(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 9.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       157,          7]
NotebookDataLength[     29501,        855]
NotebookOptionsPosition[     28296,        815]
NotebookOutlinePosition[     28779,        833]
CellTagsIndexPosition[     28736,        830]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"C2H6", " ", "Molecule", " ", "after", " ", "Kimball"}], ",", 
    RowBox[{"non", " ", "overlapping"}], ",", 
    RowBox[{
     RowBox[{"parameterized", " ", "with", " ", "G2"}], "//", 
     RowBox[{"6", "-", 
      RowBox[{"311", "g"}]}]}]}], " ", "*)"}], "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"Clear", "[", 
     RowBox[{"k1", ",", "k2", ",", "k3", ",", "s1", ",", "s2", ",", "s3"}], 
     "]"}], ";", " ", 
    RowBox[{"n", "=", "2."}], ";"}], "\[IndentingNewLine]", 
   RowBox[{"(*", " ", 
    RowBox[{"Term", " ", "from", " ", 
     RowBox[{
      RowBox[{"ChemEdu", "/", "Kimball"}], "/", 
      RowBox[{"Alkan", ".", "sys"}]}]}], " ", "*)"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"T", "=", 
     RowBox[{
      RowBox[{"2.25", "*", "n", "*", 
       RowBox[{"k1", "/", 
        RowBox[{"P", "^", "2"}]}]}], " ", "+", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"n", " ", "-", " ", "1.0"}], ")"}], "*", "2.25", "*", 
       RowBox[{"k2", "/", 
        RowBox[{"Q", "^", "2"}]}]}], " ", "+", " ", 
      RowBox[{"4.5", "*", 
       RowBox[{"(", 
        RowBox[{"n", " ", "+", " ", "1.0"}], ")"}], "*", 
       RowBox[{"k3", "/", 
        RowBox[{"R", "^", "2"}]}]}]}]}], ";"}], "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"p", " ", "=", "X"}], ";", " ", 
    RowBox[{"p2", "=", " ", 
     RowBox[{"p", "*", "p"}]}], ";", " ", 
    RowBox[{"z", "=", " ", "6."}], ";", " ", 
    RowBox[{"ad", "=", " ", 
     RowBox[{"8.", "/", "3."}]}], ";", " ", 
    RowBox[{"zd", "=", " ", 
     RowBox[{"2.", "/", " ", "3."}]}], ";", " ", 
    RowBox[{"vd", " ", "=", 
     RowBox[{"4.", "/", " ", "3."}]}], ";", " ", 
    RowBox[{"q", "=", " ", 
     RowBox[{"P", " ", "+", " ", "Q"}]}], ";", " ", 
    RowBox[{"r", "=", " ", 
     RowBox[{"P", " ", "+", " ", "R"}]}], ";"}], " ", "\[IndentingNewLine]", 
   RowBox[{
    RowBox[{"q2", "=", " ", 
     RowBox[{"q", "*", "q"}]}], ";", " ", 
    RowBox[{"r2", "=", " ", 
     RowBox[{"r", "*", "r"}]}], ";", " ", 
    RowBox[{"r2p2", "=", 
     RowBox[{"r2", "*", "p2"}]}], ";", " ", 
    RowBox[{"r2p", "=", " ", 
     RowBox[{"r2", "*", "p"}]}], ";", " ", 
    RowBox[{"qr", "=", " ", 
     RowBox[{"q", "*", "r"}]}], ";", " ", 
    RowBox[{"qrp", "=", 
     RowBox[{"qr", "*", "p"}]}], ";"}], "\[IndentingNewLine]"}]}]], "Input",
 CellChangeTimes->{3.5666538505009747`*^9, 3.5666546055735006`*^9}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"Vee", "=", 
   RowBox[{
    RowBox[{"3.0", "*", "n", "*", 
     RowBox[{"s1", "/", "P"}]}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"n", " ", "-", " ", "1.0"}], ")"}], "*", "3.0", "*", 
     RowBox[{"s2", "/", " ", "Q"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vee", "=", 
   RowBox[{"Vee", "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"n", " ", "+", " ", "1.0"}], ")"}], "*", "6.0", "*", 
     RowBox[{"s3", "/", " ", "R"}]}], " ", "+", " ", 
    RowBox[{"8.0", "/", " ", 
     RowBox[{"Sqrt", "[", "q2", "]"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vee", "=", 
   RowBox[{"Vee", "+", " ", 
    RowBox[{"24.0", "/", " ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{"zd", "*", "qr"}], "+", "q2", " ", "+", " ", "r2"}], 
      "]"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Vee", "=", 
    RowBox[{"Vee", "+", " ", 
     RowBox[{"24.0", "/", " ", 
      RowBox[{"Sqrt", "[", "r2", "]"}]}], " ", "+", " ", 
     RowBox[{"4.0", "/", 
      RowBox[{"Sqrt", "[", 
       RowBox[{"4.0", "*", "q2"}], "]"}]}]}]}], ";"}], 
  " "}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vee", "=", 
   RowBox[{"Vee", "+", " ", 
    RowBox[{"24.0", "/", " ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{"vd", "*", "qr"}], " ", "+", " ", 
       RowBox[{"4.0", "*", "q2"}], " ", "+", " ", "r2"}], "]"}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vee", "=", 
   RowBox[{"Vee", "+", " ", 
    RowBox[{"24.0", "/", " ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{"ad", "*", "r2"}], "]"}]}], " ", "+", " ", 
    RowBox[{"12.0", "/", " ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{"ad", "*", "qr"}], " ", "+", " ", 
       RowBox[{"4.0", "*", "q2"}], " ", "+", 
       RowBox[{"4.0", "*", "r2"}]}], "]"}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vee", "=", 
