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Re: NDSolve for Newtonian Orbits Question

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  • Subject: [mg47446] Re: NDSolve for Newtonian Orbits Question
  • From: mathma18 at (Narasimham G.L.)
  • Date: Mon, 12 Apr 2004 03:45:00 -0400 (EDT)
  • References: <c4jasf$dpk$>
  • Sender: owner-wri-mathgroup at

"David Park" <djmp at> wrote in message news:<c4jasf$dpk$1 at>...
> I am trying to obtain a numerical solution for Newtonian orbits... For a start I just want to solve for the radius r as a function of time.

You are the frequent solution provider ...This may not give a proper
answer.I was earlier told some non-linear equations like y y''=
constant are not so easy to solve on Mathematica, but you may find it
is not so ..

I tried to get the the earliest Newton's differential equation
involving radius solved with respect to time. [(r-th) ellipse solution
is well known.]. Wonder how Newton obtained radius as a time function,
or whether it is mentioned  in Principia. I eliminated h (angular
momentum) to get a decoupled (r-time) non-linear ODE. FWIW, please see
running thread in sci.math about < Differential equations of periodic
functions > in:
; Thomas Nordhaus, Peter Montgomery and Roger Bagula have made
interesting comments.  Best Regards, Narasimham

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