Re: inverse square law attraction

*To*: mathgroup at smc.vnet.net*Subject*: [mg34891] Re: [mg34884] inverse square law attraction*From*: BobHanlon at aol.com*Date*: Wed, 12 Jun 2002 02:15:18 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

In a message dated 6/11/02 6:38:44 AM, boardman at onetel.net.uk writes: >I have a question I would be pleased if someone would answer. > >I am studying planetary motion under the inverse square law attraction. > >I use NDSolve to find the numerical solution to > >y''[t]====-y[t]/(x[t]^2+y[t]^2)^(3/2) >x''[t]====-x[t]/(x[t]^2+y[t]^2)^93/2) >x'[0]==0 >y'[0]==1.2 >y[0]==0 >x[0]==1 > >And get a very satisfactory ellipse. However, I would like to check the >hodograph >( a parametric plot of x'[t] and y'[t] >against time. NDSolve must have calculated values for x'[t] and y'[t] but >I > cannot find them. Where are they please? > Clear[x,y,t]; soln=NDSolve[{ y''[t]==-y[t]/(x[t]^2+y[t]^2)^(3/2), x''[t]==-x[t]/(x[t]^2+y[t]^2)^(3/2), x'[0]==0, y'[0]==1.2, y[0]==0, x[0]==1}, {x[t], y[t]}, {t, 0, 15}][[1]]; x[t_] := Evaluate[x[t]/.soln]; y[t_] := Evaluate[y[t] /.soln]; ParametricPlot[{x[t], y[t]}, {t, 0, 15}, AspectRatio->1]; Plot[{x[t], x'[t]},{t,0,15}]; Plot[{y[t], y'[t]},{t,0,15}]; ParametricPlot[{x'[t], y'[t]}, {t, 0, 15}, AspectRatio->1]; Bob Hanlon Chantilly, VA USA