MathGroup Archive 1999

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3 bodies in Mathematica 3.0

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

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

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.


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