Greenspan / Lakshmikantham / Tsokos Arithmetic Applied Mathematics

1. Auflage 2014
ISBN: 978-1-4832-7985-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 174 Seiten, Web PDF

Arithmetic Applied Mathematics deals with concepts of arithmetic applied mathematics and uses a computer, rather than a continuum, approach to the deterministic theories of particle mechanics. Models of classical physical phenomena are formulated from both Newtonian and special relativistic mechanics using only arithmetic. Definitions of energy and momentum are presented that are identical to those of continuum mechanics. Comprised of nine chapters, this book begins by exploring discrete modeling as it relates to Newtonian mechanics and special relativistic mechanics, paying particular attention to gravity. The reader is then introduced to long-range forces such as gravitation and short-range forces such as molecular attraction and repulsion; the N-body problem; and conservative and non-conservative models of complex physical phenomena. Subsequent chapters focus on the foundational concepts of special relativity; arithmetic special relativistic mechanics in one space dimension and three space dimensions; and Lorentz invariant computations. This monograph will be of interest to students and practitioners in the fields of mathematics and physics.

Autoren/Hrsg.

Greenspan, Donald

Lakshmikantham, V.

Tsokos, C P

Inhaltsverzeichnis

1;Front Cover;1
2;Arithmetic Applied Mathematics;4
3;Copyright Page
;5
4;Table of Contents;6
5;Preface;8
6;Chapter 1. Gravity;10
6.1;1.1 INTRODUCTION;10
6.2;1.2 GRAVITY;10
7;Chapter 2. Long and Short Range Forces: Gravitation and Molecular Attraction and Repulsion;16
7.1;2.1 INTRODUCTION;16
7.2;2.2 GRAVITATION;16
7.3;2.3 BASIC PLANAR CONCEPTS;18
7.4;2.4 DISCRETE GRAVITATION AND PLANETARY MOTION;20
7.5;2.5 THE GENERALIZED NEWTON'S METHOD;22
7.6;2.6 AN ORBIT EXAMPLE;23
7.7;2.7 GRAVITY REVISITED;25
7.8;2.8 CLASSICAL MOLECULAR FORCES;27
7.9;2.9 REMARK;28
8;Chapter 3. The N-body Problem;29
8.1;3.1 INTRODUCTION;29
8.2;3.2 THE THREE-BODY PROBLEM;29
8.3;3.3 CONSERVATION OF ENERGY;31
8.4;3.4 SOLUTION OF THE DISCRETE THREE-BODY PROBLEM;32
8.5;3.5 CENTER OF GRAVITY;34
8.6;3.6 CONSERVATION OF LINEAR MOMENTUM;36
8.7;3.7 CONSERVATION OF ANGULAR MOMENTUM;36
8.8;3.8 THE N-BODY PROBLEM;39
8.9;3.9 REMARK;40
9;Chapter 4. Conservative Models;41
9.1;4.1 INTRODUCTION;41
9.2;4.2 THE SOLID STATE BUILDING BLOCK;41
9.3;4.3 FLOW OF HEAT IN A BAR;43
9.4;4.4 OSCILLATION OF AN ELASTIC BAR;45
9.5;4.5 LAMINAR AND TURBULENT FLUID FLOWS;48
10;Chapter 5. Nonconservative Models;53
10.1;5.1 INTRODUCTION;53
10.2;5.2 SHOCK WAVES;53
10.3;5.3 THE LEAP-FROG FORMULAS;57
10.4;5.4 THE STEFAN PROBLEM;57
10.5;5.5 EVOLUTION OF PLANETARY TYPE BODIES;73
10.6;5.6 FREE SURFACE FLUID FLOW;101
10.7;5.7 POROUS FLOW;113
11;Chapter 6. Foundational Concepts of Special Relativity;118
11.1;6.1 INTRODUCTION;118
11.2;6.2 BASIC CONCEPTS;118
11.3;6.3 EVENTS AND A SPECIAL LORENTZ TRANSFORMATION;119
11.4;6.4 A GENERAL LORENTZ TRANSFORMATION;121
12;Chapter 7. Arithmetic Special Relativistic Mechanics in One Space Dimension;124
12.1;7.1 INTRODUCTION;124
12.2;7.2 PROPER TIME;125
12.3;7.3 VELOCITY AND ACCELERATION;126
12.4;7.4 REST MASS AND MOMENTUM;128
12.5;7.5 THE DYNAMICAL DIFFERENCE EQUATION;129
12.6;7.6 ENERGY;130
12.7;7.7 THE MOMENTUM-ENERGY VECTOR;132
12.8;7.8 REMARKS;133
13;Chapter 8. Arithmetic Special Relativistic Mechanics in Three Space Dimensions;134
13.1;8.1 INTRODUCTION;134
13.2;8.2 VELOCITY, ACCELERATION, AND PROPER TIME;134
13.3;8.3 MINKOWSKI SPACE;137
13.4;8.4 4-VELOCITY AND 4-ACCELERATION;138
13.5;8.5 MOMENTUM AND ENERGY;140
13.6;8.6 THE MOMENTUM-ENERGY 4-VECTOR;141
13.7;8.7 DYNAMICS;142
14;Chapter 9. Lorentz Invariant Computations;145
14.1;9.1 INTRODUCTION;145
14.2;9.2 INVARIANT COMPUTATIONS;145
14.3;9.3 AN ARITHMETIC, NEWTONIAN HARMONIC OSCILLATOR;147
14.4;9.4 AN ARITHMETIC, RELATIVISTIC HARMONIC OSCILLATOR;150
14.5;9.5 MOTION OF AN ELECTRIC CHARGE IN A MAGNETIC FIELD;154
15;Appendix 1: Fortran Program for General N-body Interaction;157
16;Appendix 2: Fortran Program for Planetary-type Evolution;163
17;References and Sources for Further Reading;167
18;Index;172