(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 976682, 25312]*) (*NotebookOutlinePosition[ 977843, 25350]*) (* CellTagsIndexPosition[ 977752, 25344]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[ \($DebugCelleratorLoad = False\)], "Input"], Cell[BoxData[ \(False\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(<< cellerator.m\)], "Input"], Cell[BoxData[ \("Cellerator\[Trademark] Version 2.0313, loaded at Mar. 13, 2002, \ 13:47:08\n\[Copyright]2001,2002 Jet Propulsion Laboratory, California \ Institute of Technology. U.S. Government Sponsorhip Acknowledged. All rights \ reserved. Patent Pending.\nPlease no not distribute, copy, or transfer.\n\n\ Cellerator\[Trademark] now incorporates Graphelator\[Trademark]!\n\n\ $CelleratorOutputDirectory = New Team Rocket:Applications (Mac OS \ 9):Mathematica 4.1 Files"\)], "Print"], Cell[BoxData[ InterpretationBox[\("Protected symbols: "\[InvisibleSpace]{"odes", "rules", "rateConstants", "x", "y", "z", "nodes"}\), SequenceForm[ "Protected symbols: ", {"odes", "rules", "rateConstants", "x", "y", "z", "nodes"}], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox[\("Cellerator\[Trademark] 2.0313 load complete. "\ \[InvisibleSpace]"March 13, 2002 13:47:12"\), SequenceForm[ "Cellerator\[Trademark] 2.0313 load complete. ", "March 13, 2002 13:47:12"], Editable->False]], "Print"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(?mitoticOscillator\)\)], "Input"], Cell[BoxData["\<\"mitoticOscillator is an option for \!\(\* \ StyleBox[\\\"organism\\\",\\nFontWeight->\\\"Plain\\\"]\) and \!\(\* \ StyleBox[\\\"standardNode\\\",\\nFontWeight->\\\"Plain\\\"]\) that indicates \ which mitotitic oscillator should be used. The option should be used as \ mitoticOscillator\[Rule]{option\[Rule]value,option\[Rule]value,...}. \\n\\n\!\ \(\* StyleBox[\\\"Valid\\\",\\nFontVariations->{\\\"Underline\\\"->True}]\)\!\ \(\* StyleBox[\\\" \\\",\\nFontVariations->{\\\"Underline\\\"->True}]\)\!\(\* \ StyleBox[\\\"options\\\",\\nFontVariations->{\\\"Underline\\\"->True}]\)\!\(\*\ StyleBox[\\\" \\\",\\nFontVariations->{\\\"Underline\\\"->True}]\)\!\(\* \ StyleBox[\\\"are\\\",\\nFontVariations->{\\\"Underline\\\"->True}]\)\!\(\* \ StyleBox[\\\":\\\",\\nFontVariations->{\\\"Underline\\\"->True}]\)\\nname\ \[Rule]Goldbeter,Tyson2, Tyson6, Norel- select which model to use\\nthreshold\ \[Rule]see model defaults\!\(\* StyleBox[\\\" \ \\\",\\nFontSlant->\\\"Italic\\\"]\)- threshold to use to indicate cell \ division\\nthresholdVariable\[Rule]variablename - name of variable in the \ model to test against threshold (under construction)\\ninitialConditions\ \[Rule]see model defaults - initial conditions to use for the model variables\ \\nvariables\[Rule]see model defaults - names of model variables to use\\n\\n\ \!\(\* \ StyleBox[\\\"Specific\\\",\\nFontVariations->{\\\"Underline\\\"->True}]\)\!\(\ \* StyleBox[\\\" \\\",\\nFontVariations->{\\\"Underline\\\"->True}]\)\!\(\ \* StyleBox[\\\"model\\\",\\nFontVariations->{\\\"Underline\\\"->True}]\)\ \!\(\* StyleBox[\\\" \\\",\\nFontVariations->{\\\"Underline\\\"->True}]\)\ \!\(\* \ StyleBox[\\\"defaults\\\",\\nFontVariations->{\\\"Underline\\\"->True}]\)\!\(\ \* StyleBox[\\\" \\\",\\nFontVariations->{\\\"Underline\\\"->True}]\)\!\(\ \* StyleBox[\\\"and\\\",\\nFontVariations->{\\\"Underline\\\"->True}]\)\!\ \(\* StyleBox[\\\" \\\",\\nFontVariations->{\\\"Underline\\\"->True}]\)\!\ \(\* StyleBox[\\\"options\\\",\\nFontVariations->{\\\"Underline\\\"->True}\ ]\)\!\(\* \ StyleBox[\\\":\\\",\\nFontVariations->{\\\"Underline\\\"->True}]\)\\nGardner: \ under development. Reference: T. S. Gardner et. al., PNAS 95:14190 \ (1998).\\nGoldbeter: variables\[Rule]{C,M,X}, thresholdVariable\[Rule]M, \ threshold\[Rule]0.7, initialConditions\[Rule]{Random[0,0.3],0,0},rate\[Rule]1 \ (period is approximately 20/rate). Reference: A. Goldbeter, PNAS, 88:9107 \ (1991). \\nNorel: under development. {saturating\[RightArrow]True, \ e\[Rule]3.5, f\[Rule]1, g\[Rule]10, i\[Rule]1.2}. Reference: R. Norel and Z. \ Agur, Science, 251:1076 (1991).