Yukterez

Kerr Newman 3D Simulator, Doran, ZAMO

Jun 10th, 2020 (edited)
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  1. (* Simulator-Code für Photonen, geladene und neutrale Teilchen in Raindrop Doran *)
  2. (* Koordinaten, v Eingabe und Anzeige relativ zum ZAMO *)
  3.  
  4. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  5. (* |||| Mathematica | kerr.newman.yukterez.net | 06.08.2017 - 13.06.2020, Version 02 |||| *)
  6. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  7.  
  8. wp=MachinePrecision;
  9. set={"GlobalAdaptive", "MaxErrorIncreases"->100, Method->"GaussKronrodRule"}; mrec=100;
  10. mt1=Automatic;
  11. mt2={"EquationSimplification"-> "Residual"};
  12. mt3={"ImplicitRungeKutta", "DifferenceOrder"-> 20};
  13. mt4={"StiffnessSwitching", Method-> {"ExplicitRungeKutta", Automatic}};
  14. mt5={"EventLocator", "Event"-> (r[τ]-1001/1000 rA)};
  15. mta=mt1; (* mt1: Speed, mt3: Accuracy *)
  16.  
  17. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  18. (* |||||||| 1) STARTBEDINGUNGEN EINGEBEN |||||||||||||||||||||||||||||||||||||||||||||||| *)
  19. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  20.  
  21. A=a; (* pseudosphärisch [BL]: A=0, kartesisch [KS]: A=a *)
  22.  
  23. tmax=300; (* Eigenzeit *)
  24. Tmax=300; (* Koordinatenzeit *)
  25. TMax=Min[Tmax, т[plunge-1/100]]; tMax=Min[tmax, plunge-1/100]; (* Integrationsende *)
  26.  
  27. r0 = Sqrt[7^2-a^2]; (* Startradius *)
  28. r1 = r0+2; (* Endradius wenn v0=vr0=vr1 *)
  29. θ0 = π/2; (* Breitengrad *)
  30. φ0 = 0; (* Längengrad *)
  31. a = 9/10; (* Spinparameter *)
  32. ℧ = 2/5; (* spezifische Ladung des schwarzen Lochs *)
  33. q = 0; (* spezifische Ladung des Testkörpers *)
  34.  
  35. v0 = 2/5; (* Anfangsgeschwindigkeit *)
  36. α0 = 0; (* vertikaler Abschusswinkel *)
  37. i0 = ArcTan[5/6]; (* Bahninklinationswinkel *)
  38.  
  39. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  40. (* |||||||| 2) GESCHWINDIGKEITS-, ENERGIE UND DREHIMPULSKOMPONENTEN ||||||||||||||||||||| *)
  41. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  42.  
  43. vr0=v0 Sin[α0]; (* radiale Geschwindigkeitskomponente *)
  44. vθ0=v0 Cos[α0] Sin[i0]; (* longitudinale Geschwindigkeitskomponente *)
  45. vφ0=v0 Cos[α0] Cos[i0]; (* latitudinale Geschwindigkeitskomponente *)
  46.  
  47. dt[τ_]:=ю[τ]+If[R[τ]<1+Sqrt[1-a^2 Cos[Θ[τ]]^2-℧^2] && R[τ]>1-Sqrt[1-a^2 Cos[Θ[τ]]^2-℧^2],
  48. -1, +1] R'[τ] (-Sqrt[(2R[τ]-℧^2)/(a^2+R[τ]^2)])/(1-
  49. ((2R[τ]-℧^2)/(a^2+R[τ]^2)));
  50. v[τ_]:=If[μ==0, 1,
  51. (Sqrt[Δi[τ] Σi[τ]^3 Χi[τ]-ε^2 Σi[τ]^2 Χi[τ]^2-2 a Lz ε Σi[τ]^2 Χi[τ] ℧^2-
  52. a^2 Lz^2 Σi[τ]^2 ℧^4+4 a Lz ε Σi[τ]^2 Χi[τ] R[τ]+2 q ε Σi[τ] Χi[τ]^2 ℧ R[τ]+
  53. 4 a^2 Lz^2 Σi[τ]^2 ℧^2 R[τ]+2 a Lz q Σi[τ] Χi[τ] ℧^3 R[τ]-4 a^2 Lz^2 Σi[τ]^2 R[τ]^2-
  54. 4 a Lz q Σi[τ] Χi[τ] ℧ R[τ]^2-q^2 Χi[τ]^2 ℧^2 R[τ]^2])/(ε Σi[τ] Χi[τ]+
  55. a Lz Σi[τ] ℧^2-2 a Lz Σi[τ] R[τ]-q Χi[τ] ℧ R[τ])]/I;
  56. vrj[τ_]:=R'[τ]/Sqrt[Δi[τ]] Sqrt[Σi[τ] (1+μ v[τ]^2)];
  57. vθj[τ_]:=Θ'[τ] Sqrt[Σi[τ] (1+μ v[τ]^2)];
  58. vφj[τ_]:=Evaluate[(-(((a^2 Cos[θ[τ]]^2+r[τ]^2) (a^2+℧^2-2 r[τ]+r[τ]^2) Sin[θ[τ]] Sqrt[1-
  59. μ^2 v[τ]^2] (-(φ'[τ]+If[r[τ]<1+Sqrt[1-a^2 Cos[θ[τ]]^2-℧^2] && r[τ]>1-Sqrt[1-
  60. a^2 Cos[θ[τ]]^2-℧^2], -1, +1] r'[τ] a (-Sqrt[(2r[τ]-℧^2)/(a^2+r[τ]^2)])/(1-
  61. ((2r[τ]-℧^2)/(a^2+r[τ]^2)))/(a^2+r[τ]^2))-(a q ℧ r[τ])/((a^2 Cos[θ[τ]]^2+r[τ]^2) (a^2+
  62. ℧^2-2 r[τ]+r[τ]^2))+(ε Csc[θ[τ]]^2 (a (-a^2-℧^2+2 r[τ]-r[τ]^2) Sin[θ[τ]]^2+a (a^2+
  63. r[τ]^2) Sin[θ[τ]]^2))/((a^2 Cos[θ[τ]]^2+r[τ]^2) (a^2+℧^2-2 r[τ]+r[τ]^2))+(a q ℧ r[τ] (a^2+
  64. ℧^2-2 r[τ]+r[τ]^2-a^2 Sin[θ[τ]]^2))/((a^2 Cos[θ[τ]]^2+r[τ]^2)^2 (a^2+℧^2-2 r[τ]+
  65. r[τ]^2) (1-μ^2 v[τ]^2))))/((a^2+℧^2-2 r[τ]+r[τ]^2-a^2 Sin[θ[τ]]^2) Sqrt[((a^2+r[τ]^2)^2-
  66. a^2 (a^2+℧^2-2 r[τ]+r[τ]^2) Sin[θ[τ]]^2)/(a^2 Cos[θ[τ]]^2+r[τ]^2)]))) /. sol][[1]]
  67. vtj[τ_]:=Sqrt[vrj[τ]^2+vθj[τ]^2+vφj[τ]^2];
  68. vr[τ_]:=vrj[τ]/vtj[τ]*v[τ];
  69. vθ[τ_]:=vθj[τ]/vtj[τ]*v[τ];
  70. vφ[τ_]:=vφj[τ]/vtj[τ]*v[τ];
  71.  
  72. x0[A_]:=Sqrt[r0^2+A^2] Sin[θ0] Cos[φ0]; (* Anfangskoordinaten *)
  73. y0[A_]:=Sqrt[r0^2+A^2] Sin[θ0] Sin[φ0];
  74. z0[A_]:=r0 Cos[θ0];
  75.  
  76. ε0=Sqrt[δ Ξ/χ]/j[v0]+Lz ω0;
  77. ε=ε0+((q r0 ℧)/(r0^2+a^2 Cos[θ0]^2));
  78. εζ:=Sqrt[Δ Σ/Χ]/j[ν]+Lz ωζ+((q r[τ] ℧)/(r[τ]^2+a^2 Cos[θ[τ]]^2));
  79. LZ=vφ0 Ы/j[v0];
  80. Lz=LZ+((q a r0 ℧ Sin[θ0]^2)/(r0^2+a^2 Cos[θ0]^2)) j[v0]^2;
  81. Lζ:=vφ0 я/j[ν]+0((q a r[τ] ℧ Sin[θ[τ]]^2)/(r[τ]^2+a^2 Cos[θ[τ]]^2));
  82. pθ0=vθ0 Sqrt[Ξ]/j[v0]; pθζ:=θ'[τ] Σ;
  83. pr0=vr0 Sqrt[(Ξ/δ)/j[v0]^2];
  84. Qk=Limit[pθ0^2+(Lz^2 Csc[θ1]^2-a^2 (ε^2+μ)) Cos[θ1]^2, θ1->θ0]; (* Carter Konstante *)
  85. Q=Limit[pθ0^2+(Lz^2 Csc[θ1]^2-a^2 (ε^2+μ)) Cos[θ1]^2, θ1->θ0];
  86. Qζ:=pθζ^2+(Lz^2 Csc[θ[τ]]^2-a^2 (εζ^2+μ)) Cos[θ[τ]]^2;
  87. k=Q+Lz^2+a^2 (ε^2+μ); kζ:=Qζ+Lz^2+a^2 (εζ^2+μ);
  88. (* ISCO *)
  89. isco = rISCO/.Solve[0 == rISCO (6 rISCO-rISCO^2-9 ℧^2+3 a^2)+4 ℧^2 (℧^2-a^2)-
  90. 8 a (rISCO-℧^2)^(3/2) && rISCO>=rA, rISCO][[1]];
  91. μ=If[Abs[v0]==1, 0, If[Abs[v0]<1, -1, 1]]; (* Baryon: μ=-1, Photon: μ=0 *)
  92.  
