On the bondgraphic power postulate and its role in interpreting the 1905 and 1915 relativity theories Item Type text; Thesis-Reproduction (electronic) Authors Gussn, Nasser, M. N., 1968- Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 02/10/2021 22:51:28 Link to Item http://hdl.handle.net/10150/558235 ON THE SONOGRAPHIC POWER POSTULATE AND ITS ROLE IN INTERPRETING THE 1905 AND 1915 RELATIVITY THEORIES by Kasser Gmssa copyright © Nasser M. N. Gussn 1994 A Thesis Submitted to the Faculty of the DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING In Partial Fulfillment of the Requirements For the Degree of MASTER OF SCIENCE WITH A MAJOR IN ELECTRICAL ENGINEERING In the Graduate College THE UNIVERSITY OF ARIZONA 1994 2 STATEMENT BY AUTHOR This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this thesis are allowable without special permission, provided accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the copyright holder. APPROVAL BY THESIS DIRECTOR This thesis has been approved on the date shown below: Associate Professor of Electrical and Computer Engineering 3 ACKNOWLEDGMENTS I have no doubt in my mind that this work would have not been able to stand as a reality, had it not been for the will of God, who bestowed on me of his uncountabley infinite blessings what I cannot count. His true love and caring was, and will always be, the reason behind my venturing with no fear and my aspiring to loftier stratum. The author would also like to take the opportunity to thank the following people, who played an important role in the process which had led to this thesis. Although not involved directly, the company of my mother through the hard times I went through while working on this thesis, was definitely an important psychological factor that alleviated my loneliness. For her sacrifices since my birth, she can't be less than a full partner in my success. I also cannot forget the instrumental role my employer, Saudi Aramco, played in achieving this goal. In particular I would like to thank my R&OED division coordinator Mr. M. A. Al-Mubarak for his confidence and support. Also Mr. E. R. Pickinpaugh, my mentor, for his wise advising through my PDP program; Dr. K. Kessinger for salvaging my nomination by securing my admission to the U of A; and finally to the Aramco Services Company's Academic Advisors for making this an unforgettable experience. Last but not least, I would like to thank my thesis director. Dr. Francois E. Cellier and my relativity advisor. Dr. Lizhi Fang for their patience and illuminating remarks. While lingering for the visitors, Nasser M. N. Gussn Tucson, Arizona, September 5,1994. FOR THE LOVE OF HAKIMA 5 TABLE OF CONTENTS LIST OF FIGURES.................................................................................................... 8 LIST OF TABLES.................................. 9 LIST OF SYMBOLS AND ABBREVIATIONS............................................................. 10 ABSTRACT.................................................................................... 14 1 INTRODUCTION: Objectives and Directions.............................i................... 15 1 Objectives of the Thesis................................................................................. 17 2 Directions to the Reader.................................................................................. 18 2 THE ART OF MODELBUILDING................................................... ................... 19 1 Models, Systems and Theories................................................... 21 2 Classification of Models................. 25 3 Physical Domains........................ 27 4 Modelbuilding Phases.................................................................................... 29 5 Model Verification................ 30 6 Hierarchical Models....................................................................................... 32 7 The Systems Approach in Modelbuilding..................................................... 33 8 Diakoptics.............................. 36 9 Simulation and Modelbuilding.............................. 37 2 SELECTED BIBLIOGRAPHY............................... 40 3 AN INTRODUCTION TO TENSOR CALCULUS............................................. 41 1 Generalized Spaces................................................................... 42 2 Euclidean Space............................................................................................. 43 3 Orthogonal Transformations.......................................................................... 43 4 General Coordinate Transformations............................................................ 45 5 Range and Summation Conventions................ 46 6 Tensors................................................................................. 47 7 Riemannian Space.................. 49 8 Tensor Densities................................................ 50 9 Tensor Algebra............................................................................................... 50 10 Tensors Symmetry................................................ 52 11 Covariant Differentiation............. 53 6 TABLE OF CONTENTS — Continued 12 Differential Operators............................... .................................................... 54 13 Line, Surface, and Volume Integrals........................................................... 54 14 Index Gymnastics........................................................................................... 55 15 Geodesic Lines............................................................................................... 56 16 Curvature of Space............ ....................................................... ..................... 56 17 Special Spaces.................................................... 58 3 SELECTED BIBLIOGRAPHY................... :............................................... 61 4 BONBGRAPH ANALYSIS..................................................................................... 62 1 The Power Postulate........................................................ ..... ...................... 63 2 Bondgraph Anatomy...................................................................................... 68 3 Modulation of Bondgraphic MP Elements.................................................... 75 4 Structural Properties of Bondgraphic Elements .......................................... 77 5 Computational Causality..................................................................... 80 6 Lagrangian Bondgraphs, Gyrobondgraphs and Generalized Bondgraphs........................ 81 4 SELECTED BIBLIOGRAPHY.................................................................... 84 5 SPECIAL RELATIVITY: Theory and Interpretation...................... 85 1 Physics in the Nineteenth Century................................................................. 87 2 Origin of Special Relativity...................................................... 89 3 Lorentz Transformations.............................................................. 90 4 Special Relativistic Kinematics..................................................................... 92 5 The Minkowski World................................... 94 6 Special Relativistic Dynamics and Einstein's Energy Equation.................... 96 7 A Model Based on BGs.............................. 97 8 A BG Interpretation of the Field-Strength Tensor in Electrodynamics...................... 105 5 SELECTED BIBLIOGRAPHY........................ 109 6 ON MODELING GRAVITATION.........................................................................110 1 The Energy-Momentum Tensor..................................................... I l l 2 The Bridge between SR and GR....................................................................113 7 TABLE OF CONTENTS — Continued 3 The Consequences of Gravitation..................................................................114 4 Einstein's Gravitational Field Equations........................................................118 5 The BG Interpretation of GR Theory................................................. ,....... ...121 6 SELECTED BIBLIOGRAPHY......................................................................123 7 CONCLUSIONS...........................................................:..........................................124 1 On Whether Bondgraphs are the Appropriate Tool for Modeling SR and GR.......................................................................125 2 The Charm of Tensorial Power.................................................................. 125 3 The Impact of Parametrizing Mass on SR Theory........................................ 125 4 On Reconciling GR with Bondgraphics......................................................... 126 REFERENCES 127 8 LIST OF FIGURES FIGURE 4.1, The Paynter tetrahedron of state............................................................. 66 FIGURE 4.2a, The multibond representation