# Gravity & Charge, 4 Body Simulator

Feb 16th, 2019 (edited)
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1. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
2. (* ||| Mathematica Syntax || yukterez.net || 4 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 = 2π sek;
21. tMax = Min[Tmax, plunge];
22. trail = π/3 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 = 1 m^3/sek^2/G;
43. q1 = 0 Amp sek;
44.
45. x1x = 1.00231488346205 m;
46. y1y = 0 m;
47. z1z = 0 m;
48.
49. v1x = 0 m/sek;
50. v1y = 0 m/sek;
51. v1z = -0.293790277732029 m/sek;
52.
53. (* Körper 2 *)
54.
55. m2 = 1 m^3/sek^2/G;
56. q2 = 0 Amp sek;
57.
58. x2x = -0.52869409402363 m;
59. y2y = 0 m;
60. z2z = 0.567125954067238 m;
61.
62. v2x = -0.175826619093916 m/sek;
63. v2y = 0 m/sek;
64. v2z = 1.02361310165052 m/sek;
65.
66. (* Körper 3 *)
67.
68. m3 = 1 m^3/sek^2/G;
69. q3 = 0 Amp sek;
70.
71. x3x = 0.0550733045852099 m;
72. y3y = 0 m;
73. z3z = 0 m;
74.
75. v3x = 0 m/sek;
76. v3y = 0 m/sek;
77. v3z = -1.75343592556901 m/sek;
78.
79. (* Körper 4 *)
80.
81. m4 = 1 m^3/sek^2/G;
82. q4 = 0 Amp sek;
83.
84. x4x = -0.528694094023634 m;
85. y4y = 0 m;
86. z4z = -0.567125954067235 m;
87.
88. v4x = 0.175826619093915 m/sek;
89. v4y = 0 m/sek;
90. v4z = 1.02361310165051 m/sek;
91.
92. (* Differentialgleichung *)
93.
94. nds=NDSolve[{
95.
96. x1'[t] == vx1[t], y1'[t] == vy1[t], z1'[t] == vz1[t],
97. x2'[t] == vx2[t], y2'[t] == vy2[t], z2'[t] == vz2[t],
98. x3'[t] == vx3[t], y3'[t] == vy3[t], z3'[t] == vz3[t],
99. x4'[t] == vx4[t], y4'[t] == vy4[t], z4'[t] == vz4[t],
100.
101. vx1'[t] ==
102. (G m2 (x2[t]-x1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
103. (G m3 (x3[t]-x1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
104. (G m4 (x4[t]-x1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
105. If[q1 == 0, 0,
106. (-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]+
107. (-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]+
108. (-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]]+
109. Λ*c^2*x1[t]^2/Sqrt[x1[t]^2+y1[t]^2+z1[t]^2],
110.
111. vy1'[t] ==
112. (G m2 (y2[t]-y1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
113. (G m3 (y3[t]-y1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
114. (G m4 (y4[t]-y1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
115. If[q1 == 0, 0,
116. (-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]+
117. (-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]+
118. (-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]]+
119. Λ*c^2*y1[t]^2/Sqrt[x1[t]^2+y1[t]^2+z1[t]^2],
120.
121. vz1'[t] ==
122. (G m2 (z2[t]-z1[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
123. (G m3 (z3[t]-z1[t]))/Sqrt[((x3[t]-x1[t])^2+(y3[t]-y1[t])^2+(z3[t]-z1[t])^2)^3]+
124. (G m4 (z4[t]-z1[t]))/Sqrt[((x4[t]-x1[t])^2+(y4[t]-y1[t])^2+(z4[t]-z1[t])^2)^3]+
125. If[q1 == 0, 0,
126. (-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]+
127. (-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]+
128. (-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]]+
129. Λ*c^2*z1[t]^2/Sqrt[x1[t]^2+y1[t]^2+z1[t]^2],
130.
131. vx2'[t] ==
132. (G m1 (x1[t]-x2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+
133. (G m3 (x3[t]-x2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
134. (G m4 (x4[t]-x2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
135. If[q2 == 0, 0,
136. (-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]+
137. (-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]+
138. (-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]]+
139. Λ*c^2*x2[t]^2/Sqrt[x2[t]^2+y2[t]^2+z2[t]^2],
140.
141. vy2'[t] ==
142. (G m1 (y1[t]-y2[t]))/Sqrt[((x1[t]-x2[t])^2+(y1[t]-y2[t])^2+(z1[t]-z2[t])^2)^3]+
143. (G m3 (y3[t]-y2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
144. (G m4 (y4[t]-y2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
145. If[q2 == 0, 0,
146. (-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]+
147. (-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]+
148. (-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]]+
149. Λ*c^2*y2[t]^2/Sqrt[x2[t]^2+y2[t]^2+z2[t]^2],
150.