  93. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  94. (* |||||||| 3) FLUCHTGESCHWINDIGKEIT UND BENÖTIGTER ABSCHUSSWINKEL |||||||||||||||||||||| *)
  95. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  96.  
  97. vEsc=If[q==0, ж0, Abs[(\[Sqrt](r0^2 (r0^2 (δ Ξ-χ)+2 q r0 χ ℧-q^2 χ ℧^2)+
  98. 2 a^2 r0 (r0 δ Ξ-r0 χ+q χ ℧) Cos[θ0]^2+a^4 (δ Ξ-
  99. χ) Cos[θ0]^4))/(Sqrt[χ] (r0 (r0-q ℧)+a^2 Cos[θ0]^2))]];
  100. (* horizontaler Photonenkreiswinkel, i0 *)
  101. iP[r0_, a_]:=Normal[iPh/.NSolve[1/(8 (r0^2+a^2 Cos[θ0]^2)^3) (a^2+(-2+r0) r0+
  102. ℧^2) (8 r0 (r0^2+a^2 Cos[θ0]^2) Sin[iPh]^2+1/((a^2-2 r0+r0^2+℧^2) (r0^2+
  103. a^2 Cos[θ0]^2)) 8 a (Cos[iPh] Sin[θ0] (a^2-2 r0+r0^2+℧^2-a^2 Sin[θ0]^2) Sqrt[((a^2+
  104. r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)/(r0^2+a^2 Cos[θ0]^2)]+(a (a^2+r0^2) Sin[θ0]^2+
  105. a (-a^2+2 r0-r0^2-℧^2) Sin[θ0]^2) (Sqrt[((a^2-2 r0+r0^2+℧^2) (r0^2+a^2 Cos[θ0]^2))/((a^2+
  106. r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)]+(a (2 r0-℧^2) Cos[iPh] Sin[θ0] Sqrt[((a^2+
  107. r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)/(r0^2+a^2 Cos[θ0]^2)])/((a^2+r0^2)^2-a^2 (a^2-
  108. 2 r0+r0^2+℧^2) Sin[θ0]^2))) (-(1/((a^2-2 r0+r0^2+℧^2) (r0^2+
  109. a^2 Cos[θ0]^2)))2 a^2 Cot[θ0]^2 (Cos[iPh] Sin[θ0] (-a (a^2+r0^2) Sin[θ0]^2+a (a^2-2 r0+
  110. r0^2+℧^2) Sin[θ0]^2) Sqrt[((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)/(r0^2+
  111. a^2 Cos[θ0]^2)]+((a^2+r0^2)^2 Sin[θ0]^2+a^2 (-a^2+2 r0-r0^2-
  112. ℧^2) Sin[θ0]^4) (Sqrt[((a^2-2 r0+r0^2+℧^2) (r0^2+a^2 Cos[θ0]^2))/((a^2+r0^2)^2-a^2 (a^2-
  113. 2 r0+r0^2+℧^2) Sin[θ0]^2)]+(a (2 r0-℧^2) Cos[iPh] Sin[θ0] Sqrt[((a^2+r0^2)^2-a^2 (a^2-
  114. 2 r0+r0^2+℧^2) Sin[θ0]^2)/(r0^2+a^2 Cos[θ0]^2)])/((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+
  115. ℧^2) Sin[θ0]^2)))+1/((a^2-2 r0+r0^2+℧^2) (r0^2+a^2 Cos[θ0]^2)) 2 r0 (r0-
  116. ℧^2) Csc[θ0]^2 (Cos[iPh] Sin[θ0] (-a (a^2+r0^2) Sin[θ0]^2+a (a^2-2 r0+r0^2+
  117. ℧^2) Sin[θ0]^2) Sqrt[((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)/(r0^2+
  118. a^2 Cos[θ0]^2)]+((a^2+r0^2)^2 Sin[θ0]^2+a^2 (-a^2+2 r0-r0^2-℧^2) Sin[θ0]^4) (Sqrt[((a^2-
  119. 2 r0+r0^2+℧^2) (r0^2+a^2 Cos[θ0]^2))/((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)]+
  120. (a (2 r0-℧^2) Cos[iPh] Sin[θ0] Sqrt[((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)/(r0^2+
  121. a^2 Cos[θ0]^2)])/((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2))))+1/((a^2-2 r0+r0^2+
  122. ℧^2) (r0^2+a^2 Cos[θ0]^2)) 8 Csc[θ0]^2 (Cos[iPh] Sin[θ0] (-a (a^2+r0^2) Sin[θ0]^2+a (a^2-
  123. 2 r0+r0^2+℧^2) Sin[θ0]^2) Sqrt[((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)/(r0^2+
  124. a^2 Cos[θ0]^2)]+((a^2+r0^2)^2 Sin[θ0]^2+a^2 (-a^2+2 r0-r0^2-℧^2) Sin[θ0]^4) (Sqrt[((a^2-
  125. 2 r0+r0^2+℧^2) (r0^2+a^2 Cos[θ0]^2))/((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)]+
  126. (a (2 r0-℧^2) Cos[iPh] Sin[θ0] Sqrt[((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)/(r0^2+
  127. a^2 Cos[θ0]^2)])/((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2))) (1/((a^2-2 r0+r0^2+
  128. ℧^2) (r0^2+a^2 Cos[θ0]^2)) a^2 Cot[θ0]^2 (Cos[iPh] Sin[θ0] (-a (a^2+r0^2) Sin[θ0]^2+
  129. a (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2) Sqrt[((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+
  130. ℧^2) Sin[θ0]^2)/(r0^2+a^2 Cos[θ0]^2)]+((a^2+r0^2)^2 Sin[θ0]^2+a^2 (-a^2+2 r0-r0^2-
  131. ℧^2) Sin[θ0]^4) (Sqrt[((a^2-2 r0+r0^2+℧^2) (r0^2+a^2 Cos[θ0]^2))/((a^2+r0^2)^2-
  132. a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)]+(a (2 r0-℧^2) Cos[iPh] Sin[θ0] Sqrt[((a^2+
  133. r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)/(r0^2+a^2 Cos[θ0]^2)])/((a^2+r0^2)^2-a^2 (a^2-
  134. 2 r0+r0^2+℧^2) Sin[θ0]^2)))+1/((a^2-2 r0+r0^2+℧^2) (r0^2+a^2 Cos[θ0]^2)) r0 (-r0+
  135. ℧^2) Csc[θ0]^2 (Cos[iPh] Sin[θ0] (-a (a^2+r0^2) Sin[θ0]^2+a (a^2-2 r0+r0^2+
  136. ℧^2) Sin[θ0]^2) Sqrt[((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)/(r0^2+a^2 Cos[θ0]^2)]+
  137. ((a^2+r0^2)^2 Sin[θ0]^2+a^2 (-a^2+2 r0-r0^2-℧^2) Sin[θ0]^4) (Sqrt[((a^2-2 r0+r0^2+
  138. ℧^2) (r0^2+a^2 Cos[θ0]^2))/((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)]+(a (2 r0-
  139. ℧^2) Cos[iPh] Sin[θ0] Sqrt[((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)/(r0^2+
  140. a^2 Cos[θ0]^2)])/((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2))))+1/((a^2-2 r0+r0^2+
  141. ℧^2)^2 (r0^2+a^2 Cos[θ0]^2)^2) Csc[θ0]^2 (Cos[iPh] Sin[θ0] (a^2-2 r0+r0^2+℧^2-
  142. a^2 Sin[θ0]^2) Sqrt[((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)/(r0^2+a^2 Cos[θ0]^2)]+
  143. (a (a^2+r0^2) Sin[θ0]^2+a (-a^2+2 r0-r0^2-℧^2) Sin[θ0]^2) (Sqrt[((a^2-2 r0+r0^2+℧^2) (r0^2+
  144. a^2 Cos[θ0]^2))/((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)]+(a (2 r0-
  145. ℧^2) Cos[iPh] Sin[θ0] Sqrt[((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)/(r0^2+
  146. a^2 Cos[θ0]^2)])/((a^2+r0^2)^2-a^2 (a^2-2 r0+r0^2+℧^2) Sin[θ0]^2)))^2 (r0 (a^2 (3 a^2+
  147. 4 ℧^2+4 (a-℧) (a+℧) Cos[2 θ0]+a^2 Cos[4 θ0])+8 r0 (r0^3+2 a^2 r0 Cos[θ0]^2-
  148. a^2 Sin[θ0]^2))+2 a^4 Sin[2 θ0]^2))==0,iPh,Reals]][[1]]/.C[1]->0
  149.  
