An Introduction to Modern Variational Techniques in Mechanics and Engineering

Bozidar D. Vujanovic, Teodor M. Atanackovic (Autoren)

Buch | Softcover

346 Seiten

2012 | Softcover reprint of the original 1st ed. 2004
Springer-Verlag New York Inc.
978-1-4612-6467-5 (ISBN)

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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.

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.

Zusatzinfo	X, 346 p.
Verlagsort	New York
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Technik ► Maschinenbau
ISBN-10	1-4612-6467-7 / 1461264677
ISBN-13	978-1-4612-6467-5 / 9781461264675
Zustand	Neuware