# 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.
RAW Paste Data