Overview

Variational methods provide a versatile framework for several branches of theoretical mechanics. For problems in dynamics, variational formulations provide a powerful alternative to vector methods. This approach has a legacy of ideas advanced by numerous researchers including such celebrated mathematicians as d'Alembert, Lagrange, Hamilton, Jacobi, Gauss and Euler. In this volume, the subject matter is developed systematically with worked-out problems. Initially, differential variational formulations are described followed by the integral formulations. An account of the essentials of the calculus of variations is provided. While classical formulations in dynamics have a long history, the complementary formulations are relatively new. This book aims to provide a detailed development of complementary formulations and highlight certain dualities that are revealed as a consequence of the two formulations. The chapter on special applications studies problems of small amplitude oscillations about equilibrium and steady state configurations, and the problem of impulsive or spike loads. The book ends with historical sketches of the personalities associated with variational methods in dynamics. Designed for structural, mechanical and aeronautical engineers, this volume should also be useful as a graduate text in analytic dynamics.

Full Product Details

Author:   C. Tabarrok ,  F.P. Rimrott
Publisher:   Springer
Imprint:   Springer
Edition:   1994 ed.
Volume:   31
Dimensions:   Width: 21.00cm , Height: 2.20cm , Length: 29.70cm
Weight:   1.580kg
ISBN:  

9780792329237

ISBN 10:   0792329236
Pages:   368
Publication Date:   30 June 1994
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

I — Fundamentals.- II — Differential Variational Formulations.- III — Integral Variational Formulations.- IV — Canonical Transformations and the Hamilton-Jacobi Equation.- V — Rigid Body Dynamics.- VI — Special Applications.- Appendix A — The Calculus of Variations.- A.1 Functions and Functionals.- A.2 Review of Extremum Values of Functions.- A.3 Stationary Values of Definite Integrals.- A.4 A Note about Weak and Strong Variations.- A.5 An Alternative Expression for a Single Euler-Lagrange Equation.- A.6 The Brachystochrone Problem.- A.7 Path-independent Functionals.- A.8 Several Dependent Functions.- A.9 Variational Notation.- A.10 Constraint Equations.- Lagrange Multipliers.- Algebraic and Differential Equation Constraints.- A.11 Variable End Points.- Suggested Reading.- Appendix B — Developments in Mechanics — Some Historical Perspectives.- Author Index.

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