Hi,
I'm in the same situation at the moment regarding the work of
Mathis. I've just found out about his, at least at first sight,
surprising and impressive body of work, when doing research to answer
your question.
Regarding your research: We talked here on vortex-l in the past about so
called "chaotic" (stochastic) behavior.
It is my understanding that if it were not for stochastic phenomena, the
solar system would be "dead" long ago, i.e. everything would have
collapsed into stability. It's due to the fact that always new small
impulses are added to or produced in the system, that the planets
continue moving in their orbits. If you carry the CM computations far
enough, everything eventually stalls, or collapses. So, your addition of
small chaotic perturbations could be closer to the truth than what is
normally assumed.
I've also ran Newtonian simulations of the solar system in the past, to
observe the effect of outer bodies on the perihelion of the orbits of
the inner planets, with practically null results. If your addition of
small chaotic perturbations can in some cases model the advance of
Mercury's perihelion, by example, that's would be a very valuable result.
And the line of research in itself is very interesting. At a given
point, you would have to consider too how those "chaotic" effects could
take place in the solar system. And of course, I think that it would be
also very interesting to know what kind of effects you have modeled, or
produced.
Regards,
Mauro
On 09/22/2010 06:13 PM, OrionWorks - Steven V Johnson wrote:
> Mauro,
>
> Thanks for pointing me to the analysis work of Mathis. At present, I
> don't know if I can make practical use of his mathematical findings or
> not. It's probably going to make my brain hurt for quite a spell while
> attempting to get the gist of it all.
>
> To clarify what I have been doing: For several years now I have been
> researching what I have assumed is probably considered by most an
> uninteresting aspect of Newtonian based Celestial Mechanics, (CM).
> More to the point, I have focused primarily on computational feed-back
> loops where chaos is introduced into the solution. I've been plotting
> the "chaotic" results for some time now. No doubt, much of this work
> is related to emergent behavior, fractals, and what-not. It would not
> surprise me if some of Wolfram's work may have occasionally touched on
> what I have been studying. (Mike Carroll brought Worlfram's work to my
> attention.) Serendipitously, I recently discovered that Wolfram used
> his Mathematica software to study the characteristics of the empty
> foci belonging to a classic elliptical shaped satellite/planetary
> orbit. I was gratified to discover that the results Wolfram's
> Mathematica produced seemed to mirror some of my own independently
> researched findings.
>
> I have assumed (perhaps incorrectly) that the specific CM branch I'm
> studying (the chaotic aspect) is probably considered uninteresting and
> not of much practical value to most scientists & researchers. I assume
> so because of the fact that when it comes to accurately plotting the
> orbits of celestial bodies like planets, moons, and satellites the
> last thing one wants to do is introduce the effects of chaos into the
> algorithm! For obvious reasons the effects of chaos must be kept at a
> minimum in order to accurately plot a future position of a celestial
> body. This is accomplished by making sure the computational iterative
> samples one feeds into the algorithm are sufficiently small, from
> plotted point to the next plotted point. Things can quickly get
> squirrely as one's "satellite" approaches the main attractor body, and
> the plotted point-to-point positions increase in distance from each
> other geometrically.
>
> But there by the Grace of God go I. I've discovered that within the
> unpredictable realms of chaos a wealth of strange and weird-like
> behavior is worth exploring. At the razor's edge, where the boundary
> between Order and Chaos meet, I find tantalizing behavior. My chaotic
> research continues. I hope to eventually put some of my findings out
> on the net. Much more work needs to be done... It's daunting.
>
> Regards
> Steven Vincent Johnson
> www.OrionWorks.com
> www.zazzle.com/orionworks
>
>
>
