Invariant Variational Principles
Published on 14. May 2014
189 pages
978-0-08-095647-3 (ISBN)
Description
Invariant Variational Principles
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Series
Language
English
Place of publication
San Diego
United States
ISBN-13
978-0-08-095647-3 (9780080956473)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
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Additional editions
J. David Logan
Invariant Variation Principles
Book
01/1977
Academic Press
€48.91
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Content
- Front Cover
- Invariant Variational Principles
- Copyright Page
- Contents
- Preface
- Acknowledgments
- Chapter 1. Necessary Conditions for an Extremum
- 1.1 Introduction
- 1.2 Variation of Functionals
- 1.3 Single Integral Problems
- 1.4 Applications to Classical Dynamics
- 1.5 Multiple Integral Problems
- 1.6 Invariance-A Preview
- 1.7 Bibliographic Notes
- Exercises
- Chapter 2. Invariance of Single Integrals
- 2.1 r-Parameter Transformations
- 2.2 Invariance Definitions
- 2.3 The Fundamental Invariance Identities
- 2.4 The Noether Theorem and Conservation Laws
- 2.5 Particle Mechanics and the Galilean Group
- 2.6 Bibliographic Notes
- Exercises
- Chapter 3. Generalized Killing Equations
- 3.1 Introduction
- 3.2 Example-The Emden Equation
- 3.3 Killing's Equations
- 3.4 The Damped Harmonic Oscillator
- 3.5 The Inverse Problem
- Exercises
- Chapter 4. Invariance of Multiple Integrals
- 4.1 Basic Definitions
- 4.2 The Fundamental Theorems
- 4.3 Derivation of the Invariance Identities
- 4.4 Conservation Theorems
- Exercises
- Chapter 5. Invariance Principles in the Theory of Physical Fields
- 5.1 Introduction
- 5.2 Tensors
- 5.3 The Lorentz Group
- 5.4 Infinitesimal Lorentz Transformations
- 5.5 Physical Fields
- 5.6 Scalar Fields
- 5.7 The Electromagnetic Field
- 5.8 Covariant Vector Fields
- Exercises
- Chapter 6. Second-Order Variation Problems
- 6.1 The Euler-Lagrange Equations
- 6.2 Invariance Criteria for Single Integrals
- 6.3 Multiple Integrals
- 6.4 The Korteweg-devries Equation
- 6.5 Bibliographic Notes
- Exercises
- Chapter 7. Conformally Invariant Problems
- 7.1 Conformal Transformations
- 7.2 Conformal Invariance Identities for Scalar Fields
- 7.3 Conformal Conservation Laws
- 7.4 Conformal Covariance
- Exercises
- Chapter 8. Parameter-Invariant Problems
- 8.1 Introduction
- 8.2 Sufficient Conditions for Parameter-Invariance
- 8.3 The Conditions of Zermelo and Weierstrass
- 8.4 The Second Noether Theorem
- Exercises
- References
- Index
