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
