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Re: NDSolve for Newtonian Orbits Question


It's probably not new to most of you, but I have a notebook on the
Mathematica page at www.eclecticdreams.net that proves (via ODE's) the
equivalence of Kepler's Laws and Newton's gravitation law.

Bobby

mathma18 at hotmail.com (Narasimham G.L.) wrote in message news:<c5di74$nsv$1 at smc.vnet.net>...
> "David Park" <djmp at earthlink.net> wrote in message news:<c4jasf$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


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