Yukterez

Gravity & Charge, 8 Body Simulator

Feb 20th, 2019 (edited)
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  1. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  2. (* ||| Mathematica Syntax || yukterez.net || 8 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 = 2 Sqrt[15/7] Pi;
  21. tMax = Min[Tmax, plunge];
  22. trail = Tmax/20;
  23. point = 0.015;
  24. thk = 0.004;
  25. plotrange = 1.5 {{-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. (* Anfangsgeschwindigkeit und Radius *)
  41.  
  42. v0 = Sqrt[28/15];
  43. fk = 10025/10000;
  44.  
  45. (* Körper 1 *)
  46.  
  47. m1 = 1*^10;
  48. q1 = 0;
  49.  
  50. x1x = -fk;
  51. y1y = 0;
  52. z1z = 0;
  53.  
  54. v1x = 0;
  55. v1y = 0;
  56. v1z = v0;
  57.  
  58. (* Körper 2 *)
  59.  
  60. m2 = m1;
  61. q2 = 0 Amp sek;
  62.  
  63. x2x = fk;
  64. y2y = 0;
  65. z2z = 0;
  66.  
  67. v2x = 0;
  68. v2y = 0;
  69. v2z = -v0;
  70.  
  71. (* Körper 3 *)
  72.  
  73. m3 = m1;
  74. q3 = 0;
  75.  
  76. x3x = 0;
  77. y3y = 0;
  78. z3z = fk;
  79.  
  80. v3x = v0;
  81. v3y = 0;
  82. v3z = 0;
  83.  
  84. (* Körper 4 *)
  85.  
  86. m4 = m1;
  87. q4 = 0;
  88.  
  89. x4x = 0;
  90. y4y = 0;
  91. z4z = -fk;
  92.  
  93. v4x = -v0;
  94. v4y = 0;
  95. v4z = 0;
  96.  
  97. (* Körper 5 *)
  98.  
  99. m5 = m1;
  100. q5 = 0;
  101.  
  102. x5x = Sqrt[1/2] fk;
  103. y5y = 0;
  104. z5z = Sqrt[1/2] fk;
  105.  
  106. v5x = Sqrt[1/2] v0;
  107. v5y = 0;
  108. v5z = -Sqrt[1/2] v0;
  109.  
  110. (* Körper 6 *)
  111.  
  112. m6 = m1;
  113. q6 = 0;
  114.  
  115. x6x = -Sqrt[1/2] fk;
  116. y6y = 0;
  117. z6z = Sqrt[1/2] fk;
  118.  
  119. v6x = Sqrt[1/2] v0;
  120. v6y = 0;
  121. v6z = Sqrt[1/2] v0;
  122.  
  123. (* Körper 7 *)
  124.  
  125. m7 = m1;
  126. q7 = 0;
  127.  
  128. x7x = Sqrt[1/2] fk;
  129. y7y = 0;
  130. z7z = -Sqrt[1/2] fk;
  131.  
  132. v7x = -Sqrt[1/2] v0;
  133. v7y = 0;
  134. v7z = -Sqrt[1/2] v0;
  135.  
  136. (* Körper 8 *)
  137.  
  138. m8 = m1;
  139. q8 = 0;
  140.  
  141. x8x = -Sqrt[1/2] fk;
  142. y8y = 0;
  143. z8z = -Sqrt[1/2] fk;
  144.  
  145. v8x = -Sqrt[1/2] v0;
  146. v8y = 0;
  147. v8z = Sqrt[1/2] v0;
  148.  
  149. (* Differentialgleichung *)
  150.  
  151. nds=NDSolve[{
  152.  
  153. x1'[t] == vx1[t], y1'[t] == vy1[t], z1'[t] == vz1[t],
  154. x2'[t] == vx2[t], y2'[t] == vy2[t], z2'[t] == vz2[t],
  155. x3'[t] == vx3[t], y3'[t] == vy3[t], z3'[t] == vz3[t],
  156. x4'[t] == vx4[t], y4'[t] == vy4[t], z4'[t] == vz4[t],
  157. x5'[t] == vx5[t], y5'[t] == vy5[t], z5'[t] == vz5[t],
  158. x6'[t] == vx6[t], y6'[t] == vy6[t], z6'[t] == vz6[t],
  159. x7'[t] == vx7[t], y7'[t] == vy7[t], z7'[t] == vz7[t],
  160. x8'[t] == vx8[t], y8'[t] == vy8[t], z8'[t] == vz8[t],
  161.  
  162. vx1'[t] ==
  163. (G m2 (x2[t]-x1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  164. (G m3 (x3[t]-x1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
  165. (G m4 (x4[t]-x1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
  166. (G m5 (x5[t]-x1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+
  167. (G m6 (x6[t]-x1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+
  168. (G m7 (x7[t]-x1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+
  169. (G m8 (x8[t]-x1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]+
  170. If[q1 == 0, 0,
  171. (-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]+
  172. (-q1*q3/(4Pi ε0 )/m1 (x3[t]-x1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
  173. (-q1*q4/(4Pi ε0 )/m1 (x4[t]-x1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
  174. (-q1*q5/(4Pi ε0 )/m1 (x5[t]-x1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+
  175. (-q1*q6/(4Pi ε0 )/m1 (x6[t]-x1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+
  176. (-q1*q7/(4Pi ε0 )/m1 (x7[t]-x1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+
  177. (-q1*q8/(4Pi ε0 )/m1 (x8[t]-x1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]]+
  178. Λ*c^2*x1[t]^2/Sqrt[x1[t]^2+y1[t]^2+z1[t]^2],
  179.  
  180. vy1'[t] ==
  181. (G m2 (y2[t]-y1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  182. (G m3 (y3[t]-y1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
  183. (G m4 (y4[t]-y1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
  184. (G m5 (y5[t]-y1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+
  185. (G m6 (y6[t]-y1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+
  186. (G m7 (y7[t]-y1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+
  187. (G m8 (y8[t]-y1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]+
  188. If[q1 == 0, 0,
  189. (-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]+
  190. (-q1*q3/(4Pi ε0 )/m1 (y3[t]-y1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
  191. (-q1*q4/(4Pi ε0 )/m1 (y4[t]-y1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
  192. (-q1*q5/(4Pi ε0 )/m1 (y5[t]-y1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+
  193. (-q1*q6/(4Pi ε0 )/m1 (y6[t]-y1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+
  194. (-q1*q7/(4Pi ε0 )/m1 (y7[t]-y1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+
  195. (-q1*q8/(4Pi ε0 )/m1 (y8[t]-y1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]]+
  196. Λ*c^2*y1[t]^2/Sqrt[x1[t]^2+y1[t]^2+z1[t]^2],
  197.  