\\nTyson, Tyson2, or Tyson2Variable: variables\ \[Rule]{pMPF,aMPF}, thresholdVariable\[Rule]aMPF, threshold\[Rule]0.1, \ initialConditions{Random[0,0.3}, 0}, rate\[Rule]1,\[Kappa]\[Rule]0.015,k6\ \[Rule]1,k4\[Rule] 180,\[Alpha]\[Rule](0.018/180). Reference: J. J. Tyson, \ PNAS, 88:7328 (1991). aMPF is the same as \!\(\* \ StyleBox[\\\"u\\\",\\nFontFamily->\\\"Times\\\",\\nFontSlant->\\\"Italic\\\"]\ \) in the paper, and pMPF is the same as the difference \!\(\* \ StyleBox[\\\"z\\\",\\nFontFamily->\\\"Times\\\",\\nFontSlant->\\\"Italic\\\"]\ \)\!\(\* StyleBox[\\\"=\\\",\\nFontFamily->\\\"Times\\\",\\nFontSlant->\\\ \"Italic\\\"]\)\!\(\* \ StyleBox[\\\"v\\\",\\nFontFamily->\\\"Times\\\",\\nFontSlant->\\\"Italic\\\"]\ \)\!\(\* StyleBox[\\\"-\\\",\\nFontFamily->\\\"Times\\\",\\nFontSlant->\\\ \"Italic\\\"]\)\!\(\* \ StyleBox[\\\"u\\\",\\nFontFamily->\\\"Times\\\",\\nFontSlant->\\\"Italic\\\"]\ \)\!\(\* StyleBox[\\\",\\\",\\nFontFamily->\\\"Times\\\",\\nFontSlant->\\\ \"Italic\\\"]\)\!\(\* StyleBox[\\\" \ \\\",\\nFontFamily->\\\"Times\\\",\\nFontSlant->\\\"Italic\\\"]\)where\!\(\* \ StyleBox[\\\" \\\",\\nFontFamily->\\\"Times\\\",\\nFontSlant->\\\"Italic\\\ \"]\)\!\(\* \ StyleBox[\\\"v\\\",\\nFontFamily->\\\"Times\\\",\\nFontSlant->\\\"Italic\\\"]\ \)\!\(\* StyleBox[\\\" \\\",\\nFontFamily->\\\"Times\\\",\\nFontSlant->\\\ \"Italic\\\"]\)and\!\(\* StyleBox[\\\" \\\",\\nFontFamily->\\\"Times\\\",\ \\nFontSlant->\\\"Italic\\\"]\)\!\(\* \ StyleBox[\\\"u\\\",\\nFontFamily->\\\"Times\\\",\\nFontSlant->\\\"Italic\\\"]\ \)\!\(\* StyleBox[\\\" \\\",\\nFontFamily->\\\"Times\\\",\\nFontSlant->\\\ \"Italic\\\"]\)are as defined\!\(\* StyleBox[\\\" \ \\\",\\nFontSlant->\\\"Italic\\\"]\)\!\(\* StyleBox[\\\" \ \\\",\\nFontSlant->\\\"Plain\\\"]\)in the paper. \\nTyson6 or Tyson6Variable: \ variables\[Rule]{C2,CP,M,pM,Y,YP}, initialConditions-> {0, Random[0,0.3], \ 0,0,0,0}, k1aa\[Rule] .015,k2\[Rule] 0, k3\[Rule] 200, k4\[Rule] 180, k4prime\ \[Rule] 0.018, k5notP\[Rule] 0, k6\[Rule] 1, k7\[Rule] 0.6, \ k8notP\[Rule]10^6, k9\[Rule] 1000}Reference: J. J. Tyson, PNAS, 88:7328 \ (1991) (same paper as 2-variable)\"\>"], "Print", CellTags->"Info3225016037-2298124"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(q = organism[embeddings \[Rule] \ {{1, 0}, {0, 1}, {\(-1\), 0}, {\(-1\), \(-1\)}, \ {0, \(-1\)}, \ {1, \(-1\)}}, links \[Rule] \ {{1, 2}, {2, 3}, {3, 4}, \ {4, 5}, {5, 6}, {6, 1}}, force \[Rule] \ True, \ \[IndentingNewLine]mitoticOscillator \[Rule] \ {name \ \[Rule] \ Norel, rate \[Rule] .1}, stats \[Rule] \ True, species \[Rule] \ {PA, PB, PC}]\)], "Input"], Cell[BoxData[ InterpretationBox[\("Mitotic Oscillator: Norel & Agur 1991 Two-variable \ model, Variables = "\[InvisibleSpace]{C, M}\[InvisibleSpace]" initial conditions = "\[InvisibleSpace]{Hold[ Random[Real, {0, 1}]], 0.4`}\[InvisibleSpace]", threshold = "\[InvisibleSpace]"M"\ \[InvisibleSpace]" \[GreaterEqual] "\[InvisibleSpace]4\), SequenceForm[ "Mitotic Oscillator: Norel & Agur 1991 Two-variable model, Variables = \ ", {C, M}, " initial conditions = ", { Hold[ Random[ Real, {0, 1}]], 0.40000000000000002}, ", threshold = ", "M", " \[GreaterEqual] ", 4], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox[\(" WARNING: "\[InvisibleSpace]"organism"\ \[InvisibleSpace]": "\[InvisibleSpace]"links are assumed to be undirected; to \ force directed links use directed\[Rule]True"\), SequenceForm[ " WARNING: ", "organism", ": ", "links are assumed to be undirected; to force directed links use \ directed\[Rule]True"], Editable->False]], "Print"], Cell[BoxData[ \("Calculating spring force ..."