Problem using Manipulate for NDSolve

Question

I have been using NDSolve and ParametricPlot3D without problems.

This is my code:

f[x_, y_] := (x^2 + y^2)/2
superficie := 
 ParametricPlot3D[{r*Cos[t], r*Sin[t], f[r*Cos[t], r*Sin[t]]}, {r, 0, 
   3}, {t, 0, 2*Pi}, PlotStyle -> Opacity[.5], Mesh -> None]

fx[x_, y_] = D[f[x, y], x];
fy[x_, y_] = D[f[x, y], y];

EcuacionDiferencial[{x0_, y0_}, {u0_, 
   v0_}] := {x''[t] == -fx[x[t], y[t]]/Sqrt[1 + (fx[x[t], y[t]])^2], 
  y''[t] == -fy[x[t], y[t]]/Sqrt[1 + (fy[x[t], y[t]])^2], x[0] == x0, 
  x'[0] == u0, y[0] == y0, y'[0] == v0}

TiempoFinal = 17;

PuntoInicial = {0, 1.3}; VelocidadInicial = {1, 0};

Soln := Flatten[
  NDSolve[EcuacionDiferencial[PuntoInicial, VelocidadInicial], {x, 
    y}, {t, 0, TiempoFinal}]]; 

r[t_] = {x[t], y[t], f[x[t], y[t]]} /. Soln;

Show[ParametricPlot3D[r[t], {t, 0, TiempoFinal}, 
  PlotStyle -> AbsoluteThickness[1]], superficie, PlotRange -> All]

It works plotting everything.

Now, I need to use a Manipulate command to make the 1.1 inside PuntoInicial, to fluctuate beetween 0.9 and 1.3.

Any ideas of how I could do that? I have been trying for 2 hours but nothing.

Thanks!!

Answer 1

I need to use a Manipulate command to make the 1.1 inside PuntoInicial, to fluctuate beetween 0.9 and 1.3

May be this can get you started.

ps. I changed all UpperCaseStartingNames to lowerCaseStartingNames since in Mathematica it is best not to start something with UpperCase letter.

Manipulate[
puntoInicial={0,to};
soln:=Flatten[NDSolve[ecuacionDiferencial[puntoInicial,velocidadInicial],
      {x,y},{t,0,tiempoFinal}]];

r[t_]={x[t],y[t],f[x[t],y[t]]}/.soln;

Show[
    ParametricPlot3D[r[t],{t,0,tiempoFinal},
    PlotStyle->AbsoluteThickness[1],PerformanceGoal->"Quality"],
    superficie,
    PlotRange->{{-3,3},{-3,3},{0,4}}, (*add to prevent shifting*)
    ImageSize->400,
    ImagePadding->20]
,

{{to,.9,"to"},.9,1.3,.01}, (*change as needed*)

TrackedSymbols:>{to},
SynchronousUpdating->True,SynchronousInitialization->True,
    FrameMargins->1,ImageMargins->1,
Initialization:> 
(
f[x_,y_]:=(x^2+y^2)/2;
superficie:=ParametricPlot3D[{r*Cos[t],r*Sin[t],f[r*Cos[t],r*Sin[t]]},
       {r,0,3},{t,0,2*Pi},PlotStyle->Opacity[.5],Mesh->None];

fx[x_,y_]=D[f[x,y],x];
fy[x_,y_]=D[f[x,y],y];

ecuacionDiferencial[{x0_,y0_},{u0_,v0_}]:={x''[t]==-fx[x[t],y[t]]/Sqrt[1+(fx[x[t],y[t]])^2],y''[t]==-fy[x[t],y[t]]/Sqrt[1+(fy[x[t],y[t]])^2],x[0]==x0,x'[0]==u0,y[0]==y0,y'[0]==v0};

tiempoFinal=17;
velocidadInicial={1,0};

)
]