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3 bodies in Mathematica 3.0

  • To: mathgroup at smc.vnet.net
  • Subject: [mg17224] 3 bodies in Mathematica 3.0
  • From: price at math.wisc.edu (Adam Price)
  • Date: Mon, 26 Apr 1999 01:20:54 -0400
  • Organization: University of Wisconsin, Madison
  • Sender: owner-wri-mathgroup at wolfram.com

I am trying to reproduce a Poincare Section I found in an article on a
restricted three body problem (M. Henon, 1983), and not having much
success. 

The motion of the third, smallest planet relative to the center of
gravity other two is governed by x''[t]:= a function of x, y, and y',
while y''[t] := a function of x,y, and x'.

The author has computed the Jacobi Integral, which is then an equality
involving x, y, x', and y'.  

At my disposal I have Mathematica 3.0 and the VisualDSolve add-on package.
(Which is great!)  I am not having any luck with the section, though, as
the first derivatives can't be explicitly integrated.  Without knowing the
first derivatives, how can I use the second derivatives and initial
conditions to generate a graph?  SecondOrderPlot doesnt SEEM to work, as
the first derivatives are mentioned in the definitions of the second.

-Adam


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