  150. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  151. (* |||||||| 4) HORIZONTE UND ERGOSPHÄREN RADIEN ||||||||||||||||||||||||||||||||||||||||| *)
  152. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  153.  
  154. rE=1+Sqrt[1-a^2 Cos[θ]^2-℧^2]; (* äußere Ergosphäre *)
  155. RE[A_, w1_, w2_]:=Xyz[xyZ[
  156. {Sqrt[rE^2+A^2] Sin[θ] Cos[φ], Sqrt[rE^2+A^2] Sin[θ] Sin[φ], rE Cos[θ]}, w1], w2];
  157. rG=1-Sqrt[1-a^2 Cos[θ]^2-℧^2]; (* innere Ergosphäre *)
  158. RG[A_, w1_, w2_]:=Xyz[xyZ[
  159. {Sqrt[rG^2+A^2] Sin[θ] Cos[φ], Sqrt[rG^2+A^2] Sin[θ] Sin[φ], rG Cos[θ]}, w1], w2];
  160. rA=1+Sqrt[1-a^2-℧^2]; (* äußerer Horizont *)
  161. RA[A_, w1_, w2_]:=Xyz[xyZ[
  162. {Sqrt[rA^2+A^2] Sin[θ] Cos[φ], Sqrt[rA^2+A^2] Sin[θ] Sin[φ], rA Cos[θ]}, w1], w2];
  163. rI=1-Sqrt[1-a^2-℧^2]; (* innerer Horizont *)
  164. RI[A_, w1_, w2_]:=Xyz[xyZ[
  165. {Sqrt[rI^2+A^2] Sin[θ] Cos[φ], Sqrt[rI^2+A^2] Sin[θ] Sin[φ], rI Cos[θ]}, w1], w2];
  166.  
  167. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  168. (* |||||||| 5) HORIZONTE UND ERGOSPHÄREN PLOT ||||||||||||||||||||||||||||||||||||||||||| *)
  169. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  170.  
  171. horizons[A_, mesh_, w1_, w2_]:=Show[
  172. ParametricPlot3D[RE[A, w1, w2], {φ, 0, 2 π}, {θ, 0, π},
  173. Mesh -> mesh, PlotPoints -> plp, PlotStyle -> Directive[Blue, Opacity[0.10]]],
  174. ParametricPlot3D[RA[A, w1, w2], {φ, 0, 2 π}, {θ, 0, π},
  175. Mesh -> None, PlotPoints -> plp, PlotStyle -> Directive[Cyan, Opacity[0.15]]],
  176. ParametricPlot3D[RI[A, w1, w2], {φ, 0, 2 π}, {θ, 0, π},
  177. Mesh -> None, PlotPoints -> plp, PlotStyle -> Directive[Red, Opacity[0.25]]],
  178. ParametricPlot3D[RG[A, w1, w2], {φ, 0, 2 π}, {θ, 0, π},
  179. Mesh -> None, PlotPoints -> plp, PlotStyle -> Directive[Red, Opacity[0.35]]]];
  180. BLKS:=Grid[{{horizons[a, 35, 0, 0], horizons[0, 35, 0, 0]}}];
  181.  
  182. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  183. (* |||||||| 6) FUNKTIONEN ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  184. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  185.  
  186. j[v_]:=Sqrt[1-μ^2 v^2]; (* Lorentzfaktor *)
  187. mirr=Sqrt[2-℧^2+2 Sqrt[1-a^2-℧^2]]/2; (* irreduzible Masse *)
  188. я=Sqrt[Χ/Σ]Sin[θ[τ]]; (* axialer Umfangsradius *)
  189. яi[τ_]:=Sqrt[Χi[τ]/Σi[τ]]Sin[Θ[τ]];
  190. Ы=Sqrt[χ/Ξ]Sin[θ0];
  191.  
  192. Σ=r[τ]^2+a^2 Cos[θ[τ]]^2; (* poloidialer Umfangsradius *)
  193. Σi[τ_]:=R[τ]^2+a^2 Cos[Θ[τ]]^2;
  194. Ξ=r0^2+a^2 Cos[θ0]^2;
  195.  
  196. Δ=r[τ]^2-2r[τ]+a^2+℧^2;
  197. Δr[r_]:=r^2-2r+a^2+℧^2;
  198. Δi[τ_]:=R[τ]^2-2R[τ]+a^2+℧^2;
  199. δ=r0^2-2r0+a^2+℧^2;
  200.  
  201. Χ=(r[τ]^2+a^2)^2-a^2 Sin[θ[τ]]^2 Δ;
  202. Χi[τ_]:=(R[τ]^2+a^2)^2-a^2 Sin[Θ[τ]]^2 Δi[τ];
  203. χ=(r0^2+a^2)^2-a^2 Sin[θ0]^2 δ;
  204.  
  205. Xj=a Sin[θ0]^2;
  206. xJ[τ_]:=a Sin[Θ[τ]]^2;
  207. XJ=a Sin[θ[τ]]^2;
  208.  
  209. т[τ_]:=Evaluate[t[τ]/.sol][[1]]; (* Koordinatenzeit nach Eigenzeit *)
  210. д[ξ_]:=Quiet[zt /.FindRoot[т[zt]-ξ, {zt, 0}]]; (* Eigenzeit nach Koordinatenzeit *)
  211. T :=Quiet[д[tk]];
  212.  
  213. pΘ[τ_]:=Evaluate[Ξ θ'[τ] /. sol][[1]];
  214. pR[τ_]:=Evaluate[r'[τ] Ξ/δ /. sol][[1]];
  215.  
  216. ю[τ_]:=Evaluate[t'[τ]/.sol][[1]];
  217. γ[τ_]:=If[μ==0, "Infinity", ю[τ]]; (* totale ZD *)
  218. R[τ_]:=Evaluate[r[τ]/.sol][[1]]; (* Boyer-Lindquist Radius *)
  219. Φ[τ_]:=Evaluate[φ[τ]/.sol][[1]];
  220. Θ[τ_]:=Evaluate[θ[τ]/.sol][[1]];
  221. ß[τ_]:=Sqrt[X'[τ]^2+Y'[τ]^2+Z'[τ]^2 ]/ю[τ];
  222.  
  223. ς[τ_]:=Sqrt[Χi[τ]/Δi[τ]/Σi[τ]]; ς0=Sqrt[χ/δ/Ξ]; (* gravitative ZD *)
  224. ω[τ_]:=(a(2R[τ]-℧^2))/Χi[τ]; ω0=(a(2r0-℧^2))/χ; ωζ=(a(2r[τ]-℧^2))/Χ; (* F-Drag Winkelg *)
  225. Ω[τ_]:=ω[τ] Sqrt[X[τ]^2+Y[τ]^2]; (* Frame Dragging beobachtete Geschwindigkeit *)
  226. й[τ_]:=ω[τ] яi[τ] ς[τ]; й0=ω0 Ы ς0; (* Frame Dragging lokale Geschwindigkeit *)
  227.  
  228. dst[τ_]:=Quiet@NIntegrate[If[μ==0, 1, v[tau]/Abs[Sqrt[1-v[tau]^2]]], {tau, 0, τ}];
  229. tcr[τ_]:=Quiet@NIntegrate[dt[tau], {tau, 0, τ}, Method->set, MaxRecursion->mrec];
  230. ж[τ_]:=Sqrt[ς[τ]^2-1]/ς[τ]; ж0=Sqrt[ς0^2-1]/ς0; (* Fluchtgeschwindigkeit *)
  231.  
  232. epot[τ_]:=ε+μ-ekin[τ]; (* potentielle Energie *)
  233. ekin[τ_]:=If[μ==0, ς[τ], 1/Sqrt[1-v[τ]^2]-1]; (* kinetische Energie *)
  234.  
  235. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  236. (* |||||||| 7) DIFFERENTIALGLEICHUNG |||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  237. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  238.  
  239. dp= Style[\!\(\*SuperscriptBox[\(Y\),\(Y\)]\), White]; n0[z_] := Chop[Re[N[Simplify[z]]]];
  240.  