151. vz2'[t] ==
152. (G m1 (z1[t]-z2[t]))/Sqrt[((x2[t]-x1[t])^2+(y2[t]-y1[t])^2+(z2[t]-z1[t])^2)^3]+
153. (G m3 (z3[t]-z2[t]))/Sqrt[((x3[t]-x2[t])^2+(y3[t]-y2[t])^2+(z3[t]-z2[t])^2)^3]+
154. (G m4 (z4[t]-z2[t]))/Sqrt[((x4[t]-x2[t])^2+(y4[t]-y2[t])^2+(z4[t]-z2[t])^2)^3]+
155. If[q2 == 0, 0,
156. (-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]+
157. (-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]+
158. (-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]]+
159. Λ*c^2*z2[t]^2/Sqrt[x2[t]^2+y2[t]^2+z2[t]^2],
160.
161. vx3'[t] ==
162. (G m1 (x1[t]-x3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
163. (G m2 (x2[t]-x3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
164. (G m4 (x4[t]-x3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
165. If[q3 == 0, 0,
166. (-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]+
167. (-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]+
168. (-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]]+
169. Λ*c^2*x3[t]^2/Sqrt[x3[t]^2+y3[t]^2+z3[t]^2],
170.
171. vy3'[t] ==
172. (G m1 (y1[t]-y3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
173. (G m2 (y2[t]-y3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
174. (G m4 (y4[t]-y3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
175. If[q3 == 0, 0,
176. (-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]+
177. (-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]+
178. (-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]]+
179. Λ*c^2*y3[t]^2/Sqrt[x3[t]^2+y3[t]^2+z3[t]^2],
180.
181. vz3'[t] ==
182. (G m1 (z1[t]-z3[t]))/Sqrt[((x1[t]-x3[t])^2+(y1[t]-y3[t])^2+(z1[t]-z3[t])^2)^3]+
183. (G m2 (z2[t]-z3[t]))/Sqrt[((x2[t]-x3[t])^2+(y2[t]-y3[t])^2+(z2[t]-z3[t])^2)^3]+
184. (G m4 (z4[t]-z3[t]))/Sqrt[((x4[t]-x3[t])^2+(y4[t]-y3[t])^2+(z4[t]-z3[t])^2)^3]+
185. If[q3 == 0, 0,
186. (-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]+
187. (-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]+
188. (-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]]+
189. Λ*c^2*z3[t]^2/Sqrt[x3[t]^2+y3[t]^2+z3[t]^2],
190.
191. vx4'[t] ==
192. (G m1 (x1[t]-x4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
193. (G m2 (x2[t]-x4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
194. (G m3 (x3[t]-x4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
195. If[q4 == 0, 0,
196. (-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]+
197. (-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]+
198. (-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]]+
199. Λ*c^2*x4[t]^2/Sqrt[x4[t]^2+y4[t]^2+z4[t]^2],
200.
201. vy4'[t] ==
202. (G m1 (y1[t]-y4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
203. (G m2 (y2[t]-y4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
204. (G m3 (y3[t]-y4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
205. If[q4 == 0, 0,
206. (-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]+
207. (-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]+
208. (-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]]+
209. Λ*c^2*y4[t]^2/Sqrt[x4[t]^2+y4[t]^2+z4[t]^2],
210.
211. vz4'[t] ==
212. (G m1 (z1[t]-z4[t]))/Sqrt[((x1[t]-x4[t])^2+(y1[t]-y4[t])^2+(z1[t]-z4[t])^2)^3]+
213. (G m2 (z2[t]-z4[t]))/Sqrt[((x2[t]-x4[t])^2+(y2[t]-y4[t])^2+(z2[t]-z4[t])^2)^3]+
214. (G m3 (z3[t]-z4[t]))/Sqrt[((x3[t]-x4[t])^2+(y3[t]-y4[t])^2+(z3[t]-z4[t])^2)^3]+
215. If[q4 == 0, 0,
216. (-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]+
217. (-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]+
218. (-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]]+
219. Λ*c^2*z4[t]^2/Sqrt[x4[t]^2+y4[t]^2+z4[t]^2],
220.
221. x1[0] == x1x, y1[0] == y1y, z1[0] == z1z,
222. x2[0] == x2x, y2[0] == y2y, z2[0] == z2z,
223. x3[0] == x3x, y3[0] == y3y, z3[0] == z3z,
224. x4[0] == x4x, y4[0] == y4y, z4[0] == z4z,
225.
226. vx1[0] == v1x, vy1[0] == v1y, vz1[0] == v1z,
227. vx2[0] == v2x, vy2[0] == v2y, vz2[0] == v2z,
228. vx3[0] == v3x, vy3[0] == v3y, vz3[0] == v3z,
229. vx4[0] == v4x, vy4[0] == v4y, vz4[0] == v4z},
230.
231. {x1, x2, x3, x4, y1, y2, y3, y4, z1, z2, z3, z4,
232. vx1, vx2, vx3, vx4, vy1, vy2, vy3, vy4, vz1, vz2, vz3, vz4},
233.
234. {t, 0, Tmax},
235.
236. WorkingPrecision-> wp,
237. MaxSteps-> Infinity,
238. Method-> mta,
239. InterpolationOrder-> All,
240. StepMonitor :> (laststep=plunge; plunge=t;
241. stepsize=plunge-laststep;), Method->{"EventLocator",
242. "Event" :> (If[stepsize<1*^-4, 0, 1])}];
243.
