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