"A Digital Orrery," James Applegate, M. Douglas, Y. Gursel, P Hunter, C.
Seitz, Gerald Jay Sussman, in IEEE Transactions on Computers, *C-34*, No. 9,
pp. 822-831, September 1985, reprinted in Lecture Notes in Physics #267 --
Use of supercomputers in stellar dynamics, Springer Verlag, 1986.

But also look at:


http://en.wikipedia.org/wiki/Structure_and_Interpretation_of_Classical_Mechanics

which gives you a pointer to the online copy of Sussman's text on the
subject.

-- rec --

On Sat, Feb 19, 2011 at 4:53 AM, <lrudo...@meganet.net> wrote:

> With particular regard to computer simulations of
> celestial mechanics, Gerry Sussman wrote a paper
> sometime in (IIRC) the late 1970s, about the
> ultimate instability of the solar system (one
> of the classical motivations for celestial
> mechanics in general and the 3-body problem
> in particular).
>
> I could be vaguer if I tried.
>
> Lee Rudolph
>
> > Yes, the n-body system with n>2 is known to be chaotic, but subject to
> > the constraints of the KAM theorem
> > (http://en.wikipedia.org/wiki/Kolmogorov-Arnold-Moser_theorem), ie
> > there exist quasi-periodic orbits for certain initial conditions.
> >
> > This was certainly known stuff when I studied dynamical systems as an
> > undergrad in the early '80s.
> >
> > On Fri, Feb 18, 2011 at 08:17:37PM -0700, Rich Murray wrote:
> > > does classical mechanics always fail to predict or retrodict for 3 or
> > > more Newtonian gravity bodies? Rich Murray 2011.02.18
> > >
> > > Hello Steven V Johnson,
> > >
> > > Can I have a free copy of the celestial mechanics software to run on
> > > my Vista 64 bit PC?
> > >
> > > In fall, 1982, I wrote a 200-line program in Basic for the
> > > Timex-Sinclair $100 computer with 20KB RAM that would do up to 4
> > > bodies in 3D space or 5 in 2D space, about 1000 steps in an hour,
> > > saving every 10th position and velocity -- I could set it up to
> > > reverse the velocities after the orbits became chaotic after 3 1/2
> > > orbits from initial perfect symmetry as circles about the common
> > > center of gravity, finding that they always maintained chaos, never
> > > returning to the original setup -- doubling the number of steps while
> > > reducing the time interval by half never slowed the the evolution of
> > > chaos by 3 1/2 orbits -- so I doubted that there is any mathematical
> > > basis for the claim that classical mechanics predicts the past or
> > > future evolution of any system with over 2 bodies, leading to a
> > > conjecture that no successful algorithm exists, even without any close
> > > encounters.
> > >
> > > Has this been noticed by others?
> > >
> > > Rich Murray rmfor...@gmail.com  505-819-7388
> > > 1943 Otowi Road, Santa Fe, New Mexico 87505
> > >
> > > On Fri, Feb 18, 2011 at 4:30 PM,
> > > OrionWorks - "Steven V Johnson" <svj.orionwo...@gmail.com> wrote:
> > >
> > > > Just a brief side-comment...
> > > >
> > > > Some of this "lingo" is fascinating stuff to me. Having performed a
> > > > lot of theoretical computer simulation work on my own using good'ol
> > > > fashion Newtonian based Celestial Mechanics algorithms, where
> > > > typically I use "a = 1/r^2", I noticed orbital pattern behavior
> > > > transforms into something RADICALLY different, such as if I were to
> > > > change the classical algorithm to something like "a = 1/r^3". You can
> > > > also combine both of them like "a = 1/r^2 +/-  1/r^3" within the same
> > > > computer algorithm. That produces interesting side effects too. I'm
> > > > still trying to get a handle on it all.
> > > >
> > > > Regards
> > > > Steven Vincent Johnson
> > > > www.OrionWorks.com
> > > > www.zazzle.com/orionworks
> > >
> > > ============================================================
> > > FRIAM Applied Complexity Group listserv
> > > Meets Fridays 9a-11:30 at cafe at St. John's College
> > > lectures, archives, unsubscribe, maps at http://www.friam.org
> >
> > --
> >
> >
> ----------------------------------------------------------------------------
> > Prof Russell Standish                  Phone 0425 253119 (mobile)
> > Mathematics
> > UNSW SYDNEY 2052                       hpco...@hpcoders.com.au
> > Australia                                http://www.hpcoders.com.au
> >
> ----------------------------------------------------------------------------
> >
> > ============================================================
> > FRIAM Applied Complexity Group listserv
> > Meets Fridays 9a-11:30 at cafe at St. John's College
> > lectures, archives, unsubscribe, maps at http://www.friam.org
>
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> lectures, archives, unsubscribe, maps at http://www.friam.org
>
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