  198. vz1'[t] ==
  199. (G m2 (z2[t]-z1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  200. (G m3 (z3[t]-z1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
  201. (G m4 (z4[t]-z1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
  202. (G m5 (z5[t]-z1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+
  203. (G m6 (z6[t]-z1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+
  204. (G m7 (z7[t]-z1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+
  205. (G m8 (z8[t]-z1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]+
  206. If[q1 == 0, 0,
  207. (-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]+
  208. (-q1*q3/(4Pi ε0 )/m1 (z3[t]-z1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
  209. (-q1*q4/(4Pi ε0 )/m1 (z4[t]-z1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
  210. (-q1*q5/(4Pi ε0 )/m1 (z5[t]-z1[t]))/Sqrt[((x5[t]-x1[t])^2+(y5[t]-y1[t])^2+(z5[t]-z1[t])^2)^3]+
  211. (-q1*q6/(4Pi ε0 )/m1 (z6[t]-z1[t]))/Sqrt[((x6[t]-x1[t])^2+(y6[t]-y1[t])^2+(z6[t]-z1[t])^2)^3]+
  212. (-q1*q7/(4Pi ε0 )/m1 (z7[t]-z1[t]))/Sqrt[((x7[t]-x1[t])^2+(y7[t]-y1[t])^2+(z7[t]-z1[t])^2)^3]+
  213. (-q1*q8/(4Pi ε0 )/m1 (z8[t]-z1[t]))/Sqrt[((x8[t]-x1[t])^2+(y8[t]-y1[t])^2+(z8[t]-z1[t])^2)^3]]+
  214. Λ*c^2*z1[t]^2/Sqrt[x1[t]^2+y1[t]^2+z1[t]^2],
  215.  
  216. vx2'[t] ==
  217. (G m1 (x1[t]-x2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+
  218. (G m3 (x3[t]-x2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
  219. (G m4 (x4[t]-x2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
  220. (G m5 (x5[t]-x2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+
  221. (G m6 (x6[t]-x2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+
  222. (G m7 (x7[t]-x2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+
  223. (G m8 (x8[t]-x2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]+
  224. If[q2 == 0, 0,
  225. (-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]+
  226. (-q2*q3/(4Pi ε0 )/m2 (x3[t]-x2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
  227. (-q2*q4/(4Pi ε0 )/m2 (x4[t]-x2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
  228. (-q2*q5/(4Pi ε0 )/m2 (x5[t]-x2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+
  229. (-q2*q6/(4Pi ε0 )/m2 (x6[t]-x2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+
  230. (-q2*q7/(4Pi ε0 )/m2 (x7[t]-x2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+
  231. (-q2*q8/(4Pi ε0 )/m2 (x8[t]-x2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]]+
  232. Λ*c^2*x2[t]^2/Sqrt[x2[t]^2+y2[t]^2+z2[t]^2],
  233.  
  234. vy2'[t] ==
  235. (G m1 (y1[t]-y2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+
  236. (G m3 (y3[t]-y2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
  237. (G m4 (y4[t]-y2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
  238. (G m5 (y5[t]-y2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+
  239. (G m6 (y6[t]-y2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+
  240. (G m7 (y7[t]-y2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+
  241. (G m8 (y8[t]-y2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]+
  242. If[q2 == 0, 0,
  243. (-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]+
  244. (-q2*q3/(4Pi ε0 )/m2 (y3[t]-y2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
  245. (-q2*q4/(4Pi ε0 )/m2 (y4[t]-y2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
  246. (-q2*q5/(4Pi ε0 )/m2 (y5[t]-y2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+
  247. (-q2*q6/(4Pi ε0 )/m2 (y6[t]-y2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+
  248. (-q2*q7/(4Pi ε0 )/m2 (y7[t]-y2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+
  249. (-q2*q8/(4Pi ε0 )/m2 (y8[t]-y2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]]+
  250. Λ*c^2*y2[t]^2/Sqrt[x2[t]^2+y2[t]^2+z2[t]^2],
  251.  
  252. vz2'[t] ==
  253. (G m1 (z1[t]-z2[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
  254. (G m3 (z3[t]-z2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
  255. (G m4 (z4[t]-z2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
  256. (G m5 (z5[t]-z2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+
  257. (G m6 (z6[t]-z2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+
  258. (G m7 (z7[t]-z2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+
  259. (G m8 (z8[t]-z2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]+
  260. If[q2 == 0, 0,
  261. (-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]+
  262. (-q2*q3/(4Pi ε0 )/m2 (z3[t]-z2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
  263. (-q2*q4/(4Pi ε0 )/m2 (z4[t]-z2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
  264. (-q2*q5/(4Pi ε0 )/m2 (z5[t]-z2[t]))/Sqrt[((x5[t]-x2[t])^2+(y5[t]-y2[t])^2+(z5[t]-z2[t])^2)^3]+
  265. (-q2*q6/(4Pi ε0 )/m2 (z6[t]-z2[t]))/Sqrt[((x6[t]-x2[t])^2+(y6[t]-y2[t])^2+(z6[t]-z2[t])^2)^3]+
  266. (-q2*q7/(4Pi ε0 )/m2 (z7[t]-z2[t]))/Sqrt[((x7[t]-x2[t])^2+(y7[t]-y2[t])^2+(z7[t]-z2[t])^2)^3]+
  267. (-q2*q8/(4Pi ε0 )/m2 (z8[t]-z2[t]))/Sqrt[((x8[t]-x2[t])^2+(y8[t]-y2[t])^2+(z8[t]-z2[t])^2)^3]]+
  268. Λ*c^2*z2[t]^2/Sqrt[x2[t]^2+y2[t]^2+z2[t]^2],
  269.  
