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Re: NDSolve for Newtonian Orbits Question

• To: mathgroup at smc.vnet.net
• Subject: [mg47446] Re: NDSolve for Newtonian Orbits Question
• From: mathma18 at hotmail.com (Narasimham G.L.)
• Date: Mon, 12 Apr 2004 03:45:00 -0400 (EDT)
• References: <c4jasf$dpk$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

"David Park" <djmp at earthlink.net> wrote in message news:<c4jasf$dpk$1 at smc.vnet.net>...
> 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: http://groups.google.co.in/groups?dq=&hl=en&lr=&ie=UTF-8&th=63b9b64ea13f1c82
; Thomas Nordhaus, Peter Montgomery and Roger Bagula have made
interesting comments.  Best Regards, Narasimham