Overview
- Gives insight into the mechanism of vibrations and waves in order to control them in an optimal way Introduction to the systematic and intensive use of Hamilton's variational principle and its generalizations for deriving the governing equations of conservative and dissipative mechanical systems
- Presents the first principles from which the governing equations can be derived, and the adequate mathematical methods for their solving
- Presents the direct variational-asymptotic analysis and how many well-known methods in dynamics like those of Lindstedt-Poincare, Bogoliubov-Mitropolsky, Kolmogorov-Arnold-Moser (KAM), and Witham can be derived from it
- Written by leading experts in the field
Part of the book series: Interaction of Mechanics and Mathematics (IMM)
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Table of contents (8 chapters)
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Linear Theory
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Nonlinear Theory
Keywords
About this book
The above examples should make clear the necessity of understanding the mechanism of vibrations and waves in order to control them in an optimal way. However vibrations and waves are governed by differential equations which require, as a rule, rather complicated mathematical methods for their analysis. The aim of this textbook is to help students acquire both a good grasp of the first principles from which the governing equations can be derived, and the adequate mathematical methods for their solving. Its distinctive features, as seen from the title, lie in the systematic and intensive use of Hamilton's variational principle and its generalizations for deriving the governing equations of conservative and dissipative mechanical systems, and also in providing the direct variational-asymptotic analysis, whenever available, of the energy and dissipation for the solution of these equations. It will be demonstrated that many well-known methods in dynamics like those of Lindstedt-Poincare, Bogoliubov-Mitropolsky, Kolmogorov-Arnold-Moser (KAM), and Whitham are derivable from this variational-asymptotic analysis.
This book grew up from the lectures given by the author in the last decade at the Ruhr University Bochum, Germany. Since vibrations and waves are constituents of various disciplines (physics, mechanics, electrical engineering etc.) and cannot be handled in a single textbook, I have restricted myself mainly to vibrations and waves of mechanical nature. The material of this book can be recommended for a one year course in higher dynamics for graduate students of mechanical and civil engineering. For this circle of readers, the emphasis is made on the constructive methods of solution and not on the rigorous mathematical proofs ofconvergence. As compensation, various numerical simulations of the exact and approximate solutions are provided which demonstrate vividly the validity of the used methods. To help students become more proficient, each chapter ends with exercises, of which some can be solved effectively by using Mathematica.
Authors and Affiliations
Bibliographic Information
Book Title: Energy Methods in Dynamics
Authors: Khanh Chau Le
Series Title: Interaction of Mechanics and Mathematics
DOI: https://doi.org/10.1007/978-3-642-22404-1
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer Berlin Heidelberg 2012
eBook ISBN: 978-3-642-22404-1Published: 25 September 2011
Series ISSN: 1860-6245
Series E-ISSN: 1860-6253
Edition Number: 1
Number of Pages: X, 294
Number of Illustrations: 142 b/w illustrations
Topics: Vibration, Dynamical Systems, Control, Mathematical and Computational Engineering, Dynamical Systems and Ergodic Theory, Complexity