I have one Graphics3D and one ParametricPlot3D, which I need to combine. Unfortunately, the Show[] Command does not work here, maybe because I use a Manipulate[] Command. The Prolog-> also does not work.
Plot1, the Graphics 3D, is a set of 3 Points (the initial positions of Plot2):
(* Plot 1 *)
P1 = {0, 0, 0}; P2 = {-1, 0, 2}; P3 = {-3, 4, -2};
Plot1 = Graphics3D[Point[{P1, P2, P3}],
PlotRange -> {{-5, 5}, {-5, 5}, {-3, 7}}, AspectRatio -> 1];
Plot 2, the ParametricPlot3D, is a 3D simulation of the three-body-problem. I need to have the Plot1 plotted right into Plot2:
(Edit: I dont know if the Code gets lost due conversion to plain text. If so, see .nb File at http://yukterez.ist.org/3kp/3k3D.nb
(* Plot 2 *)
G = 667384/
10^16;(* Gravitationskonstante *)
M1 = 100000000; M2 = 70000000; \
M3 = 50000000;(* Massen 1,2,3 in kg *)
v1x = 1/70; v1y = -1/130; v1z =
1/20;(* v0 von M1 in m/sek *)
v2x = -1/150; v2y = 1/100; v2z =
1/90;(* v0 von M2 in m/sek *)
v3x = 1/200; v3y =
1/110; v3z = -1/170;(* v0 von M3 in m/sek *)
P1 = {0, 0, 0}; (* Position 1 XYZ *)
P2 = {-1, 0, 2}; (* Position 2 XYZ *)
P3 = {-3, 4, -2}; (* Position 3 XYZ *)
(* Container *)
Funktion[{{x10_, y10_, z10_}, {x20_, y20_, z20_}, {x30_, y30_,
z30_}}, {{vx10_, vy10_, vz10_}, {vx20_, vy20_, vz20_}, {vx30_,
vy30_, vz30_}}, {m1_, m2_, m3_}, T_, plotType : ("x" | "v"),
plotOptions___] := Module[{nds, Tmax, prolog, funcToPlot},
(* Differentialgleichung *)nds = NDSolve[{
x1'[t] == vx1[t], y1'[t] == vy1[t], z1'[t] == vz1[t],
x2'[t] == vx2[t], y2'[t] == vy2[t], z2'[t] == vz2[t],
x3'[t] == vx3[t], y3'[t] == vy3[t], z3'[t] == vz3[t],
vx1'[
t] == -((G m2 (x1[t] - x2[t]))/
Sqrt[((x1[t] - x2[t])^2 + (y1[t] - y2[t])^2 + (z1[t] -
z2[t])^2)^3]) - (G m3 (x1[t] - x3[t]))/
Sqrt[((x1[t] - x3[t])^2 + (y1[t] - y3[t])^2 + (z1[t] -
z3[t])^2)^3],
vy1'[
t] == -((G m2 (y1[t] - y2[t]))/
Sqrt[((x1[t] - x2[t])^2 + (y1[t] - y2[t])^2 + (z1[t] -
z2[t])^2)^3]) - (G m3 (y1[t] - y3[t]))/
Sqrt[((x1[t] - x3[t])^2 + (y1[t] - y3[t])^2 + (z1[t] -
z3[t])^2)^3],
vz1'[
t] == -((G m2 (z1[t] - z2[t]))/
Sqrt[((x1[t] - x2[t])^2 + (y1[t] - y2[t])^2 + (z1[t] -
z2[t])^2)^3]) - (G m3 (z1[t] - z3[t]))/
Sqrt[((x1[t] - x3[t])^2 + (y1[t] - y3[t])^2 + (z1[t] -
z3[t])^2)^3],
vx2'[t] == (G m1 (x1[t] - x2[t]))/
Sqrt[((x1[t] - x2[t])^2 + (y1[t] - y2[t])^2 + (z1[t] -
z2[t])^2)^3] - (G m3 (x2[t] - x3[t]))/
Sqrt[((x2[t] - x3[t])^2 + (y2[t] - y3[t])^2 + (z2[t] -
z3[t])^2)^3],
