Synopses & Reviews
This book is devoted to the basic variational principles of mechanics, namely the Lagrange--D'Alembert differential variational principle and the Hamilton integral variational principle. These two variational principles form the basis of contemporary analytical mechanics, and from them the body of classical dynamics can be deductively derived as a part of physical theory. In recent years variational techniques have evolved as powerful tools for the study of linear and nonlinear problems in conservative and nonconservative dynamical systems, as is emphasized in this book. Presented here are a wide range of possibilities for applying variational principles to numerous problems in analytical mechanics, including the Noether Theorem for finding conservation laws of conservative and nonconservative dynamical systems, the application of the Hamilton--Jacobi and field methods suitable for nonconservative dynamical systems, the variational approach to modern optimal control theory, and the application of variational methods to the stability and optimization of elastic rod theory. Mathematical prerequisites are kept to a minimum, and the exposition is intended to be suggestive rather than mathematically rigorous. Each chapter begins with widely understood mathematical principles and unfolds systematically toward more advanced topics. Examples and novel applications are presented throughout to clarify and enhance the theory. An Introduction to Modern Variational Techniques in Mechanics and Engineering will serve a broad audience of students, researchers, and professionals in analytical mechanics, applied variational calculus, optimal control, physics, and mechanical and aerospace engineering. The book may be used in graduate and senior undergraduate dynamics courses in engineering, applied mathematics, and physics departments, or it may also serve as a self-study reference text.
Review
"[The book has] many examples and applications throughout the chapters.... It is intended to be only a suggestive exposition for graduate and senior undergraduate students in engineering, applied mathematics and physics.... The book should be useful for students in these quoted areas and those people with some knowledge in single-integral variational problems." --Mathematical Reviews "Variational principles have great utility in solving problems in analytical mechanics. During recent years attention has been drawn to the wide area of possibilities they offer and variational techniques are applied as important tools for studying linear and nonlinear problems in conservative and nonconservative dynamical systems. This book discusses the basic variational principles of contemporary analytical mechanics, presents a wide range of possibilities for applying them, and solves numerous concrete examples.... The book is suitable for self-study, for graduate students in applied mathematics, physics, engineering, it can be used as a text in graduate and senior undergraduate courses, and researchers also can have a practical usage of it." --Bulletin of Belgian Mathematical Society
Synopsis
* Atanackovic has good track record with Birkhauser: his "Theory of Elasticity" book (4072-X) has been well reviewed. * Current text has received two excellent pre-pub reviews. * May be used as textbook in advanced undergrad/beginning grad advanced dynamics courses in engineering, physics, applied math departments. *Also useful as self-study reference for researchers and practitioners. * Many examples and novel applications throughout. Competitive literature---Meirovich, Goldstein---is outdated and does not include the synthesis of topics presented here.
Table of Contents
Preface Part I: Differential Variational Principles of Mechanics The Elements of Analytical Mechanics Expressed Using the Lagrange-D'Alembert Differential Variational Principle The Hamilton-Jacobi Method of Integration of Canonical Equations Transformation Properties of Lagrange D'Alembert Variational Principle: Conservation Laws of Nonconservative Dynamical Systems A Field Method Suitable for Application in Conservative and Nonconservative Mechanics Part II: The Hamiltonian Integral Variational Principle The Hamiltonian Variational Principle and Its Applications Variable End Points, Natural Boundary Conditions, Bolza Problems Constrained Problems Variational Principles for Elastic Rods and Columns Bibliography Index