction and trouble shooting. Outdated and theoretical material isn't covered, leaving room for modern applications such as autonomous oscillations, flow-induced vibrations, and parametric excitation Until recently, some procedures , like arbitrarily-damped, multi-dimensional problems, were impractical. New methods have made them solvable, using PC-based matrix calculation and algebraic manipulation. Modern Vibrations Primer shows how to utilize these current resources by putting problems into standard mathematical forms, which can be worked out by any of a number of widely employed software programs. This book is necessary for any professional seeking to adapt their vibrations knowledge to a modern environment.