   RowBox[{"Vee", "+", " ", 
    RowBox[{"24.0", "/", " ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{"ad", "*", "qr"}], " ", "+", " ", 
       RowBox[{"4.0", "*", "q2"}], " ", "+", " ", 
       RowBox[{"vd", "*", "r2"}]}], "]"}]}]}]}], 
  ";"}], "\[IndentingNewLine]"}], "Input",
 CellChangeTimes->{{3.5666538505009747`*^9, 3.5666538568969855`*^9}, {
  3.5666544835968866`*^9, 3.5666545139857397`*^9}, {3.5666545776806517`*^9, 
  3.5666545986782885`*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"Vne", " ", "=", 
   RowBox[{
    RowBox[{"-", "2.0"}], "*", 
    RowBox[{"(", 
     RowBox[{"n", " ", "+", " ", "1.0"}], ")"}], "*", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"3.0", " ", "-", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"p", " ", "-", " ", "1.0"}], ")"}], "*", 
          RowBox[{"(", 
           RowBox[{"1.0", " ", "+", " ", 
            RowBox[{"P", "/", " ", "R"}]}], ")"}]}], ")"}], "^", "2"}]}], 
      ")"}], "/", "R"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vne", "=", 
   RowBox[{"Vne", " ", "-", " ", 
    RowBox[{"3.0", "*", "n", "*", 
     RowBox[{"z", "/", " ", "P"}]}], "-", " ", 
    RowBox[{"4.0", "*", 
     RowBox[{"z", "/", " ", 
      RowBox[{"Sqrt", "[", "q2", "]"}]}]}], " ", "-", " ", 
    RowBox[{"12.0", "/", " ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{"zd", "*", "qrp"}], " ", "+", " ", "r2p2", " ", "+", " ", 
       "q2"}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vne", "=", 
   RowBox[{"Vne", "-", " ", 
    RowBox[{"12.0", "*", 
     RowBox[{"z", "/", " ", 
      RowBox[{"Sqrt", "[", "r2", "]"}]}]}], " ", "-", " ", 
    RowBox[{"12.0", "/", " ", 
     RowBox[{"Sqrt", "[", "r2p2", "]"}]}], " ", "-", " ", 
    RowBox[{"4.0", "*", 
     RowBox[{"z", "/", " ", 
      RowBox[{"Sqrt", "[", 
       RowBox[{"4.0", "*", "q2"}], "]"}]}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vne", "=", 
   RowBox[{"Vne", "-", " ", 
    RowBox[{"12.0", "*", 
     RowBox[{"z", "/", " ", 
      RowBox[{"Sqrt", "[", 
       RowBox[{
        RowBox[{"vd", "*", "qr"}], " ", "+", " ", 
        RowBox[{"4.0", "*", "q2"}], " ", "+", " ", "r2"}], "]"}]}]}]}]}], " ",
   ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vne", "=", 
   RowBox[{"Vne", "-", " ", 
    RowBox[{"12.0", "/", " ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{"vd", "*", "qrp"}], " ", "+", " ", "r2p2", " ", "+", " ", 
       RowBox[{"4.0", "*", "q2"}]}], "]"}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vne", "=", 
   RowBox[{"Vne", "-", " ", 
    RowBox[{"24.0", "/", " ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{"zd", "*", "r2p"}], " ", "+", " ", "r2p2", " ", "+", " ", 
       "r2"}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vne", "=", 
   RowBox[{"Vne", "-", 
    RowBox[{"12.0", "/", " ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{"vd", "*", "qr"}], " ", "+", " ", 
       RowBox[{"vd", "*", "qrp"}], " ", "+", " ", 
       RowBox[{"2.0", "*", "r2p"}], " ", "+", " ", "r2p2", " ", "+", " ", 
       RowBox[{"4.0", "*", "q2"}], " ", "+", " ", "r2"}], "]"}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vne", "=", 
   RowBox[{"Vne", "-", " ", 
    RowBox[{"24.0", "/", " ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{"vd", "*", "qr"}], " ", "+", " ", 
       RowBox[{"vd", "*", "qrp"}], " ", "-", " ", 
       RowBox[{"zd", "*", "r2p"}], " ", "+", " ", "r2p2", " ", "+", " ", 
       RowBox[{"4.0", "*", "q2"}], " ", "+", " ", "r2"}], "]"}]}]}]}], 
  ";"}], "\[IndentingNewLine]"}], "Input",
 CellChangeTimes->{{3.5666538505009747`*^9, 3.5666538652430005`*^9}, {
  3.566654325631009*^9, 3.566654468901661*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"Vnn", " ", "=", 
   RowBox[{
    RowBox[{"6.0", "*", 
     RowBox[{"z", "/", " ", 
      RowBox[{"Sqrt", "[", "r2p2", "]"}]}]}], " ", "+", " ", 
    RowBox[{"z", "*", 
     RowBox[{"z", "/", " ", 
      RowBox[{"Sqrt", "[", 
       RowBox[{"4.0", "*", "q2"}], "]"}]}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vnn", "=", 
   RowBox[{"Vnn", "+", " ", 
    RowBox[{"6.0", "*", 
     RowBox[{"z", "/", " ", 
      RowBox[{"Sqrt", "[", 
       RowBox[{
        RowBox[{"vd", "*", "qrp"}], " ", "+", " ", "r2p2", " ", "+", " ", 
        RowBox[{"4.0", "*", "q2"}]}], "]"}]}]}], " ", "+", " ", 
    RowBox[{"6.0", "/", " ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{"ad", "*", "r2p2"}], "]"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vnn", "=", 
   RowBox[{"Vnn", "+", " ", 
    RowBox[{"3.0", "/", " ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{"ad", "*", "qrp"}], " ", "+", " ", 