  270. vx3'[t] ==
  271. (G m1 (x1[t]-x3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
  272. (G m2 (x2[t]-x3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
  273. (G m4 (x4[t]-x3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
  274. (G m5 (x5[t]-x3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+
  275. (G m6 (x6[t]-x3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+
  276. (G m7 (x7[t]-x3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+
  277. (G m8 (x8[t]-x3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]+
  278. If[q3 == 0, 0,
  279. (-q3*q1/(4Pi ε0 )/m3 (x1[t]-x3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
  280. (-q3*q2/(4Pi ε0 )/m3 (x2[t]-x3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
  281. (-q3*q4/(4Pi ε0 )/m3 (x4[t]-x3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
  282. (-q3*q5/(4Pi ε0 )/m3 (x5[t]-x3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+
  283. (-q3*q6/(4Pi ε0 )/m3 (x6[t]-x3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+
  284. (-q3*q7/(4Pi ε0 )/m3 (x7[t]-x3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+
  285. (-q3*q8/(4Pi ε0 )/m3 (x8[t]-x3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]]+
  286. Λ*c^2*x3[t]^2/Sqrt[x3[t]^2+y3[t]^2+z3[t]^2],
  287.  
  288. vy3'[t] ==
  289. (G m1 (y1[t]-y3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
  290. (G m2 (y2[t]-y3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
  291. (G m4 (y4[t]-y3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
  292. (G m5 (y5[t]-y3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+
  293. (G m6 (y6[t]-y3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+
  294. (G m7 (y7[t]-y3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+
  295. (G m8 (y8[t]-y3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]+
  296. If[q3 == 0, 0,
  297. (-q3*q1/(4Pi ε0 )/m3 (y1[t]-y3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
  298. (-q3*q2/(4Pi ε0 )/m3 (y2[t]-y3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
  299. (-q3*q4/(4Pi ε0 )/m3 (y4[t]-y3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
  300. (-q3*q5/(4Pi ε0 )/m3 (y5[t]-y3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+
  301. (-q3*q6/(4Pi ε0 )/m3 (y6[t]-y3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+
  302. (-q3*q7/(4Pi ε0 )/m3 (y7[t]-y3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+
  303. (-q3*q8/(4Pi ε0 )/m3 (y8[t]-y3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]]+
  304. Λ*c^2*y3[t]^2/Sqrt[x3[t]^2+y3[t]^2+z3[t]^2],
  305.  
  306. vz3'[t] ==
  307. (G m1 (z1[t]-z3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
  308. (G m2 (z2[t]-z3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
  309. (G m4 (z4[t]-z3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
  310. (G m5 (z5[t]-z3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+
  311. (G m6 (z6[t]-z3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+
  312. (G m7 (z7[t]-z3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+
  313. (G m8 (z8[t]-z3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]+
  314. If[q3 == 0, 0,
  315. (-q3*q1/(4Pi ε0 )/m3 (z1[t]-z3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
  316. (-q3*q2/(4Pi ε0 )/m3 (z2[t]-z3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
  317. (-q3*q4/(4Pi ε0 )/m3 (z4[t]-z3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
  318. (-q3*q5/(4Pi ε0 )/m3 (z5[t]-z3[t]))/Sqrt[((x5[t]-x3[t])^2+(y5[t]-y3[t])^2+(z5[t]-z3[t])^2)^3]+
  319. (-q3*q6/(4Pi ε0 )/m3 (z6[t]-z3[t]))/Sqrt[((x6[t]-x3[t])^2+(y6[t]-y3[t])^2+(z6[t]-z3[t])^2)^3]+
  320. (-q3*q7/(4Pi ε0 )/m3 (z7[t]-z3[t]))/Sqrt[((x7[t]-x3[t])^2+(y7[t]-y3[t])^2+(z7[t]-z3[t])^2)^3]+
  321. (-q3*q8/(4Pi ε0 )/m3 (z8[t]-z3[t]))/Sqrt[((x8[t]-x3[t])^2+(y8[t]-y3[t])^2+(z8[t]-z3[t])^2)^3]]+
  322. Λ*c^2*z3[t]^2/Sqrt[x3[t]^2+y3[t]^2+z3[t]^2],
  323.  
  324. vx4'[t] ==
  325. (G m1 (x1[t]-x4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
  326. (G m2 (x2[t]-x4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
  327. (G m3 (x3[t]-x4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
  328. (G m5 (x5[t]-x4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+
  329. (G m6 (x6[t]-x4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+
  330. (G m7 (x7[t]-x4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+
  331. (G m8 (x8[t]-x4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]+
  332. If[q4 == 0, 0,
  333. (-q4*q1/(4Pi ε0 )/m4 (x1[t]-x4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
  334. (-q4*q2/(4Pi ε0 )/m4 (x2[t]-x4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
  335. (-q4*q3/(4Pi ε0 )/m4 (x3[t]-x4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
  336. (-q4*q5/(4Pi ε0 )/m4 (x5[t]-x4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+
  337. (-q4*q6/(4Pi ε0 )/m4 (x6[t]-x4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+
  338. (-q4*q7/(4Pi ε0 )/m4 (x7[t]-x4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+
  339. (-q4*q8/(4Pi ε0 )/m4 (x8[t]-x4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]]+
  340. Λ*c^2*x4[t]^2/Sqrt[x4[t]^2+y4[t]^2+z4[t]^2],
  341.  
  342. vy4'[t] ==
  343. (G m1 (y1[t]-y4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
  344. (G m2 (y2[t]-y4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
  345. (G m3 (y3[t]-y4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
  346. (G m5 (y5[t]-y4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+
  347. (G m6 (y6[t]-y4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+
  348. (G m7 (y7[t]-y4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+
  349. (G m8 (y8[t]-y4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]+
  350. If[q4 == 0, 0,
  351. (-q4*q1/(4Pi ε0 )/m4 (y1[t]-y4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
  352. (-q4*q2/(4Pi ε0 )/m4 (y2[t]-y4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
  353. (-q4*q3/(4Pi ε0 )/m4 (y3[t]-y4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
  354. (-q4*q5/(4Pi ε0 )/m4 (y5[t]-y4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+
  355. (-q4*q6/(4Pi ε0 )/m4 (y6[t]-y4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+
  356. (-q4*q7/(4Pi ε0 )/m4 (y7[t]-y4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+
  357. (-q4*q8/(4Pi ε0 )/m4 (y8[t]-y4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]]+
  358. Λ*c^2*y4[t]^2/Sqrt[x4[t]^2+y4[t]^2+z4[t]^2],
  359.  
