A Modp.rn course in aeroelasticity.(Mecbanics, dynallical syste_ ; Includes bibliographies and indexes.

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BOOK REVIEWS principles, invariance under translation and fundamental solutions, integral representation theorem, finite difference methods, finite element methods, Petrov-Galerkin finite element methods and boundary element methods. Various special iterative methods for the finite difference equations are also discussed. Chapter 4: "Dissipative Systems". The numerical methods considered in Chapter 3 are revised to deal with the advection-diffusion type equations. Nonstandard methods such as upstream weighting, solution pathology at sharp fronts, and alternating direction methods are also introduced in this chapter. Chapter 5: "Nondissipative Systems" deals with transport equations such as the Euler equations, the Burger's equation, and the wave equation. Methods of characteristic, conservative finite-difference schemes, and nonstandard Galerkin finite element methods are considered. Chapter 6: "High-Order, Nonlinear, and Coupled Systems," considers special problems such as the biharmonic equation, nonlinear diffusion equations and compositional flows in porous media. The oil reservoir modeling is discussed at great length. The above list is not complete, merely representative of the topics covered in the book.

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BOOK REVIEWS ject in a form "allowing the use of computers for finding solutions." The book consists of four parts: Mathematical Description of Vibrating Systems (56 pages), Time-Invariant Vibrating Systems (200. pages), Time-Variant Vibrating Systems (33 pages), and Mathematical Background (30 pages). Part I begins with an introductory discussion of the various classifications of vibrations. This is followed by a very brief review of kinematics, Lagrange's equations, and the momentum principles. The section closes with a chapter on the linearization of the equations of motion and their state-space representation. Part II is devoted to the study of autonomous systems. It begins with a chapter on the fundamental matrix of the system and its use in generating the general solution of the equations of motion. A chapter on stability and boundedness follows. Here, stability criteria based on the characteristic equation as well as on Liapunov's matrix equation are discussed. This is followed by chapters on free vibrations, forced vibrations, and resonance. Mode shapes, lightly damped systems, periodic excitation, vibration absorption, and parameter identification are some of the topics explored. The final chapter of this section is devoted to random vibrations. Part III consists of two chapters: the first is concerned with the solution of the (nonautonomous) equations of motion and its stability, while the second addresses parametrically excited and forced vibrations. The final part of the book presents background material on matrix algebra-one chapter on its analytical aspects and a second on its numerical aspects. It also has a brief chapter on controllability and observability. I beleive the authors do achieve their aim of presenting the results in a form convenient for computer implementation. The results are presented in such a way that when analyzing a given system, one merely needs to select a set of generalized coordinates and write down the position vectors of the various particles in terms of these coordinates. It is then a matter of "substituting into a sequence of appropriate formulas". In fact, even the simplest of examples (e.g., the double pendulum) is worked out in the book in this mechanistic manner. This book is concerned with the mathematical results associated with various aspects of linear vibration theory. The physics of the subject is underplayed. My primary criticism of the book is that I found it to be extremely concise; often, the authors simply state results (both elementary and advanced) without explanation, e.g., the section on Floquet Theory in Chapter 10. On the positive side, this book is a comprehensive source for mathematical results in linear vibration theory of discrete systems. It discusses the subject through both a state-space formulation as well as directly through the equations of motion. This is a useful feature, since it helps link the traditional mechanical engineering approach to vibrations with the more modern literature. A second attractive feature is that in order to illus...