# Energy Methods in Dynamics

• Khanh Chau Le
Book

Part of the Interaction of Mechanics and Mathematics book series (IMM)

1. Front Matter
2. ### Linear Theory

1. Front Matter
Pages 1-1
2. Khanh Chau Le
Pages 3-34
3. Khanh Chau Le
Pages 35-70
4. Khanh Chau Le
Pages 71-108
5. Khanh Chau Le
Pages 109-148
3. ### Nonlinear Theory

1. Front Matter
Pages 149-149
2. Khanh Chau Le
Pages 151-183
3. Khanh Chau Le
Pages 185-214
4. Khanh Chau Le
Pages 215-246
5. Khanh Chau Le
Pages 247-284
4. Back Matter

### Introduction

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 of convergence. 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

### Keywords

Dissipation Energy Hamilton’s Variational Principle and its Generalization Variational-Asymptotic Method

#### Authors and affiliations

• Khanh Chau Le
• 1
1. 1.Lehrstuhl für Mechanik und Material TheorieRuhr Universität BochumBochumGermany

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-22404-1
• Copyright Information Springer Berlin Heidelberg 2012
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages Engineering
• Print ISBN 978-3-642-22403-4
• Online ISBN 978-3-642-22404-1
• Series Print ISSN 1860-6245
• Series Online ISSN 1860-6253