  360. vz4'[t] ==
  361. (G m1 (z1[t]-z4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
  362. (G m2 (z2[t]-z4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
  363. (G m3 (z3[t]-z4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
  364. (G m5 (z5[t]-z4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+
  365. (G m6 (z6[t]-z4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+
  366. (G m7 (z7[t]-z4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+
  367. (G m8 (z8[t]-z4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]+
  368. If[q4 == 0, 0,
  369. (-q4*q1/(4Pi ε0 )/m4 (z1[t]-z4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
  370. (-q4*q2/(4Pi ε0 )/m4 (z2[t]-z4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
  371. (-q4*q3/(4Pi ε0 )/m4 (z3[t]-z4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
  372. (-q4*q5/(4Pi ε0 )/m4 (z5[t]-z4[t]))/Sqrt[((x5[t]-x4[t])^2+(y5[t]-y4[t])^2+(z5[t]-z4[t])^2)^3]+
  373. (-q4*q6/(4Pi ε0 )/m4 (z6[t]-z4[t]))/Sqrt[((x6[t]-x4[t])^2+(y6[t]-y4[t])^2+(z6[t]-z4[t])^2)^3]+
  374. (-q4*q7/(4Pi ε0 )/m4 (z7[t]-z4[t]))/Sqrt[((x7[t]-x4[t])^2+(y7[t]-y4[t])^2+(z7[t]-z4[t])^2)^3]+
  375. (-q4*q8/(4Pi ε0 )/m4 (z8[t]-z4[t]))/Sqrt[((x8[t]-x4[t])^2+(y8[t]-y4[t])^2+(z8[t]-z4[t])^2)^3]]+
  376. Λ*c^2*z4[t]^2/Sqrt[x4[t]^2+y4[t]^2+z4[t]^2],
  377.  
  378. vx5'[t] ==
  379. (G m1 (x1[t]-x5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+
  380. (G m2 (x2[t]-x5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+
  381. (G m3 (x3[t]-x5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+
  382. (G m4 (x4[t]-x5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+
  383. (G m6 (x6[t]-x5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+
  384. (G m7 (x7[t]-x5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+
  385. (G m8 (x8[t]-x5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]+
  386. If[q5 == 0, 0,
  387. (-q5*q1/(4Pi ε0 )/m5 (x1[t]-x5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+
  388. (-q5*q2/(4Pi ε0 )/m5 (x2[t]-x5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+
  389. (-q5*q3/(4Pi ε0 )/m5 (x3[t]-x5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+
  390. (-q5*q4/(4Pi ε0 )/m5 (x4[t]-x5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+
  391. (-q5*q6/(4Pi ε0 )/m5 (x6[t]-x5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+
  392. (-q5*q7/(4Pi ε0 )/m5 (x7[t]-x5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+
  393. (-q5*q8/(4Pi ε0 )/m5 (x8[t]-x5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]]+
  394. Λ*c^2*x5[t]^2/Sqrt[x5[t]^2+y5[t]^2+z5[t]^2],
  395.  
  396. vy5'[t] ==
  397. (G m1 (y1[t]-y5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+
  398. (G m2 (y2[t]-y5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+
  399. (G m3 (y3[t]-y5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+
  400. (G m4 (y4[t]-y5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+
  401. (G m6 (y6[t]-y5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+
  402. (G m7 (y7[t]-y5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+
  403. (G m8 (y8[t]-y5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]+
  404. If[q5 == 0, 0,
  405. (-q5*q1/(4Pi ε0 )/m5 (y1[t]-y5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+
  406. (-q5*q2/(4Pi ε0 )/m5 (y2[t]-y5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+
  407. (-q5*q3/(4Pi ε0 )/m5 (y3[t]-y5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+
  408. (-q5*q4/(4Pi ε0 )/m5 (y4[t]-y5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+
  409. (-q5*q6/(4Pi ε0 )/m5 (y6[t]-y5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+
  410. (-q5*q7/(4Pi ε0 )/m5 (y7[t]-y5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+
  411. (-q5*q8/(4Pi ε0 )/m5 (y8[t]-y5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]]+
  412. Λ*c^2*y5[t]^2/Sqrt[x5[t]^2+y5[t]^2+z5[t]^2],
  413.  
  414. vz5'[t] ==
  415. (G m1 (z1[t]-z5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+
  416. (G m2 (z2[t]-z5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+
  417. (G m3 (z3[t]-z5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+
  418. (G m4 (z4[t]-z5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+
  419. (G m6 (z6[t]-z5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+
  420. (G m7 (z7[t]-z5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+
  421. (G m8 (z8[t]-z5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]+
  422. If[q5 == 0, 0,
  423. (-q5*q1/(4Pi ε0 )/m5 (z1[t]-z5[t]))/Sqrt[((x1[t]-x5[t])^2+(y1[t]-y5[t])^2+(z1[t]-z5[t])^2)^3]+
  424. (-q5*q2/(4Pi ε0 )/m5 (z2[t]-z5[t]))/Sqrt[((x2[t]-x5[t])^2+(y2[t]-y5[t])^2+(z2[t]-z5[t])^2)^3]+
  425. (-q5*q3/(4Pi ε0 )/m5 (z3[t]-z5[t]))/Sqrt[((x3[t]-x5[t])^2+(y3[t]-y5[t])^2+(z3[t]-z5[t])^2)^3]+
  426. (-q5*q4/(4Pi ε0 )/m5 (z4[t]-z5[t]))/Sqrt[((x4[t]-x5[t])^2+(y4[t]-y5[t])^2+(z4[t]-z5[t])^2)^3]+
  427. (-q5*q6/(4Pi ε0 )/m5 (z6[t]-z5[t]))/Sqrt[((x6[t]-x5[t])^2+(y6[t]-y5[t])^2+(z6[t]-z5[t])^2)^3]+
  428. (-q5*q7/(4Pi ε0 )/m5 (z7[t]-z5[t]))/Sqrt[((x7[t]-x5[t])^2+(y7[t]-y5[t])^2+(z7[t]-z5[t])^2)^3]+
  429. (-q5*q8/(4Pi ε0 )/m5 (z8[t]-z5[t]))/Sqrt[((x8[t]-x5[t])^2+(y8[t]-y5[t])^2+(z8[t]-z5[t])^2)^3]]+
  430. Λ*c^2*z5[t]^2/Sqrt[x5[t]^2+y5[t]^2+z5[t]^2],
  431.  