  241. dr0 = (pr0 δ)/Ξ;
  242. dθ0 = pθ0/Ξ;
  243. dφ0 = 1/(δ Ξ Sin[θ0]^2) (ε (-δ Xj+a Sin[θ0]^2 (r0^2+a^2))+Lz (δ-a^2 Sin[θ0]^2)-
  244. q ℧ r0 a Sin[θ0]^2)-If[r0<1+Sqrt[1-a^2 Cos[θ0]^2-℧^2] && r0>1-Sqrt[1-a^2 Cos[θ0]^2-℧^2],
  245. -1, +1] (pr0 δ)/Ξ a (-Sqrt[(2 r0-℧^2)/(a^2+r0^2)])/(1-(Sqrt[(2 r0-℧^2)/(a^2+
  246. r0^2)])^2)/(a^2+r0^2);
  247. dt0 = Min[
  248. Max[0, N[-(1/(2 (-1+(-2 ℧^2+4 r0)/(a^2+a^2 Cos[2 θ0]+2 r0^2))))((2 Sqrt[-℧^2+2 r0] dr0)/Sqrt[a^2+
  249. r0^2]-(2 a (-℧^2+2 r0) Sin[θ0]^2 dφ0)/(a^2 Cos[θ0]^2+r0^2)+\[Sqrt](((2 Sqrt[-℧^2+
  250. 2 r0] dr0)/Sqrt[a^2+r0^2]+(2 a (℧^2-2 r0) Sin[θ0]^2 dφ0)/(a^2 Cos[θ0]^2+r0^2))^2-
  251. 4 (-1+(-2 ℧^2+4 r0)/(a^2+a^2 Cos[2 θ0]+2 r0^2)) (-μ+((a^2+a^2 Cos[2 θ0]+
  252. 2 r0^2) dr0^2)/(2 (a^2+r0^2))+(a^2 Cos[θ0]^2+r0^2) dθ0^2-(2 a Sqrt[-℧^2+
  253. 2 r0] Sin[θ0]^2 dr0 dφ0)/Sqrt[a^2+r0^2]+(Sin[θ0]^2 ((a^2+r0^2)^2-a^2 (a^2+℧^2-
  254. 2 r0+r0^2) Sin[θ0]^2) dφ0^2)/(a^2 Cos[θ0]^2+r0^2))))]],
  255. Max[0, N[1/(2 (-1+(-2 ℧^2+4 r0)/(a^2+a^2 Cos[2 θ0]+2 r0^2))) (-((2 Sqrt[-℧^2+2 r0]dr0)/Sqrt[a^2+
  256. r0^2])+(2 a (-℧^2+2 r0) Sin[θ0]^2 dφ0)/(a^2 Cos[θ0]^2+r0^2)+\[Sqrt](((2 Sqrt[-℧^2+
  257. 2 r0]dr0)/Sqrt[a^2+r0^2]+(2 a (℧^2-2 r0) Sin[θ0]^2 dφ0)/(a^2 Cos[θ0]^2+r0^2))^2-4 (-1+
  258. (-2 ℧^2+4 r0)/(a^2+a^2 Cos[2 θ0]+2 r0^2)) (-μ+((a^2+a^2 Cos[2 θ0]+2 r0^2)dr0^2)/(2 (a^2+
  259. r0^2))+(a^2 Cos[θ0]^2+r0^2) dθ0^2-(2 a Sqrt[-℧^2+2 r0] Sin[θ0]^2 dr0 dφ0)/Sqrt[a^2+
  260. r0^2]+(Sin[θ0]^2 ((a^2+r0^2)^2-a^2 (a^2+℧^2-2 r0+
  261. r0^2) Sin[θ0]^2) dφ0^2)/(a^2 Cos[θ0]^2+r0^2))))]]];
  262.  
  263. DGL={
  264.  
  265. t''[τ]==1/(8 (a^2 Cos[θ[τ]]^2+r[τ]^2)^3) (8 q ℧ (-a^4 Cos[θ[τ]]^4+r[τ]^4) r'[τ]+
  266. (8 (a^2 Cos[θ[τ]]^2+℧^2 r[τ]-r[τ]^2) (a^2 Cos[θ[τ]]^2+r[τ]^2)^2 r'[τ]^2)/(Sqrt[-℧^2+
  267. 2 r[τ]] Sqrt[a^2+r[τ]^2])+8 q ℧ Sqrt[-℧^2+2 r[τ]] Sqrt[a^2+r[τ]^2] (-a^2 Cos[θ[τ]]^2+
  268. r[τ]^2) t'[τ]+16 (a^2 Cos[θ[τ]]^2+℧^2 r[τ]-r[τ]^2) (a^2 Cos[θ[τ]]^2+r[τ]^2) r'[τ] t'[τ]+
  269. 8 Sqrt[-℧^2+2 r[τ]] (a^2 Cos[θ[τ]]^2+℧^2 r[τ]-r[τ]^2) Sqrt[a^2+r[τ]^2] t'[τ]^2-
  270. 8 a^2 q ℧ r[τ] (a^2 Cos[θ[τ]]^2+r[τ]^2) Sin[2 θ[τ]] θ'[τ]+(8 a^2 Sqrt[-℧^2+
  271. 2 r[τ]] (a^2 Cos[θ[τ]]^2+r[τ]^2)^2 Sin[2 θ[τ]] r'[τ] θ'[τ])/Sqrt[a^2+r[τ]^2]-8 a^2 (℧^2-
  272. 2 r[τ]) (a^2 Cos[θ[τ]]^2+r[τ]^2) Sin[2 θ[τ]] t'[τ] θ'[τ]+8 r[τ] Sqrt[-℧^2+
  273. 2 r[τ]] Sqrt[a^2+r[τ]^2] (a^2 Cos[θ[τ]]^2+r[τ]^2)^2 θ'[τ]^2-8 a q ℧ Sqrt[-℧^2+
  274. 2 r[τ]] Sqrt[a^2+r[τ]^2] (-a^2 Cos[θ[τ]]^2+r[τ]^2) Sin[θ[τ]]^2 φ'[τ]-
  275. 16 a (a^2 Cos[θ[τ]]^2+(℧^2-r[τ]) r[τ]) (a^2 Cos[θ[τ]]^2+r[τ]^2) Sin[θ[τ]]^2 r'[τ] φ'[τ]-
  276. 16 a Sqrt[-℧^2+2 r[τ]] (a^2 Cos[θ[τ]]^2+℧^2 r[τ]-r[τ]^2) Sqrt[a^2+
  277. r[τ]^2] Sin[θ[τ]]^2 t'[τ] φ'[τ]+16 a^3 Cos[θ[τ]] (℧^2-2 r[τ]) (a^2 Cos[θ[τ]]^2+
  278. r[τ]^2) Sin[θ[τ]]^3 θ'[τ] φ'[τ]+Sqrt[-℧^2+2 r[τ]] Sqrt[a^2+r[τ]^2] (a^4+
  279. a^4 Cos[4 θ[τ]] (-1+r[τ])+3 a^4 r[τ]+4 a^2 ℧^2 r[τ]-4 a^2 r[τ]^2+8 a^2 r[τ]^3+
  280. 8 r[τ]^5+4 a^2 Cos[2 θ[τ]] r[τ] (a^2-℧^2+r[τ]+2 r[τ]^2)) Sin[θ[τ]]^2 φ'[τ]^2),
  281.  
  282. t'[0]==dt0,
  283. t[0]==0,
  284.  
