Differential Forms on Electromagnetic Networks - 1st Edition - ISBN: 9780408700405, 9781483103242

Differential Forms on Electromagnetic Networks

1st Edition

eBook ISBN: 9781483103242
Imprint: Butterworth-Heinemann
Published Date: 1st January 1970
Page Count: 200
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Differential Forms on Electromagnetic Networks deals with the use of combinatorial techniques in electrical circuit, machine analysis, and the relationship between circuit quantities and electromagnetic fields. The monograph is also an introduction to the organization of field equations by the methods of differential forms. The book covers topics such as algebraic structural relations in an electric circuit; mesh and node-pair analysis; exterior differential structures; generalized Stoke's theorem and tensor analysis; and Maxwell's electromagnetic equation. Also covered in the book are the applications for the field network model; oscillatory behavior of electric machines; and the rotation tensor in machine differential structures. The text is recommended for engineering students who would like to be familiarized with electromagnetic networks and its related topics.

Table of Contents


List of Symbols and Units

1 Introduction

2 Algebraic Structural Relations in Electric Circuit Theory

2.1 Mesh Analysis

2.2 Node-Pair Analysis

2.3 Algebraic Diagram

2.4 Orthogonal Network Analysis

2.5 Incidence Matrices

3 Exterior Differential Structures

3.1 Exterior 1-Forms

3.2 Exterior Products

3.3 Higher Order Differential Forms

3.4 Inner Product

3.5 Hodge (Star) Operator

3.6 Exterior Derivatives

3.7 Generalized Divergence

3.8 Second Differential

3.9 Generalized Stokes' Theorem

3.10 Relation to Tensor Analysis

4 Maxwell's Electromagnetic Equations

4.1 Exterior Differential Form of Maxwell's Equations

4.2 Integral Form of Maxwell's Equations

4.3 Maxwell's Equations in Space-Time Coordinates

4.4 Tensor Density

4.5 Four-Dimensional Field Tensors

4.6 Physical Components

5 Network Model For Maxwell's Equations

5.1 Interconnected Model

5.2 Algebraic Diagram

5.3 Kron's Network Model

6 Application of Field Network Model

6.1 Two-Dimensional Electromagnetic Field Problems

6.2 Rectangular Waveguides

6.3 Numerical Computation

6.4 Electric Machines

7 Field Concepts in Electric Machines

7.1 Park's Idealized Machine

7.2 Field Model

7.3 Relation Between Field Model and Lumped Parameter Model

7.4 Co Variant Field Analysis

8 Oscillatory Behaviour of Electric Machines

8.1 Reference Frames of Park and Kron

8.2 Damping and Synchronizing Torques

8.3 Covariant Differential

8.4 Tensor Equations of Hunting

9 Rotation Tensor in Machine Differential Structures

9.1 Affine Connection

9.2 Field Equations

9.3 Hunting Equations

10 Computation and Experimental Study of Oscillations

10.1 Computation of Oscillating Torque Components

10.2 Machine Parameters

10.3 Experimental Set-Up

10.4 Experimental Determination of Inertia and Damping Torques

11 Conclusion


Appendix 1

Appendix 2

Appendix 3

Appendix 4

Appendix 5



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© Butterworth-Heinemann 1970
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