vy2'[t] == (G m1 (y1[t] - y2[t]))/
Sqrt[((x1[t] - x2[t])^2 + (y1[t] - y2[t])^2 + (z1[t] -
z2[t])^2)^3] - (G m3 (y2[t] - y3[t]))/
Sqrt[((x2[t] - x3[t])^2 + (y2[t] - y3[t])^2 + (z2[t] -
z3[t])^2)^3],
vz2'[t] == (G m1 (z1[t] - z2[t]))/
Sqrt[((x1[t] - x2[t])^2 + (y1[t] - y2[t])^2 + (z1[t] -
z2[t])^2)^3] - (G m3 (z2[t] - z3[t]))/
Sqrt[((x2[t] - x3[t])^2 + (y2[t] - y3[t])^2 + (z2[t] -
z3[t])^2)^3],
vx3'[t] == (G m1 (x1[t] - x3[t]))/
Sqrt[((x1[t] - x3[t])^2 + (y1[t] - y3[t])^2 + (z1[t] -
z3[t])^2)^3] + (G m2 (x2[t] - x3[t]))/
Sqrt[((x2[t] - x3[t])^2 + (y2[t] - y3[t])^2 + (z2[t] -
z3[t])^2)^3],
vy3'[t] == (G m1 (y1[t] - y3[t]))/
Sqrt[((x1[t] - x3[t])^2 + (y1[t] - y3[t])^2 + (z1[t] -
z3[t])^2)^3] + (G m2 (y2[t] - y3[t]))/
Sqrt[((x2[t] - x3[t])^2 + (y2[t] - y3[t])^2 + (z2[t] -
z3[t])^2)^3],
vz3'[t] == (G m1 (z1[t] - z3[t]))/
Sqrt[((x1[t] - x3[t])^2 + (y1[t] - y3[t])^2 + (z1[t] -
z3[t])^2)^3] + (G m2 (z2[t] - z3[t]))/
Sqrt[((x2[t] - x3[t])^2 + (y2[t] - y3[t])^2 + (z2[t] -
z3[t])^2)^3],
x1[0] == x10, y1[0] == y10, z1[0] == z10,
x2[0] == x20, y2[0] == y20, z2[0] == z20,
x3[0] == x30, y3[0] == y30, z3[0] == z30,
vx1[0] == vx10, vy1[0] == vy10, vz1[0] == vz10,
vx2[0] == vx20, vy2[0] == vy20, vz2[0] == vz20,
vx3[0] == vx30, vy3[0] == vy30, vz3[0] == vz30},
{x1, x2, x3, y1, y2, y3, z1, z2, z3, vx1, vx2, vx3, vy1, vy2,
vy3, vz1, vz2, vz3}, {t, 0, T}];
If[Head[nds] =!= NDSolve, Tmax = nds[[1, 1, 2, 1, 1, 2]];
funcToPlot =
If[plotType ===
"x", {{x1[t], y1[t], z1[t]}, {x2[t], y2[t], z2[t]}, {x3[t],
y3[t], z3[t]}}, {{vx1[t], vy1[t], vz1[t]}, {vx2[t], vy2[t],
vz2[t]}, {vx3[t], vy3[t], vz3[t]}}] /. nds[[1]];
(* Plot Specifications *)
prolog = {PointSize[0.3], Point[{P1, P2, P3}]};
ParametricPlot3D[Evaluate[funcToPlot], {t, 0, Tmax},
PlotStyle -> {Red, Blue, Green},
(* Plot Range und Seitenverhältnis *)
PlotRange -> {{-5, 5}, {-5, 5}, {-3, 7}}, AspectRatio -> 1,
(* Prolog -> prolog, *) MaxRecursion -> ControlActive[3, 9],
Axes -> True, plotOptions], Text["Yukterez Mod. of demonstrations.wolfram.com/PlanarThreeBodyProblem"]]] // Quiet
Plot2 = Manipulate[Funktion[
(* Positionen xy *){P1, P2, P3},
(* Geschwindigkeiten xy *){{v1x, v1y, v1z}, {v2x, v2y, v2z}, {v3x,
v3y, v3z}},
(* Massen *){M1, M2, M3},
(* Regler *)T, xv,
ImageSize -> {320, 320}],
{{xv, "x", "Position/Geschwindigkeit"},
{"x" -> "Position", "v" -> "Geschwindigkeit"}},
{{T, 1, "Zeit"}, 1, 200}, ControlPlacement -> {Bottom}]
(* http://yukterez.ist.org/3kp/3k3D.html *)
