Yukterez

Gravity & Charge, 2 Body Simulator

Feb 16th, 2019 (edited)
55
Never
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
  1. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  2. (* ||| Mathematica Syntax || yukterez.net || 2 Body Newtonian Mass & Charge Simulator ||| *)
  3. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  4.  
  5. ClearAll["Global`*"]; ClearAll["Local`*"];
  6. Needs["DifferentialEquations`NDSolveProblems`"];
  7. Needs["DifferentialEquations`NDSolveUtilities`"];
  8.  
  9. Amp = 1; kg = 1; m = 1; sek = 1; km = 1000 m; (* SI Einheiten *)
  10.  
  11. mt1 = {"StiffnessSwitching", Method-> {"ExplicitRungeKutta", Automatic}};
  12. mt2 = {"ImplicitRungeKutta", "DifferenceOrder"-> 20};
  13. mt3 = {"EquationSimplification"-> "Residual"};
  14. mt0 = Automatic;
  15. mta = mt2;
  16. wp = MachinePrecision;
  17.  
  18. (* Plot Optionen *)
  19.  
  20. Tmax = 24 sek;
  21. tMax = Min[Tmax, plunge];
  22. trail = 12 sek;
  23. point = 0.015;
  24. thk = 0.004;
  25. plotrange = 1.2 m {{-1, +1}, {-1, +1}, {-1, +1}};
  26. viewpoint = {0, Infinity, 0};
  27. imagesize = 430;
  28. startpos = 0;
  29.  
  30. (* Konstanten *)
  31.  
  32. G = 667384/10^16 m^3/kg/sek^2;
  33. Λ = 11056*^-56/m^2;
  34. ε0 = 8854187817*^-21 Amp^2 sek^4/kg/m^3;
  35. c = 299792458 m/sek;
  36. Au = 149597870700 m;
  37. dy = 24*3600 sek;
  38. yr = 36525*dy/100;
  39.  
  40. (* Körper 1 *)
  41.  
  42. m1 = 1000000000 kg;
  43. q1 = 0;
  44.  
  45. x1x = 1/2 m;
  46. y1y = 0 m;
  47. z1z = 0 m;
  48.  
  49. v1x = 0 m/sek;
  50. v1y = 0 m/sek;
  51. v1z = Sqrt[G m2] Sqrt[1/2];
  52.  
  53. (* Körper 2 *)
  54.  
  55. m2 = m1/2;
  56. q2 = 0 Amp sek;
  57.  
  58. x2x = -1/2 m;
  59. y2y = 0 m;
  60. z2z = 0 m;
  61.  
  62. v2x = 0 m/sek;
  63. v2y = 0 m/sek;
  64. v2z = -Sqrt[G m1] Sqrt[1/2];
  65.  
  66. (* Differentialgleichung *)
  67.  
  68. nds=NDSolve[{
  69.  
  70. x1'[t] == vx1[t], y1'[t] == vy1[t], z1'[t] == vz1[t],
  71. x2'[t] == vx2[t], y2'[t] == vy2[t], z2'[t] == vz2[t],
  72.  
  73. vx1'[t] ==
  74. (G m2 (x2[t]-x1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  75. If[q1 == 0, 0,
  76. (-q1*q2/(4Pi ε0 )/m1 (x2[t]-x1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]]+
  77. Λ*c^2*x1[t]^2/Sqrt[x1[t]^2+y1[t]^2+z1[t]^2],
  78.  
  79. vy1'[t] ==
  80. (G m2 (y2[t]-y1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  81. If[q1 == 0, 0,
  82. (-q1*q2/(4Pi ε0 )/m1 (y2[t]-y1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]]+
  83. Λ*c^2*y1[t]^2/Sqrt[x1[t]^2+y1[t]^2+z1[t]^2],
  84.  
  85. vz1'[t] ==
  86. (G m2 (z2[t]-z1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  87. If[q1 == 0, 0,
  88. (-q1*q2/(4Pi ε0 )/m1 (z2[t]-z1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]]+
  89. Λ*c^2*z1[t]^2/Sqrt[x1[t]^2+y1[t]^2+z1[t]^2],
  90.  
  91. vx2'[t] ==
  92. (G m1 (x1[t]-x2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+
  93. If[q2 == 0, 0,
  94. (-q2*q1/(4Pi ε0 )/m2 (x1[t]-x2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]]+
  95. Λ*c^2*x2[t]^2/Sqrt[x2[t]^2+y2[t]^2+z2[t]^2],
  96.  
  97. vy2'[t] ==
  98. (G m1 (y1[t]-y2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+
  99. If[q2 == 0, 0,
  100. (-q2*q1/(4Pi ε0 )/m2 (y1[t]-y2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]]+
  101. Λ*c^2*y2[t]^2/Sqrt[x2[t]^2+y2[t]^2+z2[t]^2],
  102.  
  103. vz2'[t] ==
  104. (G m1 (z1[t]-z2[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  105. If[q2 == 0, 0,
  106. (-q2*q1/(4Pi ε0 )/m2 (z1[t]-z2[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]]+
  107. Λ*c^2*z2[t]^2/Sqrt[x2[t]^2+y2[t]^2+z2[t]^2],
  108.  
