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 [email protected] 505-819-7388 > 1943 Otowi Road, Santa Fe, New Mexico 87505 > > On Fri, Feb 18, 2011 at 4:30 PM, > OrionWorks - "Steven V Johnson" <[email protected]> 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 [email protected] 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
