Invariant variational principles / John David Logan.

Format:

Book

Author/Creator:

Logan, J. David (John David)

Series:

Mathematics in science and engineering ; v. 138.

Mathematics in science and engineering ; v. 138

Language:

English

Subjects (All):

Calculus of variations.

Invariants.

Transformations (Mathematics).

Physical Description:

1 online resource (189 p.)

Place of Publication:

New York : Academic Press, 1977.

Language Note:

English

Summary:

Invariant variational principles

Contents:

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 NotesExercises; 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 Fields5.7 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-Invariance8.3 The Conditions of Zermelo and Weierstrass; 8.4 The Second Noether Theorem; Exercises; References; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-282-28967-5

9786612289675

0-08-095647-5

OCLC:

316563999