Classical mechanics, with computer simulation

In the comments on my post on Project Euler, plam pointed me to a physics book: Structure and Interpretation of Classical Mechanicsby Gerald Jay Sussman and Jack Wisdom with Meinhard E. Mayer (MIT Press, ©2001).  The preface of the book explains the premise nicely:

Traditional treatments of mechanics concentrate most of their effort on the extremely small class of symbolically tractable dynamical 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 different 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.

The book appears to be all on line, so I may try to learn some physics from it.

The computation is expressed in Scheme (a LISP dialect), which is an understandable choice given that the book was written at MIT at a time when the first computer science course there was taught using Scheme.  The authors make a big deal about how little syntax Scheme has, which I do not necessarily see as a good thing.  Having to count positional arguments and parentheses all the time does not lead to greater readability and debuggability of programs.

Their point

The advantage of Scheme over other languages for the exposition of classical mechanics is that the manipulation of procedures that implement mathematical functions is easier and more natural in Scheme than in other computer languages. Indeed, many theorems of mechanics are directly representable as Scheme programs.

is well-taken, though, so I will withhold judgement on whether Scheme is a suitable choice pedagogically until I’ve had a chance to read some of the book.

Judging from the first few pages of the book, this text is not intended for students to learn physics from for the first time.  There seems to be an assumption that the reader is already familiar with the differential equations that are used in Newtonian mechanics, so that the different “variational” approach used in this text can be contrasted with the Newtonian approach without ever explaining that approach.

The first equation in the first chapter is already fairly opaque, with as a path, as a function of time that measures some local property of the path , and the unexplained presumably being defined by this integral.

The first equation of the book is already pretty opaque.

I think I can work my way through the notation, but I doubt that I would give this book to a high school student for self-study.  I just hope that the mathematical elegance of the Lagrangian approach justifies slogging through some rather turgid prose.