Yukterez

Relativistische Kugelwelle

Sep 21st, 2021 (edited)
17
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  1. (* Mathematica Syntax *) (* http://notizblock.yukterez.net/viewtopic.php?p=1319#p1319 *)
  2.  
  3. vs = 1.0; (* Signalgeschwindigkeit *)
  4. vX = 0.9; (* Beobachtergeschwindigkeit *)
  5.  
  6. vw = {vs Sin[θ], 0, vs Cos[θ]};
  7.  
  8. vx = vw[[1]];
  9. vy = vw[[2]];
  10. vz = vw[[3]];
  11.  
  12. U = {vX, 0, 0};
  13. V = {vx, vy, vz};
  14. γ = 1/Sqrt[1-Norm[U]^2];
  15. W = (U+V+γ/(1+γ)(U\[Cross](U\[Cross]V)))/(1+U.V);
  16.  
  17. VX = W[[1]];
  18. VY = W[[2]];
  19. VZ = W[[3]];
  20.  
  21. g[{Vx_, Vz_, t_, n_}] :=
  22. Show[
  23. Graphics[
  24. Table[{Hue[θ/2/π, 1, 1, 1], Point[{Vx t, Vz t}]}, {θ, π/90, 2π, π/90}],
  25. PlotRange->{{-1, +1}, {-1, +1}}, Frame->True, ImageSize->350],
  26. Graphics[Table[{Hue[θ/2/π, 1, 1, 0.5], Line[{{vX t n, 0},
  27. {Vx t, Vz t}}]}, {θ, π/90, 2π, π/90}]],
  28. Graphics[{Black, Disk[{vX t n, 0}, {0.03/If[n==0, 1, γ], 0.03}]}]];
  29.  
  30. Manipulate[Grid[{
  31. {g[{vx, vz, t, 0}], g[{VX, VZ, t, 1}]},
  32. {" t"->N@t}}, Alignment->Left], {t, 0, 1.5, 1/25}]
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