\)], "Print"], Cell[BoxData[ InterpretationBox[\("Graph Statistics:\n\t"\[InvisibleSpace]6\ \[InvisibleSpace]" nodes\n\t"\[InvisibleSpace]12\[InvisibleSpace]" links\n\t"\ \[InvisibleSpace]66\[InvisibleSpace]" ODEs\n\t\ "\[InvisibleSpace]2.633333333333333`\[InvisibleSpace]" sec. total CPU \ utilization. ("\[InvisibleSpace]1.3666666666666671`\[InvisibleSpace]" sec. \ for force calculation) "\[InvisibleSpace]"Mar. 13, 2002, 13:47:22"\), SequenceForm[ "Graph Statistics:\n\t", 6, " nodes\n\t", 12, " links\n\t", 66, " ODEs\n\t", 2.6333333333333329, " sec. total CPU utilization. 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\(M[4]\)[t]\)\/\(1 + \ \(M[4]\)[t]\))\)\)}]}, {"11", \(M[5]\), \(\(M[5]\)[0] == 0.4`\), RowBox[{ RowBox[{ SuperscriptBox[\(M[5]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(0.1`\ \((3.5`\ \(C[5]\)[t] + \(C[5]\)[ t]\ \(M[5]\)[t]\^2 - \(10\ \(M[5]\)[t]\)\/\(1 + \ \(M[5]\)[t]\))\)\)}]}, {"12", \(M[6]\), \(\(M[6]\)[0] == 0.4`\), RowBox[{ RowBox[{ SuperscriptBox[\(M[6]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(0.1`\ \((3.5`\ \(C[6]\)[t] + \(C[6]\)[ t]\ \(M[6]\)[t]\^2 - \(10\ \(M[6]\)[t]\)\/\(1 + \ \(M[6]\)[t]\))\)\)}]}, {"13", \(mass[1]\), \(\(mass[1]\)[0] == 1\), RowBox[{ RowBox[{ SuperscriptBox[\(mass[1]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(mu\ \(mass[1]\)[t]\)}]}, {"14", \(mass[2]\), \(\(mass[2]\)[0] == 1\), RowBox[{ RowBox[{ SuperscriptBox[\(mass[2]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(mu\ \(mass[2]\)[t]\)}]}, {"15", \(mass[3]\), \(\(mass[3]\)[0] == 1\), RowBox[{ RowBox[{ SuperscriptBox[\(mass[3]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(mu\ \(mass[3]\)[t]\)}]}, {"16", \(mass[4]\), \(\(mass[4]\)[0] == 1\), RowBox[{ RowBox[{ SuperscriptBox[\(mass[4]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(mu\ \(mass[4]\)[t]\)}]}, {"17", \(mass[5]\), \(\(mass[5]\)[0] == 1\), RowBox[{ RowBox[{ SuperscriptBox[\(mass[5]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(mu\ \(mass[5]\)[t]\)}]}, {"18", \(mass[6]\), \(\(mass[6]\)[0] == 1\), RowBox[{ RowBox[{ SuperscriptBox[\(mass[6]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(mu\ \(mass[6]\)[t]\)}]}, {"19", \(PA[1]\), \(\(PA[1]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PA[1]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"20", \(PA[2]\), \(\(PA[2]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PA[2]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"21", \(PA[3]\), \(\(PA[3]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PA[3]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"22", \(PA[4]\), \(\(PA[4]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PA[4]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"23", \(PA[5]\), \(\(PA[5]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PA[5]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"24", \(PA[6]\), \(\(PA[6]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PA[6]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"25", \(PB[1]\), \(\(PB[1]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PB[1]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"26", \(PB[2]\), \(\(PB[2]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PB[2]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"27", \(PB[3]\), \(\(PB[3]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PB[3]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"28", \(PB[4]\), \(\(PB[4]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PB[4]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"29", \(PB[5]\), \(\(PB[5]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PB[5]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"30", \(PB[6]\), \(\(PB[6]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PB[6]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"31", \(PC[1]\), \(\(PC[1]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PC[1]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"32", \(PC[2]\), \(\(PC[2]