  432. vx6'[t] ==
  433. (G m1 (x1[t]-x6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+
  434. (G m2 (x2[t]-x6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+
  435. (G m3 (x3[t]-x6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+
  436. (G m4 (x4[t]-x6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+
  437. (G m5 (x5[t]-x6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+
  438. (G m7 (x7[t]-x6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+
  439. (G m8 (x8[t]-x6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]+
  440. If[q6 == 0, 0,
  441. (-q6*q1/(4Pi ε0 )/m6 (x1[t]-x6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+
  442. (-q6*q2/(4Pi ε0 )/m6 (x2[t]-x6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+
  443. (-q6*q3/(4Pi ε0 )/m6 (x3[t]-x6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+
  444. (-q6*q4/(4Pi ε0 )/m6 (x4[t]-x6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+
  445. (-q6*q5/(4Pi ε0 )/m6 (x5[t]-x6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+
  446. (-q6*q7/(4Pi ε0 )/m6 (x7[t]-x6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+
  447. (-q6*q8/(4Pi ε0 )/m6 (x8[t]-x6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]]+
  448. Λ*c^2*x6[t]^2/Sqrt[x6[t]^2+y6[t]^2+z6[t]^2],
  449.  
  450. vy6'[t] ==
  451. (G m1 (y1[t]-y6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+
  452. (G m2 (y2[t]-y6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+
  453. (G m3 (y3[t]-y6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+
  454. (G m4 (y4[t]-y6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+
  455. (G m5 (y5[t]-y6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+
  456. (G m7 (y7[t]-y6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+
  457. (G m8 (y8[t]-y6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]+
  458. If[q6 == 0, 0,
  459. (-q6*q1/(4Pi ε0 )/m6 (y1[t]-y6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+
  460. (-q6*q2/(4Pi ε0 )/m6 (y2[t]-y6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+
  461. (-q6*q3/(4Pi ε0 )/m6 (y3[t]-y6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+
  462. (-q6*q4/(4Pi ε0 )/m6 (y4[t]-y6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+
  463. (-q6*q5/(4Pi ε0 )/m6 (y5[t]-y6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+
  464. (-q6*q7/(4Pi ε0 )/m6 (y7[t]-y6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+
  465. (-q6*q8/(4Pi ε0 )/m6 (y8[t]-y6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]]+
  466. Λ*c^2*y6[t]^2/Sqrt[x6[t]^2+y6[t]^2+z6[t]^2],
  467.  
  468. vz6'[t] ==
  469. (G m1 (z1[t]-z6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+
  470. (G m2 (z2[t]-z6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+
  471. (G m3 (z3[t]-z6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+
  472. (G m4 (z4[t]-z6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+
  473. (G m5 (z5[t]-z6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+
  474. (G m7 (z7[t]-z6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+
  475. (G m8 (z8[t]-z6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]+
  476. If[q6 == 0, 0,
  477. (-q6*q1/(4Pi ε0 )/m6 (z1[t]-z6[t]))/Sqrt[((x1[t]-x6[t])^2+(y1[t]-y6[t])^2+(z1[t]-z6[t])^2)^3]+
  478. (-q6*q2/(4Pi ε0 )/m6 (z2[t]-z6[t]))/Sqrt[((x2[t]-x6[t])^2+(y2[t]-y6[t])^2+(z2[t]-z6[t])^2)^3]+
  479. (-q6*q3/(4Pi ε0 )/m6 (z3[t]-z6[t]))/Sqrt[((x3[t]-x6[t])^2+(y3[t]-y6[t])^2+(z3[t]-z6[t])^2)^3]+
  480. (-q6*q4/(4Pi ε0 )/m6 (z4[t]-z6[t]))/Sqrt[((x4[t]-x6[t])^2+(y4[t]-y6[t])^2+(z4[t]-z6[t])^2)^3]+
  481. (-q6*q5/(4Pi ε0 )/m6 (z5[t]-z6[t]))/Sqrt[((x5[t]-x6[t])^2+(y5[t]-y6[t])^2+(z5[t]-z6[t])^2)^3]+
  482. (-q6*q7/(4Pi ε0 )/m6 (z7[t]-z6[t]))/Sqrt[((x7[t]-x6[t])^2+(y7[t]-y6[t])^2+(z7[t]-z6[t])^2)^3]+
  483. (-q6*q8/(4Pi ε0 )/m6 (z8[t]-z6[t]))/Sqrt[((x8[t]-x6[t])^2+(y8[t]-y6[t])^2+(z8[t]-z6[t])^2)^3]]+
  484. Λ*c^2*z6[t]^2/Sqrt[x6[t]^2+y6[t]^2+z6[t]^2],
  485.  
  486. vx7'[t] ==
  487. (G m1 (x1[t]-x7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+
  488. (G m2 (x2[t]-x7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+
  489. (G m3 (x3[t]-x7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+
  490. (G m4 (x4[t]-x7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+
  491. (G m5 (x5[t]-x7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+
  492. (G m6 (x6[t]-x7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+
  493. (G m8 (x8[t]-x7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]+
  494. If[q7 == 0, 0,
  495. (-q7*q1/(4Pi ε0 )/m7 (x1[t]-x7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+
  496. (-q7*q2/(4Pi ε0 )/m7 (x2[t]-x7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+
  497. (-q7*q3/(4Pi ε0 )/m7 (x3[t]-x7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+
  498. (-q7*q4/(4Pi ε0 )/m7 (x4[t]-x7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+
  499. (-q7*q5/(4Pi ε0 )/m7 (x5[t]-x7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+
  500. (-q7*q6/(4Pi ε0 )/m7 (x6[t]-x7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+
  501. (-q7*q8/(4Pi ε0 )/m7 (x8[t]-x7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]]+
  502. Λ*c^2*x7[t]^2/Sqrt[x7[t]^2+y7[t]^2+z7[t]^2],
  503.  
