Maxima by Example: Ch. 7, 8, 9, 10, and 11

On May 2, 2009, Wolfgang Lindner wrote:
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   I remember that Gerald Jay Sussman and Jack Wisdom wrote the book
 "Structure and Interpretation of Classical Mechanics".
 There is code (using Scheme ~ Lisp) parallel to the chapters of the book.
 I once dreamed to translate this into the language of a (free) CAS ..
 now Maxima seems to be a possible platform for such ideas.
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All the topics in this book are important and their approach to the
subject is a search for qualitative understanding of nonlinear
behavior...a great subject for a book that uses Maxima.
Stavros mentions their more abstract and formal notation,
introduced to be able to make a direct connection between
differential equations and computational code. If I were
writing a book that covered the same material, I think I would
stick to the more usual (and ambiguous) notation, simply
because readers ready for this level of mechanics can fill in
the understood details of the notation themselves.

It's nice that the book is available (with table of contents) in
html on the web at
http://groups.csail.mit.edu/mac/users/gjs/6946/sicm-html/book-Z-H-3.html#%_toc_start

or just go to the fall 08 version of their course at
http://groups.csail.mit.edu/mac/users/gjs/6946/index.html
and click on Mechanics Book (HTML).
(the lisp like code is embedded in the text discussion)
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Both Wisdom and Sussman are computational physics
heroes whose work is well known for their prediction
of the long run chaotic future of the solar system.
( go to Wisdom's page
http://groups.csail.mit.edu/mac/users/wisdom/
and click on link
''Chaotic Evolution of the Solar System'' G.J. Sussman and J. Wisdom 1992, 
Science 257, 56.

Ted Woollett
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Science 22 July 1988:
Vol. 241. no. 4864, pp. 433 - 437

Numerical Evidence That the Motion of Pluto Is Chaotic
GERALD JAY SUSSMAN 1 and JACK WISDOM 2

1 Department of Electrical Engineering and Computer
   Science, Massachusetts Institute of Technology, Cambridge, MA 02139.
2 Department of Earth Atmospheric and Planetary
   Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139.

Abstract: The Digital Orrery has been used to perform an integration of
    the motion of the outer planets for 845 million years.
   This integration indicates that the long-term motion of the
    planet Pluto is chaotic. Nearby trajectories diverge exponentially
    with  an  e-folding time of only about 20 million years.

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Science 3 July 1992:
Vol. 257. no. 5066, pp. 56 - 62

Chaotic Evolution of the Solar System
Gerald Jay Sussman 1 and Jack Wisdom 2

1 Department of Electrical Engineering
    and Computer Science, Massachusetts Institute
     of Technology, Cambridge, MA 02139
2 Department of Earth Atmospheric and Planetary
    Sciences, Massachusetts Institute of Technology,
    Cambridge, MA 02139

Abstract:
The evolution of the entire planetary system has been
   numerically integrated for a time span of nearly 100
   million years. This calculation confirms that the
   evolution of the solar system as a whole is chaotic,
   with a time scale of exponential divergence of about
  4 million years. Additional numerical experiments
   indicate that the Jovian planet subsystem is chaotic,
   although some small variations in the model can yield
   quasiperiodic motion. The motion of Pluto is
    independently and robustly chaotic.

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