  109. x1[0] == x1x, y1[0] == y1y, z1[0] == z1z,
  110. x2[0] == x2x, y2[0] == y2y, z2[0] == z2z,
  111.  
  112. vx1[0] == v1x, vy1[0] == v1y, vz1[0] == v1z,
  113. vx2[0] == v2x, vy2[0] == v2y, vz2[0] == v2z},
  114.  
  115. {x1, x2, y1, y2, z1, z2,
  116. vx1, vx2, vy1, vy2, vz1, vz2},
  117.  
  118. {t, 0, Tmax},
  119.  
  120. WorkingPrecision-> wp,
  121. MaxSteps-> Infinity,
  122. Method-> mta,
  123. InterpolationOrder-> All,
  124. StepMonitor :> (laststep=plunge; plunge=t;
  125. stepsize=plunge-laststep;), Method->{"EventLocator",
  126. "Event" :> (If[stepsize<1*^-4, 0, 1])}];
  127.  
  128. (* Position, Geschwindigkeit *)
  129.  
  130. f2p[t_]={{x1[t], y1[t], z1[t]}, {x2[t], y2[t], z2[t]}}/.nds[[1]];
  131. f2v[t_]={{vx1[t], vy1[t], vz1[t]}, {vx2[t], vy2[t], vz2[t]}}/.nds[[1]];
  132. swp[t_]=(m1 Evaluate[f2p[t][[1]]]+m2 Evaluate[f2p[t][[2]]])/(m1+m2);
  133.  
  134. (* Formatierung *)
  135.  
  136. s[text_]=Style[text, FontSize->11];
  137. sw[text_]=Style[text, White, FontSize->11];
  138. colorfunc[n_]=Function[{x, y, z, t},
  139. Hue[0, n, 0.5,
  140. If[Tmax<0, Max[Min[(+T+(-t+trail))/trail, 1], 0],
  141. Max[Min[(-T+(t+trail))/trail, 1], 0]]]];
  142.  
  143. (* Animation *)
  144.  
  145. Do[Print[Rasterize[
  146. Grid[{{
  147. Show[
  148.  
  149. If[T == 0, {},
  150.  
  151. ParametricPlot3D[Evaluate[f2p[t]],
  152. {t, Max[0, T-trail], T},
  153.  
  154. PlotStyle->{
  155. {Thickness[thk], Red},
  156. {Thickness[thk], Blue}},
  157.  
  158. PlotRange->plotrange, AspectRatio->1, MaxRecursion->15, Axes->True, ImageSize->imagesize]],
  159.  
  160. Graphics3D[
  161. If[startpos==1, {
  162. {PointSize[2point/3], Lighter[Red], Point[{x1x, y1y, z1z}]},
  163. {PointSize[2point/3], Lighter[Blue],Point[{x2x, y2y, z2z}]}
  164. }, {}],
  165.  
  166. PlotRange->plotrange, AspectRatio->1, Axes->True, ImageSize->imagesize],
  167.  
  168. Graphics3D[{PointSize[point], Red, Point[Evaluate[f2p[T]][[1]]]}],
  169. Graphics3D[{PointSize[point], Blue, Point[Evaluate[f2p[T]][[2]]]}],
  170.  
  171. ViewPoint->viewpoint]},
  172.  
  173. { },
  174. {s["t"->N[T]], sw[1/2]},
  175. { },
  176. {s["p1{x,y,z}"-> Evaluate[f2p[T][[1]]]], sw[1/2]},
  177. {s["v1{x,y,z}"-> Evaluate[f2v[T][[1]]]], sw[1/2]},
  178. {s["v1{total}"->{Evaluate[Chop@Norm[f2v[T][[1]]]]}], sw[1/2]},
  179. { },
  180. {s["p2{x,y,z}"-> Evaluate[f2p[T][[2]]]], sw[1/2]},
  181. {s["v2{x,y,z}"-> Evaluate[f2v[T][[2]]]], sw[1/2]},
  182. {s["v2{total}"->{Evaluate[Chop@Norm[f2v[T][[2]]]]}], sw[1/2]},
  183. { },
  184. {s["ps{x,y,z}"-> swp[T]], sw[1/2]},
  185. {s["vs{x,y,z}"-> swp'[T]], sw[1/2]},
  186. {s["vs{total}"->{Chop@Norm[swp'[T]]}], sw[1/2]}
  187. }, Alignment->Left]]],
  188.  
  189. (* Zeitregler *)
  190.  
  191. {T, 0, tMax, tMax/5}]
  192.  
  193. (* Export als HTML Dokument *)
  194. (* Export["dateiname.html", EvaluationNotebook[], "GraphicsOutput" -> "PNG"] *)
  195. (* Export direkt als Bildsequenz *)
  196. (* ParallelDo[Export["dateiname" <> ToString[T] <> ".png", Rasterize[...] ], {T, 0, 10, 5}] *)
  197.  
  198.  
  199.  
  200.  
RAW Paste Data