Structure and Interpretation of Classical Mechanics (The MIT Press)

Book Preface

There has been a remarkable revival of interest in classical me- chanics in recent years. We now know that there is much more to classical mechanics than previously suspected. The behavior of classical systems is surprisingly rich; derivation of the equations of motion, the focus of traditional presentations of mechanics, is just the beginning. Classical systems display a complicated array of phenomena such as non-linear resonances, chaotic behavior, and transitions to chaos.

Traditional treatments of mechanics concentrate most of their e®ort on the extremely small class of symbolically tractable dy- namical systems. We concentrate on developing general methods for studying the behavior of systems, whether or not they have a symbolic solution. Typical systems exhibit behavior that is qualitatively di®erent from the solvable systems and surprisingly complicated. We focus on the phenomena of motion, and we make extensive use of computer simulation to explore this motion. Even when a system is not symbolically tractable the tools of modern dynamics allow one to extract a qualitative understand- ing. Rather than concentrating on symbolic descriptions, we con- centrate on geometric features of the set of possible trajectories. Such tools provide a basis for the systematic analysis of numerical or experimental data.

Classical mechanics is deceptively simple. It is surprisingly easy to get the right answer with fallacious reasoning or without real understanding. Traditional mathematical notation contributes to this problem. Symbols have ambiguous meanings, which de- pend on context, and often even change within a given context.1