  285. r''[τ]==1/(8 (a^2 Cos[θ[τ]]^2+r[τ]^2)^3) (-8 q ℧ Sqrt[-℧^2+2 r[τ]] Sqrt[a^2+
  286. r[τ]^2] (-a^2 Cos[θ[τ]]^2+r[τ]^2) r'[τ]+(8 a^2 q ℧ Sqrt[-℧^2+2 r[τ]] (-a^2 Cos[θ[τ]]^2+
  287. r[τ]^2) Sin[θ[τ]]^2 r'[τ])/Sqrt[a^2+r[τ]^2]+(4 (a^2 Cos[θ[τ]]^2+
  288. r[τ]^2)^2 (a^2 Cos[2 θ[τ]] (-1+r[τ])-a^2 (1+r[τ])+2 r[τ] (-℧^2+r[τ])) r'[τ]^2)/(a^2+
  289. r[τ]^2)-4 q ℧ (2 a^2 Cos[θ[τ]]^2-2 r[τ]^2) (a^2+r[τ]^2) (1+(℧^2-
  290. 2 r[τ])/(a^2 Cos[θ[τ]]^2+r[τ]^2)) t'[τ]+(8 a^2 q ℧ (℧^2-2 r[τ]) (a^2 Cos[θ[τ]]^2-
  291. r[τ]^2) Sin[θ[τ]]^2 t'[τ])/(a^2 Cos[θ[τ]]^2+r[τ]^2)-(16 Sqrt[-℧^2+
  292. 2 r[τ]] (a^2 Cos[θ[τ]]^2+℧^2 r[τ]-r[τ]^2) (a^2 Cos[θ[τ]]^2+
  293. r[τ]^2) r'[τ] t'[τ])/Sqrt[a^2+r[τ]^2]+8 (a^2 Cos[θ[τ]]^2+℧^2 r[τ]-r[τ]^2) (a^2+
  294. ℧^2-2 r[τ]+r[τ]^2) t'[τ]^2+8 a^2 (a^2 Cos[θ[τ]]^2+r[τ]^2)^2 Sin[2 θ[τ]] r'[τ] θ'[τ]+
  295. 8 r[τ] (a^2 Cos[θ[τ]]^2+r[τ]^2)^2 (a^2+℧^2-2 r[τ]+r[τ]^2) θ'[τ]^2+(8 a q ℧ (℧^2-
  296. 2 r[τ]) (a^2 Cos[θ[τ]]^2-r[τ]^2) (a^2+r[τ]^2) Sin[θ[τ]]^2 φ'[τ])/(a^2 Cos[θ[τ]]^2+
  297. r[τ]^2)-(4 a q ℧ (2 a^2 Cos[θ[τ]]^2-2 r[τ]^2) (-(a^2+r[τ]^2)^2 Sin[θ[τ]]^2+a^2 (a^2+
  298. ℧^2+(-2+r[τ]) r[τ]) Sin[θ[τ]]^4) φ'[τ])/(a^2 Cos[θ[τ]]^2+r[τ]^2)-(8 a Sqrt[-℧^2+
  299. 2 r[τ]] (a^2 Cos[θ[τ]]^2+r[τ]^2) (a^2 (-1+r[τ])+a^2 Cos[2 θ[τ]] (-1+r[τ])+
  300. 2 r[τ] (-℧^2+r[τ]+r[τ]^2)) Sin[θ[τ]]^2 r'[τ] φ'[τ])/Sqrt[a^2+r[τ]^2]-
  301. 16 a (a^2 Cos[θ[τ]]^2+(℧^2-r[τ]) r[τ]) (a^2+℧^2-2 r[τ]+
  302. r[τ]^2) Sin[θ[τ]]^2 t'[τ] φ'[τ]+(a^2+℧^2-2 r[τ]+r[τ]^2) (a^4+a^4 Cos[4 θ[τ]] (-1+
  303. r[τ])+3 a^4 r[τ]+4 a^2 ℧^2 r[τ]-4 a^2 r[τ]^2+8 a^2 r[τ]^3+8 r[τ]^5+
  304. 4 a^2 Cos[2 θ[τ]] r[τ] (a^2-℧^2+r[τ]+2 r[τ]^2)) Sin[θ[τ]]^2 φ'[τ]^2),
  305.  
  306. r'[0]==dr0,
  307. r[0]==r0,
  308.  
  309. θ''[τ]==-1/(2 (a^2 Cos[θ[τ]]^2+r[τ]^2)^4) ((2 a^2 Cos[θ[τ]] (a^2 Cos[θ[τ]]^2+
  310. r[τ]^2)^3 Sin[θ[τ]] r'[τ]^2)/(a^2+r[τ]^2)-2 a^2 q ℧ (℧^2-2 r[τ]) r[τ] Sin[2 θ[τ]] t'[τ]+
  311. a^2 q ℧ r[τ] (a^2+2 ℧^2+a^2 Cos[2 θ[τ]]-4 r[τ]+2 r[τ]^2) Sin[2 θ[τ]] t'[τ]+
  312. 2 a^2 Cos[θ[τ]] (℧^2-2 r[τ]) (a^2 Cos[θ[τ]]^2+r[τ]^2) Sin[θ[τ]] t'[τ]^2+
  313. 4 r[τ] (a^2 Cos[θ[τ]]^2+r[τ]^2)^3 r'[τ] θ'[τ]-2 a^2 Cos[θ[τ]] (a^2 Cos[θ[τ]]^2+
  314. r[τ]^2)^3 Sin[θ[τ]] θ'[τ]^2-4 a^3 q ℧ Cos[θ[τ]] (℧^2-2 r[τ]) r[τ] Sin[θ[τ]]^3 φ'[τ]+
  315. 4 a q ℧ Cot[θ[τ]] r[τ] (-(a^2+r[τ]^2)^2 Sin[θ[τ]]^2+a^2 (a^2+℧^2+(-2+
  316. r[τ]) r[τ]) Sin[θ[τ]]^4) φ'[τ]+(2 a Sqrt[-℧^2+2 r[τ]] (a^2 Cos[θ[τ]]^2+
  317. r[τ]^2)^3 Sin[2 θ[τ]] r'[τ] φ'[τ])/Sqrt[a^2+r[τ]^2]-2 a (℧^2-2 r[τ]) (a^2+
  318. r[τ]^2) (a^2 Cos[θ[τ]]^2+r[τ]^2) Sin[2 θ[τ]] t'[τ] φ'[τ]+(a^2 Cos[θ[τ]]^2+
  319. r[τ]^2) (2 a^2 Cos[θ[τ]] Sin[θ[τ]]^3 (-(a^2+r[τ]^2)^2+a^2 (a^2+℧^2+(-2+
  320. r[τ]) r[τ]) Sin[θ[τ]]^2)+(a^2 Cos[θ[τ]]^2+r[τ]^2) (4 a^2 Cos[θ[τ]] (a^2+℧^2+
  321. (-2+r[τ]) r[τ]) Sin[θ[τ]]^3-(a^2+r[τ]^2)^2 Sin[2 θ[τ]])) φ'[τ]^2),
  322.  
  323. θ'[0]==dθ0,
  324. θ[0]==θ0,
  325.  
  326. φ''[τ]==1/(4 (a^2 Cos[θ[τ]]^2+r[τ]^2)^3) ((4 a q ℧ (-a^4 Cos[θ[τ]]^4+r[τ]^4) r'[τ])/(a^2+
  327. r[τ]^2)+(4 a (a^2 Cos[θ[τ]]^2+℧^2 r[τ]-r[τ]^2) (a^2 Cos[θ[τ]]^2+
  328. r[τ]^2)^2 r'[τ]^2)/(Sqrt[-℧^2+2 r[τ]] (a^2+r[τ]^2)^(3/2))+(4 a q ℧ Sqrt[-℧^2+
  329. 2 r[τ]] (-a^2 Cos[θ[τ]]^2+r[τ]^2) t'[τ])/Sqrt[a^2+r[τ]^2]+(8 a (a^2 Cos[θ[τ]]^2+(℧^2-
  330. r[τ]) r[τ]) (a^2 Cos[θ[τ]]^2+r[τ]^2) r'[τ] t'[τ])/(a^2+r[τ]^2)+(4 a Sqrt[-℧^2+
  331. 2 r[τ]] (a^2 Cos[θ[τ]]^2+℧^2 r[τ]-r[τ]^2) t'[τ]^2)/Sqrt[a^2+r[τ]^2]-
  332. 8 a q ℧ Cot[θ[τ]] r[τ] (a^2 Cos[θ[τ]]^2+r[τ]^2) θ'[τ]+(8 a Cot[θ[τ]] Sqrt[-℧^2+
  333. 2 r[τ]] (a^2 Cos[θ[τ]]^2+r[τ]^2)^2 r'[τ] θ'[τ])/Sqrt[a^2+r[τ]^2]-8 a Cot[θ[τ]] (℧^2-
  334. 2 r[τ]) (a^2 Cos[θ[τ]]^2+r[τ]^2) t'[τ] θ'[τ]+(4 a r[τ] Sqrt[-℧^2+2 r[τ]] (a^2 Cos[θ[τ]]^2+
  335. r[τ]^2)^2 θ'[τ]^2)/Sqrt[a^2+r[τ]^2]-(4 a^2 q ℧ Sqrt[-℧^2+2 r[τ]] (-a^2 Cos[θ[τ]]^2+
  336. r[τ]^2) Sin[θ[τ]]^2 φ'[τ])/Sqrt[a^2+r[τ]^2]+(8 (a^2 Cos[θ[τ]]^2+
  337. r[τ]^2) (a^4 Cos[θ[τ]]^2 (-1+r[τ])-r[τ] (a^2 (a^2+℧^2-r[τ])+2 a^2 Cot[θ[τ]]^2 (a^2+
  338. r[τ]^2)+Csc[θ[τ]]^2 (-a^4+r[τ]^4))) Sin[θ[τ]]^2 r'[τ] φ'[τ])/(a^2+r[τ]^2)-
  339. (8 a^2 Sqrt[-℧^2+2 r[τ]] (a^2 Cos[θ[τ]]^2+℧^2 r[τ]-
  340. r[τ]^2) Sin[θ[τ]]^2 t'[τ] φ'[τ])/Sqrt[a^2+r[τ]^2]-Cot[θ[τ]] (a^2 Cos[θ[τ]]^2+
  341. r[τ]^2) (a^2 (3 a^2-4 ℧^2+4 (a^2+℧^2) Cos[2 θ[τ]]+a^2 Cos[4 θ[τ]])+
  342. 16 a^2 Cos[θ[τ]]^2 r[τ]^2+8 r[τ]^4+16 a^2 r[τ] Sin[θ[τ]]^2) θ'[τ] φ'[τ]+
  343. (4 a Sqrt[-℧^2+2 r[τ]] Sin[θ[τ]]^2 (r[τ] (-a^4+r[τ]^4+a^2 (a^2+℧^2-r[τ]) Sin[θ[τ]]^2)+
  344. Cos[θ[τ]]^2 (2 a^2 r[τ] (a^2+r[τ]^2)-a^4 (-1+r[τ]) Sin[θ[τ]]^2)) φ'[τ]^2)/Sqrt[a^2+r[τ]^2]),
  345.  