       RowBox[{"4.0", "*", "r2p2"}], " ", "+", " ", 
       RowBox[{"4.0", "*", "q2"}]}], "]"}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vnn", "=", 
   RowBox[{"Vnn", "+", " ", 
    RowBox[{"6.0", "/", " ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{"ad", "*", "qrp"}], " ", "+", " ", 
       RowBox[{"vd", "*", "r2p2"}], " ", "+", " ", 
       RowBox[{"4.0", "*", "q2"}]}], "]"}]}]}]}], 
  ";"}], "\[IndentingNewLine]"}], "Input",
 CellChangeTimes->{{3.5666538505009747`*^9, 3.5666538774110217`*^9}, {
  3.5666545296949673`*^9, 3.5666545640462275`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"func", " ", "=", " ", 
    RowBox[{
    "T", " ", "+", " ", "Vne", " ", "+", " ", "Vee", " ", "+", " ", "Vnn"}]}],
    ";"}], "\[IndentingNewLine]", 
  RowBox[{"(*", " ", 
   RowBox[{"Parameterliste", " ", "c"}], " ", "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"c", " ", "=", " ", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"k1", " ", "->", " ", "1.02246687"}], ",", 
     RowBox[{"k2", " ", "->", " ", "1.37426345"}], ",", 
     RowBox[{"k3", " ", "->", " ", "1.20537762"}], ",", 
     RowBox[{"s1", " ", "->", " ", "0.30582536"}], ",", 
     RowBox[{"s2", " ", "->", " ", "0.30677632"}], ",", 
     RowBox[{"s3", " ", "->", " ", "0.35441063"}]}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"func", "=", 
    RowBox[{"func", " ", "/.", " ", "c"}]}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{"t", " ", "=", " ", 
  RowBox[{"FindMinimum", "[", 
   RowBox[{"func", ",", 
    RowBox[{"{", 
     RowBox[{"P", ",", "0.26"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"Q", ",", "1.19"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"R", ",", "1.25"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"X", ",", "1.35"}], "}"}], ",", " ", 
    RowBox[{"Method", "\[Rule]", "\"\<Newton\>\""}]}], 
   "]"}]}], "\[IndentingNewLine]"}], "Input",
 CellChangeTimes->{{3.5666538505009747`*^9, 3.56665388792544*^9}, {
  3.566653982243206*^9, 3.5666540601185427`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"-", "79.63122262216285`"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"P", "\[Rule]", "0.26141206364711966`"}], ",", 
     RowBox[{"Q", "\[Rule]", "1.1782401150045392`"}], ",", 
     RowBox[{"R", "\[Rule]", "1.27097249267703`"}], ",", 
     RowBox[{"X", "\[Rule]", "1.3575746411984353`"}]}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{3.5666546349171524`*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"u", " ", "=", " ", 
   RowBox[{"t", "[", 
    RowBox[{"[", "2", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"N", "[", 
  RowBox[{
   RowBox[{"Vne", " ", "/.", "u"}], ",", "10"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"N", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"Vee", " ", "/.", "u"}], " ", "/.", "c"}], ",", "9"}], 
  "]"}], "\[IndentingNewLine]", 
 RowBox[{"N", "[", 
  RowBox[{
   RowBox[{"Vnn", " ", "/.", "u"}], ",", "8"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"ch", " ", "=", " ", 
   RowBox[{
    RowBox[{"X", "*", 
     RowBox[{"(", 
      RowBox[{"P", " ", "+", " ", "R"}], ")"}]}], " ", "/.", "u"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"dch", " ", "=", " ", 
   RowBox[{"ch", "*", "0.529177"}]}], "  ", 
  RowBox[{"(*", " ", 
   RowBox[{"C", "-", 
    RowBox[{"H", " ", "Abstand"}]}], " ", "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"cc", " ", "=", " ", 
   RowBox[{
    RowBox[{"2.", "*", 
     RowBox[{"(", 
      RowBox[{"P", " ", "+", " ", "Q"}], ")"}]}], " ", "/.", "u"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"dcc", "=", 
   RowBox[{"cc", "*", "0.529177"}]}], "  ", 
  RowBox[{"(*", " ", 
   RowBox[{"C", "-", 
    RowBox[{"C", " ", "Abstand"}]}], " ", "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"N", "[", 
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"(", 
         RowBox[{"Vne", " ", "+", " ", "Vee", " ", "+", " ", "Vnn"}], ")"}]}],
        "/", "T"}], " ", "/.", "u"}], " ", "/.", "c"}], ",", "9"}], "]"}], 
  "  ", 
  RowBox[{"(*", " ", 
   RowBox[{"Virial", " ", "Theorem"}], " ", "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     RowBox[{"-", 
      RowBox[{"t", "[", 
       RowBox[{"[", "1", "]"}], "]"}]}], " ", "-", " ", 
     RowBox[{"n", "*", "37.784301"}], " ", "-", " ", "n", " ", "-", " ", 
     "1.0"}], ")"}], "*", "627.50956"}], " ", 
  RowBox[{"(*", 
   RowBox[{"Atomisierungsenergie", " ", "0", " ", "K", " ", "in", " ", 
    RowBox[{"kcal", "/", "mol"}]}], " ", 
   "*)"}]}], "\[IndentingNewLine]"}], "Input",
 CellChangeTimes->{{3.5666538505009747`*^9, 3.566653896505455*^9}}],