  504. vy7'[t] ==
  505. (G m1 (y1[t]-y7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+
  506. (G m2 (y2[t]-y7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+
  507. (G m3 (y3[t]-y7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+
  508. (G m4 (y4[t]-y7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+
  509. (G m5 (y5[t]-y7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+
  510. (G m6 (y6[t]-y7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+
  511. (G m8 (y8[t]-y7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]+
  512. If[q7 == 0, 0,
  513. (-q7*q1/(4Pi ε0 )/m7 (y1[t]-y7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+
  514. (-q7*q2/(4Pi ε0 )/m7 (y2[t]-y7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+
  515. (-q7*q3/(4Pi ε0 )/m7 (y3[t]-y7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+
  516. (-q7*q4/(4Pi ε0 )/m7 (y4[t]-y7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+
  517. (-q7*q5/(4Pi ε0 )/m7 (y5[t]-y7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+
  518. (-q7*q6/(4Pi ε0 )/m7 (y6[t]-y7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+
  519. (-q7*q8/(4Pi ε0 )/m7 (y8[t]-y7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]]+
  520. Λ*c^2*y7[t]^2/Sqrt[x7[t]^2+y7[t]^2+z7[t]^2],
  521.  
  522. vz7'[t] ==
  523. (G m1 (z1[t]-z7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+
  524. (G m2 (z2[t]-z7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+
  525. (G m3 (z3[t]-z7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+
  526. (G m4 (z4[t]-z7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+
  527. (G m5 (z5[t]-z7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+
  528. (G m6 (z6[t]-z7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+
  529. (G m8 (z8[t]-z7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]+
  530. If[q7 == 0, 0,
  531. (-q7*q1/(4Pi ε0 )/m7 (z1[t]-z7[t]))/Sqrt[((x1[t]-x7[t])^2+(y1[t]-y7[t])^2+(z1[t]-z7[t])^2)^3]+
  532. (-q7*q2/(4Pi ε0 )/m7 (z2[t]-z7[t]))/Sqrt[((x2[t]-x7[t])^2+(y2[t]-y7[t])^2+(z2[t]-z7[t])^2)^3]+
  533. (-q7*q3/(4Pi ε0 )/m7 (z3[t]-z7[t]))/Sqrt[((x3[t]-x7[t])^2+(y3[t]-y7[t])^2+(z3[t]-z7[t])^2)^3]+
  534. (-q7*q4/(4Pi ε0 )/m7 (z4[t]-z7[t]))/Sqrt[((x4[t]-x7[t])^2+(y4[t]-y7[t])^2+(z4[t]-z7[t])^2)^3]+
  535. (-q7*q5/(4Pi ε0 )/m7 (z5[t]-z7[t]))/Sqrt[((x5[t]-x7[t])^2+(y5[t]-y7[t])^2+(z5[t]-z7[t])^2)^3]+
  536. (-q7*q6/(4Pi ε0 )/m7 (z6[t]-z7[t]))/Sqrt[((x6[t]-x7[t])^2+(y6[t]-y7[t])^2+(z6[t]-z7[t])^2)^3]+
  537. (-q7*q8/(4Pi ε0 )/m7 (z8[t]-z7[t]))/Sqrt[((x8[t]-x7[t])^2+(y8[t]-y7[t])^2+(z8[t]-z7[t])^2)^3]]+
  538. Λ*c^2*z7[t]^2/Sqrt[x7[t]^2+y7[t]^2+z7[t]^2],
  539.  
  540. vx8'[t] ==
  541. (G m1 (x1[t]-x8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+
  542. (G m2 (x2[t]-x8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+
  543. (G m3 (x3[t]-x8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+
  544. (G m4 (x4[t]-x8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+
  545. (G m5 (x5[t]-x8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+
  546. (G m6 (x6[t]-x8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+
  547. (G m7 (x7[t]-x8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]+
  548. If[q8 == 0, 0,
  549. (-q8*q1/(4Pi ε0 )/m8 (x1[t]-x8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+
  550. (-q8*q2/(4Pi ε0 )/m8 (x2[t]-x8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+
  551. (-q8*q3/(4Pi ε0 )/m8 (x3[t]-x8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+
  552. (-q8*q4/(4Pi ε0 )/m8 (x4[t]-x8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+
  553. (-q8*q5/(4Pi ε0 )/m8 (x5[t]-x8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+
  554. (-q8*q6/(4Pi ε0 )/m8 (x6[t]-x8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+
  555. (-q8*q7/(4Pi ε0 )/m8 (x7[t]-x8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]]+
  556. Λ*c^2*x8[t]^2/Sqrt[x8[t]^2+y8[t]^2+z8[t]^2],
  557.  
  558. vy8'[t] ==
  559. (G m1 (y1[t]-y8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+
  560. (G m2 (y2[t]-y8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+
  561. (G m3 (y3[t]-y8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+
  562. (G m4 (y4[t]-y8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+
  563. (G m5 (y5[t]-y8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+
  564. (G m6 (y6[t]-y8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+
  565. (G m7 (y7[t]-y8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]+
  566. If[q8 == 0, 0,
  567. (-q8*q1/(4Pi ε0 )/m8 (y1[t]-y8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+
  568. (-q8*q2/(4Pi ε0 )/m8 (y2[t]-y8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+
  569. (-q8*q3/(4Pi ε0 )/m8 (y3[t]-y8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+
  570. (-q8*q4/(4Pi ε0 )/m8 (y4[t]-y8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+
  571. (-q8*q5/(4Pi ε0 )/m8 (y5[t]-y8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+
  572. (-q8*q6/(4Pi ε0 )/m8 (y6[t]-y8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+
  573. (-q8*q7/(4Pi ε0 )/m8 (y7[t]-y8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]]+
  574. Λ*c^2*y8[t]^2/Sqrt[x8[t]^2+y8[t]^2+z8[t]^2],
  575.  