  346. φ'[0]==dφ0,
  347. φ[0]==φ0
  348.  
  349. };
  350.  
  351. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  352. (* |||||||| 8) INTEGRATION |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  353. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  354.  
  355. sol=NDSolve[DGL, {t, r, θ, φ}, {τ, 0, tmax+1/1000},
  356. WorkingPrecision-> wp,
  357. MaxSteps-> Infinity,
  358. Method-> mta,
  359. InterpolationOrder-> All,
  360. StepMonitor :> (laststep=plunge; plunge=τ;
  361. stepsize=plunge-laststep;), Method->{"EventLocator",
  362. "Event" :> (If[stepsize<1*^-4, 0, 1])}];
  363.  
  364. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  365. (* |||||||| 9) KOORDINATEN |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  366. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  367.  
  368. X[τ_]:=Evaluate[Sqrt[r[τ]^2+a^2] Sin[θ[τ]] Cos[φ[τ]]/.sol][[1]]; (* kartesisch *)
  369. Y[τ_]:=Evaluate[Sqrt[r[τ]^2+a^2] Sin[θ[τ]] Sin[φ[τ]]/.sol][[1]];
  370. Z[τ_]:=Evaluate[r[τ] Cos[θ[τ]]/.sol][[1]];
  371.  
  372. x[τ_]:=Evaluate[Sqrt[r[τ]^2+A^2] Sin[θ[τ]] Cos[φ[τ]]/.sol][[1]]; (* Plotkoordinaten *)
  373. y[τ_]:=Evaluate[Sqrt[r[τ]^2+A^2] Sin[θ[τ]] Sin[φ[τ]]/.sol][[1]];
  374. z[τ_]:=Z[τ];
  375.  
  376. XYZ[τ_]:=Sqrt[X[τ]^2+Y[τ]^2+Z[τ]^2]; XY[τ_]:=Sqrt[X[τ]^2+Y[τ]^2]; (* kartesischer Radius *)
  377.  
  378. Xyz[{x_, y_, z_}, α_]:={x Cos[α]-y Sin[α], x Sin[α]+y Cos[α], z}; (* Rotationsmatrix *)
  379. xYz[{x_, y_, z_}, β_]:={x Cos[β]+z Sin[β], y, z Cos[β]-x Sin[β]};
  380. xyZ[{x_, y_, z_}, ψ_]:={x, y Cos[ψ]-z Sin[ψ], y Sin[ψ]+z Cos[ψ]};
  381.  
  382. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  383. (* |||||||| 10) PLOT EINSTELLUNGEN |||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  384. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  385.  
  386. PR=r1; (* Plot Range *)
  387. VP={r0, r0, r0}; (* Perspektive x,y,z *)
  388. d1=10; (* Schweiflänge *)
  389. plp=50; (* Flächenplot Details *)
  390. Plp=Automatic; (* Kurven Details *)
  391.  
  392. w1l=0; w2l=0; w1r=0; w2r=0; (* Startperspektiven *)
  393. Mrec=100; mrec=10; (* Parametric Plot Subdivisionen *)
  394. imgsize=380; (* Bildgröße *)
  395.  
  396. s[text_]:=Style[text, FontFamily->"Consolas", FontSize->11]; (* Anzeigestil *)
  397.  
  398. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  399. (* |||||||| 11) PLOT NACH EIGENZEIT ||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  400. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  401.  
  402. Plot[R[tt], {tt, 0, plunge},
  403. Frame->True, PlotStyle->Red, AspectRatio->1/5, ImagePadding->{{40, 10}, {20, 10}},
  404. ImageSize->600, PlotRange->{{0, plunge}, All}, GridLines->{{}, {rA, rI}},
  405. PlotLabel -> "r(τ)"]
  406.  
  407. Plot[Mod[180/Pi Θ[tt], 360], {tt, 0, plunge},
  408. Frame->True, PlotStyle->Cyan, AspectRatio->1/5, ImagePadding->{{40, 10}, {20, 10}},
  409. ImageSize->600, PlotRange->{{0, plunge}, {0, 360}}, GridLines->{{}, {90, 180, 270}},
  410. PlotLabel -> "θ(τ)"]
  411.  
  412. Plot[Mod[180/Pi Φ[tt], 360], {tt, 0, plunge},
  413. Frame->True, PlotStyle->Magenta, AspectRatio->1/5, ImagePadding->{{40, 10}, {20, 10}},
  414. ImageSize->600, PlotRange->{{0, plunge}, {0, 360}}, GridLines->{{}, {90, 180, 270}},
  415. PlotLabel -> "φ(τ)"]
  416.  
  417. Plot[v[tt], {tt, 0, plunge},
  418. Frame->True, PlotStyle->Orange, AspectRatio->1/5, ImagePadding->{{40, 10}, {20, 10}},
  419. ImageSize->600, PlotRange->{{0, plunge}, All}, GridLines->{{}, {0, 1}},
  420. PlotLabel -> "v(τ)"]
  421.  
  422. displayP[T_]:=Grid[{
  423. {If[μ==0, s[" affineP"], s[" τ propr"]], " = ", s[n0[T]], s["GM/c³"], s[dp]},
  424. {s[" t doran"], " = ", s[n0[т[tp]]], s["GM/c³"], s[dp]},
  425. {s[" t bookp"], " = ", s[n0[tcr[tp]]], s["GM/c³"], s[dp]},
  426. {s[" ṫ total"], " = ", s[n0[dt[tp]]], s["dt/dτ"], s[dp]},
  427. {s[" ς gravt"], " = ", s[n0[ς[tp]]], s["dt/dτ"], s[dp]},
  428. {s[" γ kinet"], " = ", s[n0[1/Sqrt[1-v[tp]^2]]], s["dt/dτ"], s[dp]},
  429. {s[" R carts"], " = ", s[n0[XYZ[tp]]], s["GM/c²"], s[dp]},
  430. {s[" x carts"], " = ", s[n0[X[tp]]], s["GM/c²"], s[dp]},
  431. {s[" y carts"], " = ", s[n0[Y[tp]]], s["GM/c²"], s[dp]},
  432. {s[" z carts"], " = ", s[n0[Z[tp]]], s["GM/c²"], s[dp]},
  433.  
  434. {s[" r coord"], " = ", s[n0[R[tp]]], s["GM/c²"], s[dp]},
  435. {s[" φ longd"], " = ", s[n0[Φ[tp] 180/π]], s["deg"], s[dp]},
  436. {s[" θ lattd"], " = ", s[n0[Θ[tp] 180/π]], s["deg"], s[dp]},
  437. {s[" d¹r/dτ¹"], " = ", s[n0[R'[tp]]], s["c"], s[dp]},
  438. {s[" d¹φ/dτ¹"], " = ", s[n0[Φ'[tp]]], s["c\.b3/G/M"], s[dp]},
  439. {s[" d¹θ/dτ¹"], " = ", s[n0[Θ'[tp]]], s["c\.b3/G/M"], s[dp]},
  440. {s[" d\.b2r/dτ\.b2"], " = ", s[n0[R''[tp]]], s["c⁴/G/M"], s[dp]},
  441. {s[" d\.b2φ/dτ\.b2"], " = ", s[n0[Φ''[tp]]], s["c⁶/G\.b2/M\.b2"], s[dp]},
  442. {s[" d\.b2θ/dτ\.b2"], " = ", s[n0[Θ''[tp]]], s["c⁶/G\.b2/M\.b2"], s[dp]},
  443. {s[" a SpinP"], " = ", s[n0[a]], s["GM²/c"], s[dp]},
  444.  
