The study and application of N-body problems has had an important role in the history of mathematics. In recent years, the availability of modern computer technology has added to their significance, since computers can now be used to model material bodies as atomic and molecular configurations, i.e. as N-body configurations.
This book can serve either as a handbook or as a text. Methodology, intuition, and applications are interwoven throughout. Nonlinearity and determinism are emphasized. The book can be used on any level provided that the reader has at least some ability with numerical methodology, computer programming, and basic physics. It will be of interest to mathematicians, engineers, computer scientists, physicists, chemists, and biologists.
Some unique features of the book include: (1) development of turbulent flow which is consistent with experimentation, unlike any continuum model; (2) applicability to rotating tops with nonuniform density; (3) conservative methodology which conserves the same energy and momentum as continuous systems.
Contents:
- Nonlinear Oscillation
- Relativistic Oscillation, Perihelion Motion
- The Fundamental Problem of Electrostatics
- Toda and Calogero Hamiltonians
- Shock Waves
- Cracks and Fractures
- Laminar and Turbulent Flow
- Contact Angles of Adhesion
- Fluid Bubbles
- Rotating Tops
- Biological Self Reorganization, Bouncing Elastic Balls
- Solitons
- Minimal Surfaces
- Discrete Conservation Laws
Readership: Graduate students and researchers in mathematics, physics, materials science, fluid dynamics, and electrical and mechanical engineering.