  576. vz8'[t] ==
  577. (G m1 (z1[t]-z8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+
  578. (G m2 (z2[t]-z8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+
  579. (G m3 (z3[t]-z8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+
  580. (G m4 (z4[t]-z8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+
  581. (G m5 (z5[t]-z8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+
  582. (G m6 (z6[t]-z8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+
  583. (G m7 (z7[t]-z8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]+
  584. If[q8 == 0, 0,
  585. (-q8*q1/(4Pi ε0 )/m8 (z1[t]-z8[t]))/Sqrt[((x1[t]-x8[t])^2+(y1[t]-y8[t])^2+(z1[t]-z8[t])^2)^3]+
  586. (-q8*q2/(4Pi ε0 )/m8 (z2[t]-z8[t]))/Sqrt[((x2[t]-x8[t])^2+(y2[t]-y8[t])^2+(z2[t]-z8[t])^2)^3]+
  587. (-q8*q3/(4Pi ε0 )/m8 (z3[t]-z8[t]))/Sqrt[((x3[t]-x8[t])^2+(y3[t]-y8[t])^2+(z3[t]-z8[t])^2)^3]+
  588. (-q8*q4/(4Pi ε0 )/m8 (z4[t]-z8[t]))/Sqrt[((x4[t]-x8[t])^2+(y4[t]-y8[t])^2+(z4[t]-z8[t])^2)^3]+
  589. (-q8*q5/(4Pi ε0 )/m8 (z5[t]-z8[t]))/Sqrt[((x5[t]-x8[t])^2+(y5[t]-y8[t])^2+(z5[t]-z8[t])^2)^3]+
  590. (-q8*q6/(4Pi ε0 )/m8 (z6[t]-z8[t]))/Sqrt[((x6[t]-x8[t])^2+(y6[t]-y8[t])^2+(z6[t]-z8[t])^2)^3]+
  591. (-q8*q7/(4Pi ε0 )/m8 (z7[t]-z8[t]))/Sqrt[((x7[t]-x8[t])^2+(y7[t]-y8[t])^2+(z7[t]-z8[t])^2)^3]]+
  592. Λ*c^2*z8[t]^2/Sqrt[x8[t]^2+y8[t]^2+z8[t]^2],
  593.  
  594. x1[0] == x1x, y1[0] == y1y, z1[0] == z1z,
  595. x2[0] == x2x, y2[0] == y2y, z2[0] == z2z,
  596. x3[0] == x3x, y3[0] == y3y, z3[0] == z3z,
  597. x4[0] == x4x, y4[0] == y4y, z4[0] == z4z,
  598. x5[0] == x5x, y5[0] == y5y, z5[0] == z5z,
  599. x6[0] == x6x, y6[0] == y6y, z6[0] == z6z,
  600. x7[0] == x7x, y7[0] == y7y, z7[0] == z7z,
  601. x8[0] == x8x, y8[0] == y8y, z8[0] == z8z,
  602.  
  603. vx1[0] == v1x, vy1[0] == v1y, vz1[0] == v1z,
  604. vx2[0] == v2x, vy2[0] == v2y, vz2[0] == v2z,
  605. vx3[0] == v3x, vy3[0] == v3y, vz3[0] == v3z,
  606. vx4[0] == v4x, vy4[0] == v4y, vz4[0] == v4z,
  607. vx5[0] == v5x, vy5[0] == v5y, vz5[0] == v5z,
  608. vx6[0] == v6x, vy6[0] == v6y, vz6[0] == v6z,
  609. vx7[0] == v7x, vy7[0] == v7y, vz7[0] == v7z,
  610. vx8[0] == v8x, vy8[0] == v8y, vz8[0] == v8z},
  611.  
  612. {x1, x2, x3, x4, x5, x6, x7, x8, y1, y2, y3, y4, y5, y6, y7, y8, z1, z2, z3, z4, z5, z6, z7, z8,
  613. vx1, vx2, vx3, vx4, vx5, vx6, vx7, vx8, vy1, vy2, vy3, vy4, vy5, vy6, vy7, vy8, vz1, vz2, vz3, vz4, vz5, vz6, vz7, vz8},
  614.  
  615. {t, 0, Tmax},
  616.  
  617. WorkingPrecision-> wp,
  618. MaxSteps-> Infinity,
  619. Method-> mta,
  620. InterpolationOrder-> All,
  621. StepMonitor :> (laststep=plunge; plunge=t;
  622. stepsize=plunge-laststep;), Method->{"EventLocator",
  623. "Event" :> (If[stepsize<1*^-4, 0, 1])}];
  624.  
  625. (* Position, Geschwindigkeit *)
  626.  
  627. f2p[t_]={{x1[t], y1[t], z1[t]}, {x2[t], y2[t], z2[t]}, {x3[t], y3[t], z3[t]}, {x4[t], y4[t], z4[t]}, {x5[t], y5[t], z5[t]}, {x6[t], y6[t], z6[t]}, {x7[t], y7[t], z7[t]}, {x8[t], y8[t], z8[t]}}/.nds[[1]];
  628. f2v[t_]={{vx1[t], vy1[t], vz1[t]}, {vx2[t], vy2[t], vz2[t]}, {vx3[t], vy3[t], vz3[t]}, {vx4[t], vy4[t], vz4[t]}, {vx5[t], vy5[t], vz5[t]}, {vx6[t], vy6[t], vz6[t]}, {vx7[t], vy7[t], vz7[t]}, {vx8[t], vy8[t], vz8[t]}}/.nds[[1]];
  629. swp[t_]=(m1 Evaluate[f2p[t][[1]]]+m2 Evaluate[f2p[t][[2]]]+m3 Evaluate[f2p[t][[3]]]+m4 Evaluate[f2p[t][[4]]]+m5 Evaluate[f2p[t][[5]]]+m6 Evaluate[f2p[t][[6]]]+m7 Evaluate[f2p[t][[7]]]+m8 Evaluate[f2p[t][[8]]])/(m1+m2+m3+m4+m5+m6+m7+m8);
  630.  
  631. (* Formatierung *)
  632.  
  633. s[text_]=Style[text, FontSize->11];
  634. sw[text_]=Style[text, White, FontSize->11];
  635. colorfunc[n_]=Function[{x, y, z, t},
  636. Hue[0, n, 0.5,
  637. If[Tmax<0, Max[Min[(+T+(-t+trail))/trail, 1], 0],
  638. Max[Min[(-T+(t+trail))/trail, 1], 0]]]];
  639.  
  640. (* Animation *)
  641.  
  642. Do[Print[Rasterize[
  643. Grid[{{
  644. Show[
  645.  
  646. If[T == 0, {},
  647.  
  648. ParametricPlot3D[Evaluate[f2p[t]],
  649. {t, Max[0, T-trail], T},
  650.  