  445. {s[" ℧ cntrl"], " = ", s[n0[℧]], s["Q/M"], s[dp]},
  446. {s[" q prtcl"], " = ", s[n0[q]], s["q/m"], s[dp]},
  447. {s[" M irred"], " = ", s[N[mirr]], s["M"], s[dp]},
  448. {s[" E kinet"], " = ", s[n0[ekin[tp]]], s["mc²"], s[dp]},
  449. {s[" E poten"], " = ", s[n0[epot[tp]]], s["mc²"], s[dp]},
  450. {s[" E total"], " = ", s[n0[ε]], s["mc²"], s[dp]},
  451. {s[" CarterQ"], " = ", s[n0[Qk]], s["GMm/c"], s[dp]},
  452. {s[" L axial"], " = ", s[n0[Lz]], s["GMm/c"], s[dp]},
  453. {s[" L polar"], " = ", s[n0[pΘ[tp]]], s["GMm/c"], s[dp]},
  454. {s[" g acclr"], " = ", s[n0[v'[tp]]], s["c⁴/G/M"], s[dp]},
  455.  
  456. {s[" ω fdrag"], " = ", s[n0[Abs[ω[tp]]]], s["c³/G/M"], s[dp]},
  457. {s[" v fdrag"], " = ", s[n0[Abs[й[tp]]]], s["c"], s[dp]},
  458. {s[" Ω fdrag"], " = ", s[n0[Abs[Ω[tp]]]], s["c"], s[dp]},
  459. {s[" v propr"], " = ", s[n0[v[tp]/Sqrt[1-v[tp]^2]]], s["c"], s[dp]},
  460. {s[" v escpe"], " = ", s[n0[ж[tp]]], s["c"], s[dp]},
  461. {s[" v obsvd"], " = ", s[n0[ß[tp]]], s["c"], s[dp]},
  462. {s[" v r,loc"], " = ", s[n0[vr[tp]]], s["c"], s[dp]},
  463. {s[" v θ,loc"], " = ", s[n0[vθ[tp]]], s["c"], s[dp]},
  464. {s[" v φ,loc"], " = ", s[n0[vφ[tp]]], s["c"], s[dp]},
  465. {s[" v local"], " = ", s[n0[v[tp]]], s["c"], s[dp]},
  466. {s[" "], s[" "], s[" "], s[" "]}},
  467. Alignment-> Left, Spacings-> {0, 0}];
  468.  
  469. plot1b[{xx_, yy_, zz_, tk_, w1_, w2_}]:= (* Animation *)
  470. Show[
  471.  
  472. Graphics3D[{
  473. {PointSize[0.011], Red, Point[
  474. Xyz[xyZ[{x[tp], y[tp], z[tp]}, w1], w2]]}},
  475. ImageSize-> imgsize,
  476. PlotRange-> {
  477. {-(2 Sign[Abs[xx]]+1) PR, +(2 Sign[Abs[xx]]+1) PR},
  478. {-(2 Sign[Abs[yy]]+1) PR, +(2 Sign[Abs[yy]]+1) PR},
  479. {-(2 Sign[Abs[zz]]+1) PR, +(2 Sign[Abs[zz]]+1) PR}
  480. },
  481. SphericalRegion->False,
  482. ImagePadding-> 1],
  483.  
  484. horizons[A, None, w1, w2],
  485.  
  486. If[a==0, {}, ParametricPlot3D[
  487. Xyz[xyZ[{
  488. Sin[prm] a,
  489. Cos[prm] a,
  490. 0}, w1], w2],
  491. {prm, 0, 2π},
  492. PlotStyle -> {Thickness[0.005], Orange}]],
  493.  
  494. If[a==0, {},
  495. Graphics3D[{{PointSize[0.009], Purple, Point[
  496. Xyz[xyZ[{
  497. Sin[-φ0-ω0 т[tp]+π/2] Sqrt[x0[A]^2+y0[A]^2],
  498. Cos[-φ0-ω0 т[tp]+π/2] Sqrt[x0[A]^2+y0[A]^2],
  499. z0[A]}, w1], w2]]}}]],
  500.  
  501. If[tk==0, {}, If[a==0, {},
  502. ParametricPlot3D[
  503. Xyz[xyZ[{
  504. Sin[-φ0-ω0 т[tt]+π/2] Sqrt[x0[A]^2+y0[A]^2],
  505. Cos[-φ0-ω0 т[tt]+π/2] Sqrt[x0[A]^2+y0[A]^2],
  506. z0[A]}, w1], w2],
  507. {tt, Max[0, д[т[tp]-1/2 π/ω0]], tp},
  508. PlotStyle -> {Thickness[0.001], Dashed, Purple},
  509. PlotPoints-> Automatic,
  510. MaxRecursion-> 12]]],
  511.  
  512. If[tk==0, {},
  513. Block[{$RecursionLimit = Mrec},
  514. ParametricPlot3D[
  515. Xyz[xyZ[{x[tt], y[tt], z[tt]}, w1], w2], {tt, If[tp<0, Min[0, tp+d1], Max[0, tp-d1]], tp},
  516. PlotStyle-> {Thickness[0.004]},
  517. ColorFunction-> Function[{x, y, z, t},
  518. Hue[0, 1, 0.5, If[tp<0,
  519. Max[Min[(+tp+(-t+d1))/d1, 1], 0], Max[Min[(-tp+(t+d1))/d1, 1], 0]]]],
  520. ColorFunctionScaling-> False,
  521. PlotPoints-> Automatic,
  522. MaxRecursion-> mrec]]],
  523.  
  524. If[tk==0, {},
  525. Block[{$RecursionLimit = Mrec},
  526. ParametricPlot3D[
  527. Xyz[xyZ[{x[tt], y[tt], z[tt]}, w1], w2],
  528. {tt, 0, If[tp<0, Min[-1*^-16, tp+d1/3], Max[1*^-16, tp-d1/3]]},
  529. PlotStyle-> {Thickness[0.004], Opacity[0.6], Darker[Gray]},
  530. PlotPoints-> Plp,
  531. MaxRecursion-> mrec]]],
  532.  
  533. ViewPoint-> {xx, yy, zz}];
  534.  
  535. Do[
  536. Print[Rasterize[Grid[{{
  537. plot1b[{0, -Infinity, 0, tp, w1l, w2l}],
  538. plot1b[{0, 0, +Infinity, tp, w1r, w2r}],
  539. displayP[tp]
  540. }, {" ", " ", " "}
  541. }, Alignment->Left]]],
  542. {tp, 0, tMax, tMax/1}]
  543.  
  544. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  545. (* |||||||| 12) PLOT NACH KOORDINATENZEIT ||||||||||||||||||||||||||||||||||||||||||||||| *)
  546. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  547.  
  548. Plot[R[д[tt]], {tt, 0, TMax},
  549. Frame->True, PlotStyle->Red, AspectRatio->1/5, ImagePadding->{{40, 10}, {20, 10}},
  550. ImageSize->600, PlotRange->{{0, TMax}, All}, GridLines->{{}, {rA, rI}}, PlotLabel -> "r(t)"]
  551.  
  552. Plot[Mod[180/Pi Θ[д[tt]], 360], {tt, 0, TMax},
  553. Frame->True, PlotStyle->Cyan, AspectRatio->1/5, ImagePadding->{{40, 10}, {20, 10}},
  554. ImageSize->600, PlotRange->{{0, TMax}, {0, 360}}, GridLines->{{}, {90, 180, 270}}, PlotLabel -> "θ(t)"]
  555.  
  556. Plot[Mod[180/Pi Φ[д[tt]], 360], {tt, 0, TMax},
  557. Frame->True, PlotStyle->Magenta, AspectRatio->1/5, ImagePadding->{{40, 10}, {20, 10}},
  558. ImageSize->600, PlotRange->{{0, TMax}, {0, 360}}, GridLines->{{}, {90, 180, 270}}, PlotLabel -> "φ(t)"]
  559.  
  560. Plot[v[д[tt]], {tt, 0, TMax},
  561. Frame->True, PlotStyle->Orange, AspectRatio->1/5, ImagePadding->{{40, 10}, {20, 10}},
  562. ImageSize->600, PlotRange->{{0, TMax}, All}, GridLines->{{}, {0, 1}}, PlotLabel -> "v(t)"]
  563.  
  564. displayC[T_]:=Grid[{
  565. {s[" t doran"], " = ", s[n0[tk]], s["GM/c³"], s[dp]},
  566. {s[" t bookp"], " = ", s[n0[tcr[T]]], s["GM/c³"], s[dp]},
  567. {If[μ==0, s[" affineP"], s[" τ propr"]], " = ", s[n0[T]], s["GM/c³"], s[dp]},
  568. {s[" ṫ total"], " = ", s[n0[dt[T]]], s["dt/dτ"], s[dp]},
  569. {s[" ς gravt"], " = ", s[n0[ς[T]]], s["dt/dτ"], s[dp]},
  570. {s[" γ kinet"], " = ", s[n0[1/Sqrt[1-v[T]^2]]], s["dt/dτ"], s[dp]},
  571. {s[" R carts"], " = ", s[n0[XYZ[T]]], s["GM/c²"], s[dp]},
  572. {s[" x carts"], " = ", s[n0[X[T]]], s["GM/c²"], s[dp]},
  573. {s[" y carts"], " = ", s[n0[Y[T]]], s["GM/c²"], s[dp]},
  574. {s[" z carts"], " = ", s[n0[Z[T]]], s["GM/c²"], s[dp]},
  575.  
