Arithmetic Applied Mathematics
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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.
Table of Contents
Preface
Chapter 1 Gravity
1.1 Introduction
1.2 Gravity
Chapter 2 Long and Short Range Forces: Gravitation and Molecular Attraction and Repulsion
2.1 Introduction
2.2 Gravitation
2.3 Basic Planar Concepts
2.4 Discrete Gravitation and Planetary Motion
2.5 The Generalized Newton's Method
2.6 An Orbit Example
2.7 Gravity Revisited
2.8 Classical Molecular Forces
2.9 Remark
Chapter 3 The N-Body Problem
3.1 Introduction
3.2 The Three-Body Problem
3.3 Conservation of Energy
3.4 Solution of the Discrete Three-Body Problem
3.5 Center of Gravity
3.6 Conservation of Linear Momentum
3.7 Conservation of Angular Momentum
3.8 The N-Body Problem
3.9 Remark
Chapter 4 Conservative Models
4.1 Introduction
4.2 The Solid State Building Block
4.3 Flow of Heat in a Bar
4.4 Oscillation of an Elastic Bar
4.5 Laminar and Turbulent Fluid Flows
Chapter 5 Nonconservative Models
5.1 Introduction
5.2 Shock Waves
5.3 The Leap-Frog Formulas
5.4 The Stefan Problem
5.5 Evolution of Planetary Type Bodies
5.6 Free Surface Fluid Flow
5.7 Porous Flow
Chapter 6 Foundational Concepts of Special Relativiy
6.1 Introduction
6.2 Basic Concepts
6.3 Events and a Special Lorentz Transformation
6.4 A General Lorentz Transformation
Chapter 7 Arithmetic Special Relativistic Mechanisms in One Space Dimension
7.1 Introduction
7.2 Proper Time
7.3 Velocity and Acceleration
7.4 Rest Mass and Momentum
7.5 The Dynamical Difference Equation
7.6 Energy
7.7 The Momentum-Energy Vector
7.8 Remarks
Chapter 8 Arithmetic Special Relativistic Mechanics in Three Space Dimensions
8.1 Introduction
8.2 Velocity, Acceleration, and Proper Time
8.3 Minkowski Space
8.4 4-Velocity and 4-Acceleration
8.5 Momentum and Energy
8.6 The Momentum-Energy 4-Vector
8.7 Dynamics
Chapter 9 Lorentz Invariant Computations
9.1 Introduction
9.2 Invariant Computations
9.3 An Arithmetic, Newtonian Harmonic Oscillator
9.4 An Arithmetic, Relativistic Harmonic Oscillator
9.5 Motion of an Electric Charge in a Magnetic Field
Appendix 1 Fortran Program for General N-Body Interaction
Appendix 2 Fortran Program for Planetary-Type Evolution
References and Sources for Further Reading
Index
Product details
- No. of pages: 174
- Language: English
- Copyright: © Pergamon 1980
- Published: January 1, 1980
- Imprint: Pergamon
- eBook ISBN: 9781483279855
About the Author
Donald Greenspan
About the Editors
V. Lakshmikantham
Affiliations and Expertise
University of Texas at Arlington, USA
C P Tsokos
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