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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.