Differential Forms on Electromagnetic Networks

ContentsList of Symbols and Units1 Introduction2 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 Matrices3 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 Analysis4 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 Components5 Network Model For Maxwell's Equations 5.1 Interconnected Model 5.2 Algebraic Diagram 5.3 Kron's Network Model6 Application of Field Network Model 6.1 Two-Dimensional Electromagnetic Field Problems 6.2 Rectangular Waveguides 6.3 Numerical Computation 6.4 Electric Machines7 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 Analysis8 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 Hunting9 Rotation Tensor in Machine Differential Structures 9.1 Affine Connection 9.2 Field Equations 9.3 Hunting Equations10 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 Torques11 ConclusionAppendices Appendix 1 Appendix 2 Appendix 3 Appendix 4 Appendix 5References