ParametricPlot of multiple ODEs only displays 1 PlotLegend instead of all

Questions
,
1

Hey there,
I’m quite new to Mathematica, but am required to use it by university. Anyways.
The topic actually says it all. I try to get a parametric plot, which works just fine. But Mathematica does not label my functions completely (and the one label that is applied was applied to the wrong function, 1 MeV is supposed to be the blue one).
Here’s the Code:

solution[energy_] := 

  NDSolve[{2 (z*e^2)/(r*(x[t]^2 + y[t]^2)^(3/2))*x[t] == m*x''[t], 

    2 (z*e^2)/(r*(x[t]^2 + y[t]^2)^(3/2))*y[t] == m*y''[t], y[0] == p,

     y'[0] == 0, x'[0] == v[energy], x[0] == a}, {x, y}, {t, 0, max}];
sol = {solution[1], solution[10 ], solution[50]};

ParametricPlot[

 {

  {Evaluate[{x[t], y[t]}  /. sol[[1]]]},

  {Evaluate[{x[t], y[t]}  /. sol[[2]]]},

  {Evaluate[{x[t], y[t]}  /. sol[[3]]]}

  }, {t, 0, max}, PlotRange -> {-5*10^-12, 5*10^-12}, 

 AxesLabel -> {"x[t]", "y[t]"}, 

 PlotLegends -> {"1 MeV", "10 MeV", "50 MeV"}, ImageSize -> Large]

Also on a side note:
Is it possible to directly use solution in parametric plot without using the workaround with sol ={..} ? I’d like to use a manipulate plot with it. :slight_smile:
Edit:
Is it possible to scale the x and y axis in a Parametric Plot differently?

Next Edit:
When I se PlotLegend->“Expressions” it seems to write everything in one line
I managed to workarond it using PlotLegends->SwatchLegends

2

what is your max value.. and what are the parameter values?

you can just upload nb code, intead of copying and pasting..

3

Here’s the file and code:

(* Konstanten *)

m = 4*1.672621777*10^-27;(* Masse Alpha-Teilchen *)

e = 1.60218 * 10^-19  ; (* Elementarladung *)

z = 79 ;(* Ordnungszahl Gold *)

r = 4*Pi*8.854*10^-12; (* 4 Pi Epsilon Null *)

(* Variablen *)

p[k_] := k*10^-14; (* Stoßparameter *)

a = -1 * 10^-10; (* Abstand vom Atom *)

v[energy_] := Sqrt[

  2*energy*10^6 * e /

   m]; (* Geschwindigkeit, Abhänging von Energie in MeV *)

max = 10^-15; (* maximale Zeit zu der berechnet wird *)



(* Numerisches Lösen der DGL *)

solution[energy_, k_] := 

  NDSolve[{2 (z*e^2)/(r*(x[t]^2 + y[t]^2)^(3/2))*x[t] == m*x''[t], 

    2 (z*e^2)/(r*(x[t]^2 + y[t]^2)^(3/2))*y[t] == m*y''[t], 

    y[0] == p[k], y'[0] == 0, x'[0] == v[energy], x[0] == a}, {x, 

    y}, {t, 0, max}];









sol1 = {solution[1, 1], solution[10, 1], solution[50, 1]};

sol5 = {solution[1, 5], solution[10, 5], solution[50, 5]};

sol10 = {solution[1, 10], solution[10, 10], solution[50, 10]};







(* Plot für p = 10fm *)

ParametricPlot[

 {

  {Evaluate[{x[t], y[t]}  /. sol1[[1]]]},

  {Evaluate[{x[t], y[t]}  /. sol1[[2]]]},

  {Evaluate[{x[t], y[t]}  /. sol1[[3]]]}

  }, {t, 0, max}, PlotRange -> {-5*10^-12, 5*10^-12}, 

 AxesLabel -> {"x[t]", "y[t]"}, ImageSize -> Large, 

 PlotStyle -> {Blue, Red, Green}, 

 PlotLegends -> 

  SwatchLegend[{Blue, Red, Green}, {"1 MeV", "10 MeV", "50 MeV"}], 

 PlotLabel -> Style["p = 10fm", FontSize -> 18]]

(* Plot für 50fm *)

ParametricPlot[

 {

  {Evaluate[{x[t], y[t]}  /. sol5[[1]]]},

  {Evaluate[{x[t], y[t]}  /. sol5[[2]]]},

  {Evaluate[{x[t], y[t]}  /. sol5[[3]]]}

  }, {t, 0, max}, PlotRange -> {-5*10^-12, 5*10^-12}, 

 AxesLabel -> {"x[t]", "y[t]"}, ImageSize -> Large, 

 PlotStyle -> {Blue, Red, Green}, 

 PlotLegends -> 

  SwatchLegend[{Blue, Red, Green}, {"1 MeV", "10 MeV", "50 MeV"}], 

 PlotLabel -> Style["p = 50fm", FontSize -> 18]]

(*Plot für 100fm*)

ParametricPlot[

 {

  {Evaluate[{x[t], y[t]}  /. sol10[[1]]]},

  {Evaluate[{x[t], y[t]}  /. sol10[[2]]]},

  {Evaluate[{x[t], y[t]}  /. sol10[[3]]]}

  }, {t, 0, max}, PlotRange -> {-5*10^-12, 5*10^-12}, 

 AxesLabel -> {"x[t]", "y[t]"}, ImageSize -> Large, 

 PlotStyle -> {Blue, Red, Green}, 

 PlotLegends -> 

  SwatchLegend[{Blue, Red, Green}, {"1 MeV", "10 MeV", "50 MeV"}], 

 PlotLabel -> Style["p = 100fm", FontSize -> 18]]