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]]
Attachments:
