Arithmetic Applied Mathematics

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. Content: INTERNATIONAL SERIES INNONLINEAR MATHEMATICS: Theory, Methods and Applications, Page ii Front Matter, Page iii Copyright, Page iv Preface, Page vii Chapter 1 - Gravity, Pages 1-6 Chapter 2 - Long and Short Range Forces: Gravitation and Molecular Attraction and Repulsion, Pages 7-19 Chapter 3 - The N-body Problem, Pages 20-31 Chapter 4 - Conservative Models, Pages 32-43 Chapter 5 - Nonconservative Models, Pages 44-108 Chapter 6 - Foundational Concepts of Special Relativity, Pages 109-114 Chapter 7 - Arithmetic Special Relativistic Mechanics in One Space Dimension, Pages 115-124 Chapter 8 - Arithmetic Special Relativistic Mechanics in Three Space Dimensions, Pages 125-135 Chapter 9 - Lorentz Invariant Computations, Pages 136-147 Appendix 1 - Fortran Program for General N-body Interaction, Pages 148-153 Appendix 2 - Fortran Program for Planetary-type Evolution, Pages 154-157 References and Sources for Further Reading, Pages 158-161 Index, Pages 163-165