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PC[2]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"33", \(PC[3]\), \(\(PC[3]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PC[3]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"34", \(PC[4]\), \(\(PC[4]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PC[4]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"35", \(PC[5]\), \(\(PC[5]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PC[5]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"36", \(PC[6]\), \(\(PC[6]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(PC[6]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", "0"}]}, {"37", \(splv[1]\), \(\(splv[1]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(splv[1]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(UnitStep[\(-4\) + \(M[1]\)[t]]\)}]}, {"38", \(splv[2]\), \(\(splv[2]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(splv[2]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(UnitStep[\(-4\) + \(M[2]\)[t]]\)}]}, {"39", \(splv[3]\), \(\(splv[3]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(splv[3]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(UnitStep[\(-4\) + \(M[3]\)[t]]\)}]}, {"40", \(splv[4]\), \(\(splv[4]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(splv[4]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(UnitStep[\(-4\) + \(M[4]\)[t]]\)}]}, {"41", \(splv[5]\), \(\(splv[5]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(splv[5]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(UnitStep[\(-4\) + \(M[5]\)[t]]\)}]}, {"42", \(splv[6]\), \(\(splv[6]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(splv[6]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(UnitStep[\(-4\) + \(M[6]\)[t]]\)}]}, {"43", \(tspl[1]\), \(\(tspl[1]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(tspl[1]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(UnitStep[\(-1.`*^-8\) + \(splv[1]\)[t]]\)}]}, {"44", \(tspl[2]\), \(\(tspl[2]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(tspl[2]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(UnitStep[\(-1.`*^-8\) + \(splv[2]\)[t]]\)}]}, {"45", \(tspl[3]\), \(\(tspl[3]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(tspl[3]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(UnitStep[\(-1.`*^-8\) + \(splv[3]\)[t]]\)}]}, {"46", \(tspl[4]\), \(\(tspl[4]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(tspl[4]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(UnitStep[\(-1.`*^-8\) + \(splv[4]\)[t]]\)}]}, {"47", \(tspl[5]\), \(\(tspl[5]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(tspl[5]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(UnitStep[\(-1.`*^-8\) + \(splv[5]\)[t]]\)}]}, {"48", \(tspl[6]\), \(\(tspl[6]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(tspl[6]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(UnitStep[\(-1.`*^-8\) + \(splv[6]\)[t]]\)}]}, {"49", \(x[1]\), \(\(x[1]\)[0] == 1\), RowBox[{ RowBox[{ SuperscriptBox[\(x[1]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[1]\ \((\(-\(x[1]\)[t]\) + \(x[2]\)[t])\)\ \ \((\(-\(\(\(mass[1]\)[t]\^\(1/3\) + \(mass[2]\)[t]\^\(1/3\)\)\/\@2\)\) + \@\(\ \((\(-\(x[1]\)[t]\) + \(x[2]\)[t])\)\^2 + \((\(-\(y[1]\)[t]\) + \ \(y[2]\)[t])\)\^2 + \((\(-\(z[1]\)[t]\) + \ \(z[2]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[1]\)[t]\) + \(x[2]\)[t])\)\^2 + \ \((\(-\(y[1]\)[t]\) + \(y[2]\)[t])\)\^2 + \((\(-\(z[1]\)[t]\) + \ \(z[2]\)[t])\)\^2\) + \(k[2]\ \((\(-\(x[1]\)[t]\) + \(x[6]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[1]\)[t]\^\(1/3\)\) - \(mass[6]\)[t]\^\(1/3\))\) + \ \@\(\((\(-\(x[1]\)[t]\) + \(x[6]\)[t])\)\^2 + \((\(-\(y[1]\)[t]\) + \ \(y[6]\)[t])\)\^2 + \((\(-\(z[1]\)[t]\) + \ \(z[6]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[1]\)[t]\) + \(x[6]\)[t])\)\^2 + \ \((\(-\(y[1]\)[t]\) + \(y[6]\)[t])\)\^2 + \((\(-\(z[1]\)[t]\) + \ \(z[6]\)[t])\)\^2\)\)}]}, {"50", \(x[2]\), \(\(x[2]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(x[2]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[3]\ \((\(x[1]\)[t] - \(x[2]\)[t])\)\ \ \((\(-\(\(\(mass[1]\)[t]\^\(1/3\) + \(mass[2]\)[t]\^\(1/3\)\)\/\@2\)\) + \@\(\ \((\(x[1]\)[t] - \(x[2]\)[t])\)\^2 + \((\(y[1]\)[t] - \(y[2]\)[t])\)\^2 + \((\ \(z[1]\)[t] - \(z[2]\)[t])\)\^2\))\)\)\/\@\(\((\(x[1]\)[t] - \ \(x[2]\)[t])\)\^2 + \((\(y[1]\)[t] - \(y[2]\)[t])\)\^2 + \((\(z[1]\)[t] - \ \(z[2]\)[t])\)\^2\) + \(k[4]\ \((\(-\(x[2]\)[t]\) + \(x[3]\)[t])\)\ \ \((\(-\(\(\(mass[2]\)[t]\^\(1/3\) + \(mass[3]\)[t]\^\(1/3\)\)\/\@2\)\) + \@\(\ \((\(-\(x[2]\)[t]\) + \(x[3]\)[t])\)\^2 + \((\(-\(y[2]\)[t]\) + \ \(y[3]\)[t])\)\^2 + \((\(-\(z[2]\)[t]\) + \ \(z[3]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[2]\)[t]\) + \(x[3]\)[t])\)\^2 + \ \((\(-\(y[2]\)[t]\) + \(y[3]\)[t])\)\^2 + \((\(-\(z[2]\)[t]\) + \ \(z[3]\)[t])\)\^2\)\)}]}, {"51", \(x[3]\), \(\(x[3]\)[0] == \(-1\)\), RowBox[{ RowBox[{ SuperscriptBox[\(x[3]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[5]\ \((\(x[2]\)[t] - \(x[3]\)[t])\)\ \ \((\(-\(\(\(mass[2]\)[t]\^\(1/3\) + \(mass[3]\)[t]\^\(1/3\)\)\/\@2\)\) + \@\(\ \((\(x[2]\)[t] - \(x[3]\)[t])\)\^2 + \((\(y[2]\)[t] - \(y[3]\)[t])\)\^2 + \((\ \(z[2]\)[t] - \(z[3]\)[t])\)\^2\))\)\)\/\@\(\((\(x[2]\)[t] - \ \(x[3]\)[t])\)\^2 + \((\(y[2]\)[t] - \(y[3]\)[t])\)\^2 + \((\(z[2]\)[t] - \ \(z[3]\)[t])\)\^2\) + \(k[6]\ \((\(-\(x[3]\)[t]\) + \(x[4]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[3]\)[t]\^\(1/3\)\) - \(mass[4]\)[t]\^\(1/3\))\) + \ \@\(\((\(-\(x[3]\)[t]\) + \(x[4]\)[t])\)\^2 + \((\(-\(y[3]\)[t]\) + \ \(y[4]\)[t])\)\^2 + \((\(-\(z[3]\)[t]\) + \ \(z[4]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[3]\)[t]\) + \(x[4]\)[t])\)\^2 + \ \((\(-\(y[3]\)[t]\) + \(y[4]\)[t])\)\^2 + \((\(-\(z[3]\)[t]\) + \ \(z[4]\)[t])\)\^2\)\)}]}, {"52", \(x[4]\), \(\(x[4]\)[0] == \(-1\)\), RowBox[{ RowBox[{ SuperscriptBox[\(x[4]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[7]\ \((\(x[3]\)[t] - \(x[4]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[3]\)[t]\^\(1/3\)\) - \(mass[4]\)[t]\^\(1/3\))\) + \ \@\(\((\(x[3]\)[t] - \(x[4]\)[t])\)\^2 + \((\(y[3]\)[t] - \(y[4]\)[t])\)\^2 + \ \((\(z[3]\)[t] - \(z[4]\)[t])\)\^2\))\)\)\/\@\(\((\(x[3]\)[t] - \ \(x[4]\)[t])\)\^2 + \((\(y[3]\)[t] - \(y[4]\)[t])\)\^2 + \((\(z[3]\)[t] - \ \(z[4]\)[t])\)\^2\) + \(k[8]\ \((\(-\(x[4]\)[t]\) + \(x[5]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[4]\)[t]\^\(1/3\)\) - \(mass[5]\)[t]\^\(1/3\))\) + \ \@\(\((\(-\(x[4]\)[t]\) + \(x[5]\)[t])\)\^2 + \((\(-\(y[4]\)[t]\) + \ \(y[5]\)[t])\)\^2 + \((\(-\(z[4]\)[t]\) + \ \(z[5]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[4]\)[t]\) + \(x[5]\)[t])\)\^2 + \ \((\(-\(y[4]\)[t]\) + \(y[5]\)[t])\)\^2 + \((\(-\(z[4]\)[t]\) + \ \(z[5]\)[t])\)\^2\)\)}]}, {"53", \(x[5]\), \(\(x[5]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(x[5]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[9]\ \((\(x[4]\)[t] - \(x[5]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[4]\)[t]\^\(1/3\)\) - \(mass[5]\)[t]\^\(1/3\))\) + \ \@\(\((\(x[4]\)[t] - \(x[5]\)[t])\)\^2 + \((\(y[4]\)[t] - \(y[5]\)[t])\)\^2 + \ \((\(z[4]\)[t] - \(z[5]\)[t])\)\^2\))\)\)\/\@\(\((\(x[4]\)[t] - \ \(x[5]\)[t])\)\^2 + \((\(y[4]\)[t] - \(y[5]\)[t])\)\^2 + \((\(z[4]\)[t] - \ \(z[5]\)[t])\)\^2\) + \(k[10]\ \((\(-\(x[5]\)[t]\) + \(x[6]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[5]\)[t]\^\(1/3\)\) - \(mass[6]\)[t]\^\(1/3\))\) + \ \@\(\((\(-\(x[5]\)[t]\) + \(x[6]\)[t])\)\^2 + \((\(-\(y[5]\)[t]\) + \ \(y[6]\)[t])\)\^2 + \((\(-\(z[5]\)[t]\) + \ \(z[6]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[5]\)[t]\) + \(x[6]\)[t])\)\^2 + \ \((\(-\(y[5]\)[t]\) + \(y[6]\)[t])\)\^2 + \((\(-\(z[5]\)[t]\) + \ \(z[6]\)[t])\)\^2\)\)}]}, {"54", \(x[6]\), \(\(x[6]\)[0] == 1\), RowBox[{ RowBox[{ SuperscriptBox[\(x[6]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[11]\ \((\(x[1]\)[t] - \(x[6]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[1]\)[t]\^\(1/3\)\) - \(mass[6]\)[t]\^\(1/3\))\) + \ \@\(\((\(x[1]\)[t] - \(x[6]\)[t])\)\^2 + \((\(y[1]\)[t] - \(y[6]\)[t])\)\^2 + \ \((\(z[1]\)[t] - \(z[6]\)[t])\)\^2\))\)\)\/\@\(\((\(x[1]\)[t] - \ \(x[6]\)[t])\)\^2 + \((\(y[1]\)[t] - \(y[6]\)[t])\)\^2 + \((\(z[1]\)[t] - \ \(z[6]\)[t])\)\^2\) + \(k[12]\ \((\(x[5]\)[t] - \(x[6]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[5]\)[t]\^\(1/3\)\) - \(mass[6]\)[t]\^\(1/3\))\) + \ \@\(\((\(x[5]\)[t] - \(x[6]\)[t])\)\^2 + \((\(y[5]\)[t] - \(y[6]\)[t])\)\^2 + \ \((\(z[5]\)[t] - \(z[6]\)[t])\)\^2\))\)\)\/\@\(\((\(x[5]\)[t] - \ \(x[6]\)[t])\)\^2 + \((\(y[5]\)[t] - \(y[6]\)[t])\)\^2 + \((\(z[5]\)[t] - \ \(z[6]\)[t])\)\^2\)\)}]}, {"55", \(y[1]\), \(\(y[1]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(y[1]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[1]\ \((\(-\(y[1]\)[t]\) + \(y[2]\)[t])\)\ \ \((\(-\(\(\(mass[1]\)[t]\^\(1/3\) + \(mass[2]\)[t]\^\(1/3\)\)\/\@2\)\) + \@\(\ \((\(-\(x[1]\)[t]\) + \(x[2]\)[t])\)\^2 + \((\(-\(y[1]\)[t]\) + \ \(y[2]\)[t])\)\^2 + \((\(-\(z[1]\)[t]\) + \ \(z[2]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[1]\)[t]\) + \(x[2]\)[t])\)\^2 + \ \((\(-\(y[1]\)[t]\) + \(y[2]\)[t])\)\^2 + \((\(-\(z[1]\)[t]\) + \ \(z[2]\)[t])\)\^2\) + \(k[2]\ \((\(-\(y[1]\)[t]\) + \(y[6]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[1]\)[t]\^\(1/3\)\) - \(mass[6]\)[t]\^\(1/3\))\) + \ \@\(\((\(-\(x[1]\)[t]\) + \(x[6]\)[t])\)\^2 + \((\(-\(y[1]\)[t]\) + \ \(y[6]\)[t])\)\^2 + \((\(-\(z[1]\)[t]\) + \ \(z[6]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[1]\)[t]\) + \(x[6]\)[t])\)\^2 + \ \((\(-\(y[1]\)[t]\) + \(y[6]\)[t])\)\^2 + \((\(-\(z[1]\)[t]\) + \ \(z[6]\)[t])\)\^2\)\)}]}, {"56", \(y[2]\), \(\(y[2]\)[0] == 1\), RowBox[{ RowBox[{ SuperscriptBox[\(y[2]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[3]\ \((\(y[1]\)[t] - \(y[2]\)[t])\)\ \ \((\(-\(\(\(mass[1]\)[t]\^\(1/3\) + \(mass[2]\)[t]\^\(1/3\)\)\/\@2\)\) + \@\(\ \((\(x[1]\)[t] - \(x[2]\)[t])\)\^2 + \((\(y[1]\)[t] - \(y[2]\)[t])\)\^2 + \((\ \(z[1]\)[t] - \(z[2]\)[t])\)\^2\))\)\)\/\@\(\((\(x[1]\)[t] - \ \(x[2]\)[t])\)\^2 + \((\(y[1]\)[t] - \(y[2]\)[t])\)\^2 + \((\(z[1]\)[t] - \ \(z[2]\)[t])\)\^2\) + \(k[4]\ \((\(-\(y[2]\)[t]\) + \(y[3]\)[t])\)\ \ \((\(-\(\(\(mass[2]\)[t]\^\(1/3\) + \(mass[3]\)[t]\^\(1/3\)\)\/\@2\)\) + \@\(\ \((\(-\(x[2]\)[t]\) + \(x[3]\)[t])\)\^2 + \((\(-\(y[2]\)[t]\) + \ \(y[3]\)[t])\)\^2 + \((\(-\(z[2]\)[t]\) + \ \(z[3]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[2]\)[t]\) + \(x[3]\)[t])\)\^2 + \ \((\(-\(y[2]\)[t]\) + \(y[3]\)[t])\)\^2 + \((\(-\(z[2]\)[t]\) + \ \(z[3]\)[t])\)\^2\)\)}]}, {"57", \(y[3]\), \(\(y[3]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(y[3]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[5]\ \((\(y[2]\)[t] - \(y[3]\)[t])\)\ \ \((\(-\(\(\(mass[2]\)[t]\^\(1/3\) + \(mass[3]\)[t]\^\(1/3\)\)\/\@2\)\) + \@\(\ \((\(x[2]\)[t] - \(x[3]\)[t])\)\^2 + \((\(y[2]\)[t] - \(y[3]\)[t])\)\^2 + \((\ \(z[2]\)[t] - \(z[3]\)[t])\)\^2\))\)\)\/\@\(\((\(x[2]\)[t] - \ \(x[3]\)[t])\)\^2 + \((\(y[2]\)[t] - \(y[3]\)[t])\)\^2 + \((\(z[2]\)[t] - \ \(z[3]\)[t])\)\^2\) + \(k[6]\ \((\(-\(y[3]\)[t]\) + \(y[4]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[3]\)[t]\^\(1/3\)\) - \(mass[4]\)[t]\^\(1/3\))\) + \ \@\(\((\(-\(x[3]\)[t]\) + \(x[4]\)[t])\)\^2 + \((\(-\(y[3]\)[t]\) + \ \(y[4]\)[t])\)\^2 + \((\(-\(z[3]\)[t]\) + \ \(z[4]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[3]\)[t]\) + \(x[4]\)[t])\)\^2 + \ \((\(-\(y[3]\)[t]\) + \(y[4]\)[t])\)\^2 + \((\(-\(z[3]\)[t]\) + \ \(z[4]\)[t])\)\^2\)\)}]}, {"58", \(y[4]\), \(\(y[4]\)[0] == \(-1\)\), RowBox[{ RowBox[{ SuperscriptBox[\(y[4]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[7]\ \((\(y[3]\)[t] - \(y[4]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[3]\)[t]\^\(1/3\)\) - \(mass[4]\)[t]\^\(1/3\))\) + \ \@\(\((\(x[3]\)[t] - \(x[4]\)[t])\)\^2 + \((\(y[3]\)[t] - \(y[4]\)[t])\)\^2 + \ \((\(z[3]\)[t] - \(z[4]\)[t])\)\^2\))\)\)\/\@\(\((\(x[3]\)[t] - \ \(x[4]\)[t])\)\^2 + \((\(y[3]\)[t] - \(y[4]\)[t])\)\^2 + \((\(z[3]\)[t] - \ \(z[4]\)[t])\)\^2\) + \(k[8]\ \((\(-\(y[4]\)[t]\) + \(y[5]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[4]\)[t]\^\(1/3\)\) - \(mass[5]\)[t]\^\(1/3\))\) + \ \@\(\((\(-\(x[4]\)[t]\) + \(x[5]\)[t])\)\^2 + \((\(-\(y[4]\)[t]\) + \ \(y[5]\)[t])\)\^2 + \((\(-\(z[4]\)[t]\) + \ \(z[5]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[4]\)[t]\) + \(x[5]\)[t])\)\^2 + \ \((\(-\(y[4]\)[t]\) + \(y[5]\)[t])\)\^2 + \((\(-\(z[4]\)[t]\) + \ \(z[5]\)[t])\)\^2\)\)}]}, {"59", \(y[5]\), \(\(y[5]\)[0] == \(-1\)\), RowBox[{ RowBox[{ SuperscriptBox[\(y[5]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[9]\ \((\(y[4]\)[t] - \(y[5]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[4]\)[t]\^\(1/3\)\) - \(mass[5]\)[t]\^\(1/3\))\) + \ \@\(\((\(x[4]\)[t] - \(x[5]\)[t])\)\^2 + \((\(y[4]\)[t] - \(y[5]\)[t])\)\^2 + \ \((\(z[4]\)[t] - \(z[5]\)[t])\)\^2\))\)\)\/\@\(\((\(x[4]\)[t] - \ \(x[5]\)[t])\)\^2 + \((\(y[4]\)[t] - \(y[5]\)[t])\)\^2 + \((\(z[4]\)[t] - \ \(z[5]\)[t])\)\^2\) + \(k[10]\ \((\(-\(y[5]\)[t]\) + \(y[6]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[5]\)[t]\^\(1/3\)\) - \(mass[6]\)[t]\^\(1/3\))\) + \ \@\(\((\(-\(x[5]\)[t]\) + \(x[6]\)[t])\)\^2 + \((\(-\(y[5]\)[t]\) + \ \(y[6]\)[t])\)\^2 + \((\(-\(z[5]\)[t]\) + \ \(z[6]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[5]\)[t]\) + \(x[6]\)[t])\)\^2 + \ \((\(-\(y[5]\)[t]\) + \(y[6]\)[t])\)\^2 + \((\(-\(z[5]\)[t]\) + \ \(z[6]\)[t])\)\^2\)\)}]}, {"60", \(y[6]\), \(\(y[6]\)[0] == \(-1\)\), RowBox[{ RowBox[{ SuperscriptBox[\(y[6]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[11]\ \((\(y[1]\)[t] - \(y[6]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[1]\)[t]\^\(1/3\)\) - \(mass[6]\)[t]\^\(1/3\))\) + \ \@\(\((\(x[1]\)[t] - \(x[6]\)[t])\)\^2 + \((\(y[1]\)[t] - \(y[6]\)[t])\)\^2 + \ \((\(z[1]\)[t] - \(z[6]\)[t])\)\^2\))\)\)\/\@\(\((\(x[1]\)[t] - \ \(x[6]\)[t])\)\^2 + \((\(y[1]\)[t] - \(y[6]\)[t])\)\^2 + \((\(z[1]\)[t] - \ \(z[6]\)[t])\)\^2\) + \(k[12]\ \((\(y[5]\)[t] - \(y[6]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[5]\)[t]\^\(1/3\)\) - \(mass[6]\)[t]\^\(1/3\))\) + \ \@\(\((\(x[5]\)[t] - \(x[6]\)[t])\)\^2 + \((\(y[5]\)[t] - \(y[6]\)[t])\)\^2 + \ \((\(z[5]\)[t] - \(z[6]\)[t])\)\^2\))\)\)\/\@\(\((\(x[5]\)[t] - \ \(x[6]\)[t])\)\^2 + \((\(y[5]\)[t] - \(y[6]\)[t])\)\^2 + \((\(z[5]\)[t] - \ \(z[6]\)[t])\)\^2\)\)}]}, {"61", \(z[1]\), \(\(z[1]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(z[1]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[1]\ \((\(-\(z[1]\)[t]\) + \(z[2]\)[t])\)\ \ \((\(-\(\(\(mass[1]\)[t]\^\(1/3\) + \(mass[2]\)[t]\^\(1/3\)\)\/\@2\)\) + \@\(\ \((\(-\(x[1]\)[t]\) + \(x[2]\)[t])\)\^2 + \((\(-\(y[1]\)[t]\) + \ \(y[2]\)[t])\)\^2 + \((\(-\(z[1]\)[t]\) + \ \(z[2]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[1]\)[t]\) + \(x[2]\)[t])\)\^2 + \ \((\(-\(y[1]\)[t]\) + \(y[2]\)[t])\)\^2 + \((\(-\(z[1]\)[t]\) + \ \(z[2]\)[t])\)\^2\) + \(k[2]\ \((\(-\(z[1]\)[t]\) + \(z[6]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[1]\)[t]\^\(1/3\)\) - \(mass[6]\)[t]\^\(1/3\))\) + \ \@\(\((\(-\(x[1]\)[t]\) + \(x[6]\)[t])\)\^2 + \((\(-\(y[1]\)[t]\) + \ \(y[6]\)[t])\)\^2 + \((\(-\(z[1]\)[t]\) + \ \(z[6]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[1]\)[t]\) + \(x[6]\)[t])\)\^2 + \ \((\(-\(y[1]\)[t]\) + \(y[6]\)[t])\)\^2 + \((\(-\(z[1]\)[t]\) + \ \(z[6]\)[t])\)\^2\)\)}]}, {"62", \(z[2]\), \(\(z[2]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(z[2]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[3]\ \((\(-\(\(\(mass[1]\)[t]\^\(1/3\) + \ \(mass[2]\)[t]\^\(1/3\)\)\/\@2\)\) + \@\(\((\(x[1]\)[t] - \(x[2]\)[t])\)\^2 + \ \((\(y[1]\)[t] - \(y[2]\)[t])\)\^2 + \((\(z[1]\)[t] - \(z[2]\)[t])\)\^2\))\)\ \ \((\(z[1]\)[t] - \(z[2]\)[t])\)\)\/\@\(\((\(x[1]\)[t] - \(x[2]\)[t])\)\^2 + \ \((\(y[1]\)[t] - \(y[2]\)[t])\)\^2 + \((\(z[1]\)[t] - \(z[2]\)[t])\)\^2\) + \ \(k[4]\ \((\(-\(z[2]\)[t]\) + \(z[3]\)[t])\)\ \((\(-\(\(\(mass[2]\)[t]\^\(1/3\ \) + \(mass[3]\)[t]\^\(1/3\)\)\/\@2\)\) + \@\(\((\(-\(x[2]\)[t]\) + \ \(x[3]\)[t])\)\^2 + \((\(-\(y[2]\)[t]\) + \(y[3]\)[t])\)\^2 + \ \((\(-\(z[2]\)[t]\) + \(z[3]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[2]\)[t]\) + \ \(x[3]\)[t])\)\^2 + \((\(-\(y[2]\)[t]\) + \(y[3]\)[t])\)\^2 + \ \((\(-\(z[2]\)[t]\) + \(z[3]\)[t])\)\^2\)\)}]}, {"63", \(z[3]\), \(\(z[3]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(z[3]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[5]\ \((\(-\(\(\(mass[2]\)[t]\^\(1/3\) + \ \(mass[3]\)[t]\^\(1/3\)\)\/\@2\)\) + \@\(\((\(x[2]\)[t] - \(x[3]\)[t])\)\^2 + \ \((\(y[2]\)[t] - \(y[3]\)[t])\)\^2 + \((\(z[2]\)[t] - \(z[3]\)[t])\)\^2\))\)\ \ \((\(z[2]\)[t] - \(z[3]\)[t])\)\)\/\@\(\((\(x[2]\)[t] - \(x[3]\)[t])\)\^2 + \ \((\(y[2]\)[t] - \(y[3]\)[t])\)\^2 + \((\(z[2]\)[t] - \(z[3]\)[t])\)\^2\) + \ \(k[6]\ \((\(-\(z[3]\)[t]\) + \(z[4]\)[t])\)\ \((1\/2\ \((\(-\(mass[3]\)[t]\^\ \(1/3\)\) - \(mass[4]\)[t]\^\(1/3\))\) + \@\(\((\(-\(x[3]\)[t]\) + \ \(x[4]\)[t])\)\^2 + \((\(-\(y[3]\)[t]\) + \(y[4]\)[t])\)\^2 + \ \((\(-\(z[3]\)[t]\) + \(z[4]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[3]\)[t]\) + \ \(x[4]\)[t])\)\^2 + \((\(-\(y[3]\)[t]\) + \(y[4]\)[t])\)\^2 + \ \((\(-\(z[3]\)[t]\) + \(z[4]\)[t])\)\^2\)\)}]}, {"64", \(z[4]\), \(\(z[4]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(z[4]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[7]\ \((1\/2\ \((\(-\(mass[3]\)[t]\^\(1/3\)\) - \ \(mass[4]\)[t]\^\(1/3\))\) + \@\(\((\(x[3]\)[t] - \(x[4]\)[t])\)\^2 + \ \((\(y[3]\)[t] - \(y[4]\)[t])\)\^2 + \((\(z[3]\)[t] - \(z[4]\)[t])\)\^2\))\)\ \ \((\(z[3]\)[t] - \(z[4]\)[t])\)\)\/\@\(\((\(x[3]\)[t] - \(x[4]\)[t])\)\^2 + \ \((\(y[3]\)[t] - \(y[4]\)[t])\)\^2 + \((\(z[3]\)[t] - \(z[4]\)[t])\)\^2\) + \ \(k[8]\ \((\(-\(z[4]\)[t]\) + \(z[5]\)[t])\)\ \((1\/2\ \((\(-\(mass[4]\)[t]\^\ \(1/3\)\) - \(mass[5]\)[t]\^\(1/3\))\) + \@\(\((\(-\(x[4]\)[t]\) + \ \(x[5]\)[t])\)\^2 + \((\(-\(y[4]\)[t]\) + \(y[5]\)[t])\)\^2 + \ \((\(-\(z[4]\)[t]\) + \(z[5]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[4]\)[t]\) + \ \(x[5]\)[t])\)\^2 + \((\(-\(y[4]\)[t]\) + \(y[5]\)[t])\)\^2 + \ \((\(-\(z[4]\)[t]\) + \(z[5]\)[t])\)\^2\)\)}]}, {"65", \(z[5]\), \(\(z[5]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(z[5]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[9]\ \((1\/2\ \((\(-\(mass[4]\)[t]\^\(1/3\)\) - \ \(mass[5]\)[t]\^\(1/3\))\) + \@\(\((\(x[4]\)[t] - \(x[5]\)[t])\)\^2 + \ \((\(y[4]\)[t] - \(y[5]\)[t])\)\^2 + \((\(z[4]\)[t] - \(z[5]\)[t])\)\^2\))\)\ \ \((\(z[4]\)[t] - \(z[5]\)[t])\)\)\/\@\(\((\(x[4]\)[t] - \(x[5]\)[t])\)\^2 + \ \((\(y[4]\)[t] - \(y[5]\)[t])\)\^2 + \((\(z[4]\)[t] - \(z[5]\)[t])\)\^2\) + \ \(k[10]\ \((\(-\(z[5]\)[t]\) + \(z[6]\)[t])\)\ \((1\/2\ \ \((\(-\(mass[5]\)[t]\^\(1/3\)\) - \(mass[6]\)[t]\^\(1/3\))\) + \ \@\(\((\(-\(x[5]\)[t]\) + \(x[6]\)[t])\)\^2 + \((\(-\(y[5]\)[t]\) + \ \(y[6]\)[t])\)\^2 + \((\(-\(z[5]\)[t]\) + \ \(z[6]\)[t])\)\^2\))\)\)\/\@\(\((\(-\(x[5]\)[t]\) + \(x[6]\)[t])\)\^2 + \ \((\(-\(y[5]\)[t]\) + \(y[6]\)[t])\)\^2 + \((\(-\(z[5]\)[t]\) + \ \(z[6]\)[t])\)\^2\)\)}]}, {"66", \(z[6]\), \(\(z[6]\)[0] == 0\), RowBox[{ RowBox[{ SuperscriptBox[\(z[6]\), "\[Prime]", MultilineFunction->None], "[", "t", "]"}], "==", \(\(k[11]\ \((1\/2\ \((\(-\(mass[1]\)[t]\^\(1/3\)\) - \ \(mass[6]\)[t]\^\(1/3\))\) + \@\(\((\(x[1]\)[t] - \(x[6]\)[t])\)\^2 + \ \((\(y[1]\)[t] - \(y[6]\)[t])\)\^2 + \((\(z[1]\)[t] - \(z[6]\)[t])\)\^2\))\)\ \ \((\(z[1]\)[t] - \(z[6]\)[t])\)\)\/\@\(\((\(x[1]\)[t] - \(x[6]\)[t])\)\^2 + \ \((\(y[1]\)[t] - \(y[6]\)[t])\)\^2 + \((\(z[1]\)[t] - 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