Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Structure and Interpretation of Classical Mechanics



I ran into Gerry Sussman in Indianapolis last week.

With co-author Jack Wisdom, he recently wrote a book called
_Structure and Interpretation of Classical Mechanics_

This is a very good book. It is amazing to see so much
originality applied to such an old topic. It is original
without being eccentric; this is how it _should_ have
been done all along. All other books on the topic are
obsolete.

One of the reviews on amazon.com suggested it might be
suitable for high schools, but I don't think so -- not
at any high school I know about. Even before it gets
to page 1 it uses partial differential equations. It
could be used as a textbook at the undergrad level,
before, after, or concurrent with a first quantum-mechanics
course. It is quite readable, even engaging.

It's in bookstores, but for those who can't afford to
buy it, or aren't sure they want to buy it, the whole
thing is on the web at
http://mitpress.mit.edu/SICM/book.html

I quote from the preface:
http://mitpress.mit.edu/SICM/book-Z-H-5.html
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 system....

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
that depend on context, and often even change within a given
context.
....
This book is the result of teaching classical mechanics at MIT
for the past six years. The contents of our class began with
ideas from a class on nonlinear dynamics and solar system
dynamics by Wisdom and ideas about how computation can be
used to formulate methodology developed in an introductory
computer science class by Abelson and Sussman. When we
started we expected that using this approach to formulate
mechanics would be easy. We quickly learned that many things
we thought we understood we did not in fact understand. Our
requirement that our mathematical notations be explicit and
precise enough that they can be interpreted automatically, as
by a computer, is very effective in uncovering puns and flaws in
reasoning. The resulting struggle to make the mathematics
precise, yet clear and computationally effective, lasted far
longer than we anticipated. We learned a great deal about both
mechanics and computation by this process.

I enjoyed the quotations from other
authors about the problems they faced:

``In almost all textbooks, even the
best, this principle is presented so
that it is impossible to understand.''
(K. Jacobi, Lectures on Dynamics, 1842-1843).

``It is necessary to use the apparatus of partial derivatives, in
which even the notation is ambiguous.'' V.I. Arnold,
Mathematical Methods of Classical Mechanics p. 258.