Table of Contents
- Abstract, preface, references
- 1: Introduction
- 2: Fundamentals
- 3: Examples
- 4: Findings (part 1)
- 5: Findings (part 2)
- 6: Double pendulum analysis (part 1)
- 7: Double pendulum analysis (part 2)
- 8: Double pendulum analysis (part 3)
- 9: Double pendulum analysis (part 4)
- 10: Magnetic pendulum analysis
- 11: Issues in extending finding to complex real-world systems
- 12: Real-world systems
Chapter 2. Fundamentals
This chapter is a somewhat more technical and detailed explanation of the fundamentals of systems than found in Chapter 1. It mentions energy conserving or frictionless systems as opposed to energy dissipating system, which shed energy over time. The four natural forces holding the parts of natural systems in position are gravity, electromagnetic, and the nuclear strong and weak forces. The Morse curve applying to intra-molecular forces is displayed. It’s a proxy for similar forces where attracting and repelling forces keep the parts of a system held togeher, but yet kept separate. Oscillations produce waveforms, which is the main way we study them. More is said about the key role of energy in dynamic systems. Chaos is remarkably complex and attempts to define it are described. Periodic, quasi-periodic, and chaotic oscillations are described. The Lyapunov Exponent is one way to determine whether a system is chaotic, as are related tests for sensitive dependence or (SDIC).
Described here are some of the tools needed to study systems dynamics and chaos. Simulation models are key, and are much used in this book. They produce phase-space plots as well as waveforms.