  576. {s[" r coord"], " = ", s[n0[R[T]]], s["GM/c²"], s[dp]},
  577. {s[" φ longd"], " = ", s[n0[Φ[T] 180/π]], s["deg"], s[dp]},
  578. {s[" θ lattd"], " = ", s[n0[Θ[T] 180/π]], s["deg"], s[dp]},
  579. {s[" d¹r/dτ¹"], " = ", s[n0[R'[T]]], s["c"], s[dp]},
  580. {s[" d¹φ/dτ¹"], " = ", s[n0[Φ'[T]]], s["c\.b3/G/M"], s[dp]},
  581. {s[" d¹θ/dτ¹"], " = ", s[n0[Θ'[T]]], s["c\.b3/G/M"], s[dp]},
  582. {s[" d\.b2r/dτ\.b2"], " = ", s[n0[R''[T]]], s["c⁴/G/M"], s[dp]},
  583. {s[" d\.b2φ/dτ\.b2"], " = ", s[n0[Φ''[T]]], s["c⁶/G\.b2/M\.b2"], s[dp]},
  584. {s[" d\.b2θ/dτ\.b2"], " = ", s[n0[Θ''[T]]], s["c⁶/G\.b2/M\.b2"], s[dp]},
  585. {s[" a SpinP"], " = ", s[n0[a]], s["GM²/c"], s[dp]},
  586.  
  587. {s[" ℧ cntrl"], " = ", s[n0[℧]], s["Q/M"], s[dp]},
  588. {s[" q prtcl"], " = ", s[n0[q]], s["q/m"], s[dp]},
  589. {s[" M irred"], " = ", s[N[mirr]], s["M"], s[dp]},
  590. {s[" E kinet"], " = ", s[n0[ekin[T]]], s["mc²"], s[dp]},
  591. {s[" E poten"], " = ", s[n0[epot[T]]], s["mc²"], s[dp]},
  592. {s[" E total"], " = ", s[n0[ε]], s["mc²"], s[dp]},
  593. {s[" CarterQ"], " = ", s[n0[Qk]], s["GMm/c"], s[dp]},
  594. {s[" L axial"], " = ", s[n0[Lz]], s["GMm/c"], s[dp]},
  595. {s[" L polar"], " = ", s[n0[pΘ[T]]], s["GMm/c"], s[dp]},
  596. {s[" g acclr"], " = ", s[n0[v'[T]]], s["c⁴/G/M"], s[dp]},
  597.  
  598. {s[" ω fdrag"], " = ", s[n0[Abs[ω[T]]]], s["c³/G/M"], s[dp]},
  599. {s[" v fdrag"], " = ", s[n0[Abs[й[T]]]], s["c"], s[dp]},
  600. {s[" Ω fdrag"], " = ", s[n0[Abs[Ω[T]]]], s["c"], s[dp]},
  601. {s[" v propr"], " = ", s[n0[v[T]/Sqrt[1-v[T]^2]]], s["c"], s[dp]},
  602. {s[" v escpe"], " = ", s[n0[ж[T]]], s["c"], s[dp]},
  603. {s[" v obsvd"], " = ", s[n0[ß[T]]], s["c"], s[dp]},
  604. {s[" v r,loc"], " = ", s[n0[vr[T]]], s["c"], s[dp]},
  605. {s[" v θ,loc"], " = ", s[n0[vθ[T]]], s["c"], s[dp]},
  606. {s[" v φ,loc"], " = ", s[n0[vφ[T]]], s["c"], s[dp]},
  607. {s[" v local"], " = ", s[n0[v[T]]], s["c"], s[dp]},
  608. {s[" "], s[" "], s[" "], s[" "]}},
  609. Alignment-> Left, Spacings-> {0, 0}];
  610.  
  611. plot1a[{xx_, yy_, zz_, tk_, w1_, w2_}]:= (* Animation *)
  612. Show[
  613.  
  614. Graphics3D[{
  615. {PointSize[0.011], Red, Point[
  616. Xyz[xyZ[{x[T], y[T], z[T]}, w1], w2]]}},
  617. ImageSize-> imgsize,
  618. PlotRange-> {
  619. {-(2 Sign[Abs[xx]]+1) PR, +(2 Sign[Abs[xx]]+1) PR},
  620. {-(2 Sign[Abs[yy]]+1) PR, +(2 Sign[Abs[yy]]+1) PR},
  621. {-(2 Sign[Abs[zz]]+1) PR, +(2 Sign[Abs[zz]]+1) PR}
  622. },
  623. SphericalRegion->False,
  624. ImagePadding-> 1],
  625.  
  626. horizons[A, None, w1, w2],
  627.  
  628. If[a==0, {}, ParametricPlot3D[
  629. Xyz[xyZ[{
  630. Sin[prm] a,
  631. Cos[prm] a,
  632. 0}, w1], w2],
  633. {prm, 0, 2π},
  634. PlotStyle -> {Thickness[0.005], Orange}]],
  635.  
  636. If[a==0, {},
  637. Graphics3D[{{PointSize[0.009], Purple, Point[
  638. Xyz[xyZ[{
  639. Sin[-φ0-ω0 tk+π/2] Sqrt[x0[A]^2+y0[A]^2],
  640. Cos[-φ0-ω0 tk+π/2] Sqrt[x0[A]^2+y0[A]^2],
  641. z0[A]}, w1], w2]]}}]],
  642.  
  643. If[tk==0, {}, If[a==0, {},
  644. ParametricPlot3D[
  645. Xyz[xyZ[{
  646. Sin[-φ0-ω0 tt+π/2] Sqrt[x0[A]^2+y0[A]^2],
  647. Cos[-φ0-ω0 tt+π/2] Sqrt[x0[A]^2+y0[A]^2],
  648. z0[A]}, w1], w2],
  649. {tt, Max[0, tk-1/2 π/ω0], tk},
  650. PlotStyle -> {Thickness[0.001], Dashed, Purple},
  651. PlotPoints-> Automatic,
  652. MaxRecursion-> mrec]]],
  653.  
  654. Block[{$RecursionLimit = Mrec},
  655. If[tk==0, {},
  656. ParametricPlot3D[
  657. Xyz[xyZ[{x[tt], y[tt], z[tt]}, w1], w2], {tt, If[TMax<0, Min[0, T+d1], Max[0, T-d1]], T},
  658. PlotStyle-> {Thickness[0.004]},
  659. ColorFunction-> Function[{x, y, z, t},
  660. Hue[0, 1, 0.5, If[TMax<0, Max[Min[(+T+(-t+d1))/d1, 1], 0]
  661. , Max[Min[(-T+(t+d1))/d1, 1], 0]]]],
  662. ColorFunctionScaling-> False,
  663. PlotPoints-> Automatic,
  664. MaxRecursion-> mrec]]],
  665.  
  666. If[tk==0, {},
  667. Block[{$RecursionLimit = Mrec},
  668. ParametricPlot3D[
  669. Xyz[xyZ[{x[tt], y[tt], z[tt]}, w1], w2],
  670. {tt, 0, If[Tmax<0, Min[-1*^-16, T+d1/3], Max[1*^-16, T-d1/3]]},
  671. PlotStyle-> {Thickness[0.004], Opacity[0.6], Darker[Gray]},
  672. PlotPoints-> Plp,
  673. MaxRecursion-> mrec]]],
  674.  
  675. ViewPoint-> {xx, yy, zz}];
  676.  
  677. Quiet[Do[
  678. Print[Rasterize[Grid[{{
  679. plot1a[{0, -Infinity, 0, tk, w1l, w2l}],
  680. plot1a[{0, 0, Infinity, tk, w1r, w2r}],
  681. displayC[Quiet[д[tk]]]
  682. }, {" ", " ", " "}
  683. }, Alignment->Left]]],
  684. {tk, 0, TMax, TMax/1}]]
  685.  
  686. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  687. (* |||||||| 13) EXPORTOPTIONEN |||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  688. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  689.  
  690. (* Export als HTML Dokument *)
  691. (* Export["Y:\\export\\dateiname.html", EvaluationNotebook[], "GraphicsOutput" -> "PNG"] *)
  692. (* Export direkt als Bildsequenz *)
  693. (* Do[Export["Y:\\export\\dateiname" <> ToString[tk] <> ".png", Rasterize[...] *)
  694.  
  695. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
  696. (* |||||||||||| http://kerr.newman.yukerez.net ||||| Simon Tyran, Vienna |||||||||||||||| *)
  697. (* |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| *)
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