  651. PlotStyle->{
  652. {Thickness[thk], Red},
  653. {Thickness[thk], Blue},
  654. {Thickness[thk], Green},
  655. {Thickness[thk], Magenta},
  656. {Thickness[thk], Cyan},
  657. {Thickness[thk], Orange},
  658. {Thickness[thk], Purple},
  659. {Thickness[thk], Pink}},
  660.  
  661. PlotRange->plotrange, AspectRatio->1, MaxRecursion->15, Axes->True, ImageSize->imagesize]],
  662.  
  663. Graphics3D[
  664. If[startpos==1, {
  665. {PointSize[2point/3], Lighter[Red], Point[{x1x, y1y, z1z}]},
  666. {PointSize[2point/3], Lighter[Blue], Point[{x2x, y2y, z2z}]},
  667. {PointSize[2point/3], Lighter[Green], Point[{x3x, y3y, z3z}]},
  668. {PointSize[2point/3], Lighter[Magenta], Point[{x4x, y4y, z4z}]},
  669. {PointSize[2point/3], Lighter[Cyan], Point[{x5x, y5y, z5z}]},
  670. {PointSize[2point/3], Lighter[Orange], Point[{x6x, y6y, z6z}]},
  671. {PointSize[2point/3], Lighter[Purple], Point[{x7x, y7y, z7z}]},
  672. {PointSize[2point/3], Lighter[Pink], Point[{x8x, y8y, z8z}]}
  673. }, {}],
  674.  
  675. PlotRange->plotrange, AspectRatio->1, Axes->True, ImageSize->imagesize],
  676.  
  677. Graphics3D[{PointSize[point], Red, Point[Evaluate[f2p[T]][[1]]]}],
  678. Graphics3D[{PointSize[point], Blue, Point[Evaluate[f2p[T]][[2]]]}],
  679. Graphics3D[{PointSize[point], Green, Point[Evaluate[f2p[T]][[3]]]}],
  680. Graphics3D[{PointSize[point], Magenta, Point[Evaluate[f2p[T]][[4]]]}],
  681. Graphics3D[{PointSize[point], Cyan, Point[Evaluate[f2p[T]][[5]]]}],
  682. Graphics3D[{PointSize[point], Orange, Point[Evaluate[f2p[T]][[6]]]}],
  683. Graphics3D[{PointSize[point], Purple, Point[Evaluate[f2p[T]][[7]]]}],
  684. Graphics3D[{PointSize[point], Pink, Point[Evaluate[f2p[T]][[8]]]}],
  685.  
  686. ViewPoint->viewpoint]},
  687.  
  688. { },
  689. {s["t"->N[T-trail]], sw[1/2]},
  690. { },
  691. {s["p1{x,y,z}"-> Evaluate[f2p[T][[1]]]], sw[1/2]},
  692. {s["v1{x,y,z}"-> Evaluate[f2v[T][[1]]]], sw[1/2]},
  693. {s["v1{total}"->{Evaluate[Chop@Norm[f2v[T][[1]]]]}], sw[1/2]},
  694. { },
  695. {s["p2{x,y,z}"-> Evaluate[f2p[T][[2]]]], sw[1/2]},
  696. {s["v2{x,y,z}"-> Evaluate[f2v[T][[2]]]], sw[1/2]},
  697. {s["v2{total}"->{Evaluate[Chop@Norm[f2v[T][[2]]]]}], sw[1/2]},
  698. { },
  699. {s["p3{x,y,z}"-> Evaluate[f2p[T][[3]]]], sw[1/2]},
  700. {s["v3{x,y,z}"-> Evaluate[f2v[T][[3]]]], sw[1/2]},
  701. {s["v3{total}"->{Evaluate[Chop@Norm[f2v[T][[3]]]]}], sw[1/2]},
  702. { },
  703. {s["p4{x,y,z}"-> Evaluate[f2p[T][[4]]]], sw[1/2]},
  704. {s["v4{x,y,z}"-> Evaluate[f2v[T][[4]]]], sw[1/2]},
  705. {s["v4{total}"->{Evaluate[Chop@Norm[f2v[T][[4]]]]}], sw[1/2]},
  706. { },
  707. {s["p5{x,y,z}"-> Evaluate[f2p[T][[5]]]], sw[1/2]},
  708. {s["v5{x,y,z}"-> Evaluate[f2v[T][[5]]]], sw[1/2]},
  709. {s["v5{total}"->{Evaluate[Chop@Norm[f2v[T][[5]]]]}], sw[1/2]},
  710. { },
  711. {s["p6{x,y,z}"-> Evaluate[f2p[T][[6]]]], sw[1/2]},
  712. {s["v6{x,y,z}"-> Evaluate[f2v[T][[6]]]], sw[1/2]},
  713. {s["v6{total}"->{Evaluate[Chop@Norm[f2v[T][[6]]]]}], sw[1/2]},
  714. { },
  715. {s["p7{x,y,z}"-> Evaluate[f2p[T][[7]]]], sw[1/2]},
  716. {s["v7{x,y,z}"-> Evaluate[f2v[T][[7]]]], sw[1/2]},
  717. {s["v7{total}"->{Evaluate[Chop@Norm[f2v[T][[7]]]]}], sw[1/2]},
  718. { },
  719. {s["p8{x,y,z}"-> Evaluate[f2p[T][[8]]]], sw[1/2]},
  720. {s["v8{x,y,z}"-> Evaluate[f2v[T][[8]]]], sw[1/2]},
  721. {s["v8{total}"->{Evaluate[Chop@Norm[f2v[T][[8]]]]}], sw[1/2]},
  722. { },
  723. {s["ps{x,y,z}"-> swp[T]], sw[1/2]},
  724. {s["vs{x,y,z}"-> swp'[T]], sw[1/2]},
  725. {s["vs{total}"->{Chop@Norm[swp'[T]]}], sw[1/2]}
  726. }, Alignment->Left]]],
  727.  
  728. (* Zeitregler *)
  729.  
  730. {T, trail, Tmax/2+trail, trail}]
  731.  
  732. (* Export als HTML Dokument *)
  733. (* Export["dateiname.html", EvaluationNotebook[], "GraphicsOutput" -> "PNG"] *)
  734. (* Export direkt als Bildsequenz *)
  735. (* ParallelDo[Export["dateiname" <> ToString[T] <> ".png", Rasterize[...] ], {T, 0, 10, 5}] *)
  736.  
  737.  
  738.  
  739.  
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