An Introduction to Modern Variational Techniques in Mechanics and Engineering

This book is devoted to the basic variational principles of mechanics: the Lagrange-D'Alembert differential variational principle and the Hamilton integral variational principle. These two variational principles form the main subject of contemporary analytical mechanics, and from them the whole colossal corpus of classical dynamics can be deductively derived as a part of physical theory. In recent years students and researchers of engineering and physics have begun to realize the utility of variational principles and the vast possi bilities that they offer, and have applied them as a powerful tool for the study of linear and nonlinear problems in conservative and nonconservative dynamical systems. The present book has evolved from a series of lectures to graduate stu dents and researchers in engineering given by the authors at the Depart ment of Mechanics at the University of Novi Sad Serbia, and numerous foreign universities. The objective of the authors has been to acquaint the reader with the wide possibilities to apply variational principles in numerous problems of contemporary analytical mechanics, for example, the Noether theory for finding conservation laws of conservative and nonconservative dynamical systems, application of the Hamilton-Jacobi method and the field method suitable for nonconservative dynamical systems,the variational approach to the modern optimal control theory, the application of variational methods to stability and determining the optimal shape in the elastic rod theory, among others.

List of contents

I Differential Variational Principles of Mechanics.- 1 The Elements of Analytical Mechanics Expressed Using the Lagrange-D'Alembert Differential Variational Principle.- 2 The Hamilton-Jacobi Method of Integration of Canonical Equations.- 3 Transformation Properties of Lagrange-D'Alembert Variational Principle: Conservation Laws of Nonconservative Dynamical Systems.- 4 A Field Method Suitable for Application in Conservative and Nonconservative Mechanics.- II The Hamiltonian Integral Variational Principle.- 5 The Hamiltonian Variational Principle and Its Applications.- 6 Variable End Points, Natural Boundary Conditions, Bolza Problems.- 7 Constrained Problems.- 8 Variational Principles for Elastic Rods and Columns.

Summary

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.
"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.

Additional text

"[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
 

Report

"[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
 

Product details

• Authors: Teodor M Atanackovic, Teodor M. Atanackovic, Bozidar Vujanovic, Bozidar D Vujanovic, Bozidar D. Vujanovic
• Publisher: Springer, Basel
• Languages: English
• Product format: Hardback
• Released: 11.02.2004
• EAN: 9780817633998
• ISBN: 978-0-8176-3399-8
• No. of pages: 346
• Weight: 628 g
• Illustrations: X, 346 p.
• Subject: Natural sciences, medicine, IT, technology > Technology > Mechanical engineering, production engineering