244. (* Position, Geschwindigkeit *)
245.
246. 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]}}/.nds[[1]];
247. 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]}}/.nds[[1]];
248. swp[t_]=(m1 Evaluate[f2p[t][[1]]]+m2 Evaluate[f2p[t][[2]]]+m3 Evaluate[f2p[t][[3]]]+m4 Evaluate[f2p[t][[4]]])/(m1+m2+m3+m4);
249.
250. (* Formatierung *)
251.
252. s[text_]=Style[text, FontSize->11];
253. sw[text_]=Style[text, White, FontSize->11];
254. colorfunc[n_]=Function[{x, y, z, t},
255. Hue[0, n, 0.5,
256. If[Tmax<0, Max[Min[(+T+(-t+trail))/trail, 1], 0],
257. Max[Min[(-T+(t+trail))/trail, 1], 0]]]];
258.
259. (* Animation *)
260.
261. Do[Print[Rasterize[
262. Grid[{{
263. Show[
264.
265. If[T == 0, {},
266.
267. ParametricPlot3D[Evaluate[f2p[t]],
268. {t, Max[0, T-trail], T},
269.
270. PlotStyle->{
271. {Thickness[thk], Red},
272. {Thickness[thk], Blue},
273. {Thickness[thk], Green},
274. {Thickness[thk], Magenta}},
275.
276. PlotRange->plotrange, AspectRatio->1, MaxRecursion->15, Axes->True, ImageSize->imagesize]],
277.
278. Graphics3D[
279. If[startpos==1, {
280. {PointSize[2point/3], Lighter[Red], Point[{x1x, y1y, z1z}]},
281. {PointSize[2point/3], Lighter[Blue], Point[{x2x, y2y, z2z}]},
282. {PointSize[2point/3], Lighter[Green], Point[{x3x, y3y, z3z}]},
283. {PointSize[2point/3], Lighter[Magenta], Point[{x4x, y4y, z4z}]}
284. }, {}],
285.
286. PlotRange->plotrange, AspectRatio->1, Axes->True, ImageSize->imagesize],
287.
288. Graphics3D[{PointSize[point], Red, Point[Evaluate[f2p[T]][[1]]]}],
289. Graphics3D[{PointSize[point], Blue, Point[Evaluate[f2p[T]][[2]]]}],
290. Graphics3D[{PointSize[point], Green, Point[Evaluate[f2p[T]][[3]]]}],
291. Graphics3D[{PointSize[point], Magenta, Point[Evaluate[f2p[T]][[4]]]}],
292.
293. ViewPoint->viewpoint]},
294.
295. { },
296. {s["t"->N[T]], sw[1/2]},
297. { },
298. {s["p1{x,y,z}"-> Evaluate[f2p[T][[1]]]], sw[1/2]},
299. {s["v1{x,y,z}"-> Evaluate[f2v[T][[1]]]], sw[1/2]},
300. {s["v1{total}"->{Evaluate[Chop@Norm[f2v[T][[1]]]]}], sw[1/2]},
301. { },
302. {s["p2{x,y,z}"-> Evaluate[f2p[T][[2]]]], sw[1/2]},
303. {s["v2{x,y,z}"-> Evaluate[f2v[T][[2]]]], sw[1/2]},
304. {s["v2{total}"->{Evaluate[Chop@Norm[f2v[T][[2]]]]}], sw[1/2]},
305. { },
306. {s["p3{x,y,z}"-> Evaluate[f2p[T][[3]]]], sw[1/2]},
307. {s["v3{x,y,z}"-> Evaluate[f2v[T][[3]]]], sw[1/2]},
308. {s["v3{total}"->{Evaluate[Chop@Norm[f2v[T][[3]]]]}], sw[1/2]},
309. { },
310. {s["p4{x,y,z}"-> Evaluate[f2p[T][[4]]]], sw[1/2]},
311. {s["v4{x,y,z}"-> Evaluate[f2v[T][[4]]]], sw[1/2]},
312. {s["v4{total}"->{Evaluate[Chop@Norm[f2v[T][[4]]]]}], sw[1/2]},
313. { },
314. {s["ps{x,y,z}"-> swp[T]], sw[1/2]},
315. {s["vs{x,y,z}"-> swp'[T]], sw[1/2]},
316. {s["vs{total}"->{Chop@Norm[swp'[T]]}], sw[1/2]}
317. }, Alignment->Left]]],
318.
319. (* Zeitregler *)
320.
321. {T, 0, tMax, tMax/5}]
322.
323. (* Export als HTML Dokument *)
324. (* Export["dateiname.html", EvaluationNotebook[], "GraphicsOutput" -> "PNG"] *)
325. (* Export direkt als Bildsequenz *)
326. (* ParallelDo[Export["dateiname" <> ToString[T] <> ".png", Rasterize[...] ], {T, 0, 10, 5}] *)
327.
328.
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