Cell[BoxData[
 RowBox[{"-", "271.1254029661546`"}]], "Output",
 CellChangeTimes->{3.566654634932752*^9}],

Cell[BoxData["69.66048834219667`"], "Output",
 CellChangeTimes->{3.566654634932752*^9}],

Cell[BoxData["42.20246937944781`"], "Output",
 CellChangeTimes->{3.566654634932752*^9}],

Cell[BoxData["1.1008608909028728`"], "Output",
 CellChangeTimes->{3.566654634932752*^9}],

Cell[BoxData["1.523661641884698`"], "Output",
 CellChangeTimes->{3.566654634932752*^9}],

Cell[BoxData["1.9999999999976843`"], "Output",
 CellChangeTimes->{3.566654634932752*^9}],

Cell[BoxData["666.8045990603384`"], "Output",
 CellChangeTimes->{3.566654634948352*^9}]
}, Open  ]],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.5666538505009747`*^9, 3.566653909687478*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"plot1", " ", "=", " ", 
   RowBox[{
    RowBox[{"Graphics", "[", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"Circle", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{"-", 
            RowBox[{"(", 
             RowBox[{"P", " ", "+", " ", "Q"}], ")"}]}], ",", "0"}], "}"}], 
         ",", "P"}], "]"}], ",", 
       RowBox[{"Disk", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{"-", 
            RowBox[{"(", 
             RowBox[{"P", " ", "+", " ", "Q"}], ")"}]}], ",", "0"}], "}"}], 
         ",", "0.1"}], "]"}], ",", 
       RowBox[{"Circle", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{"P", " ", "+", " ", "Q"}], ",", "0"}], "}"}], ",", "P"}], 
        "]"}], ",", 
       RowBox[{"Disk", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{"P", " ", "+", " ", "Q"}], ",", "0"}], "}"}], ",", "0.1"}],
         "]"}], ",", 
       RowBox[{"Circle", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"0", ",", "0"}], "}"}], ",", "Q"}], "]"}], ",", 
       RowBox[{"Circle", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             RowBox[{"(", 
              RowBox[{"P", " ", "+", " ", "Q"}], ")"}]}], "-", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{"P", " ", "+", " ", "R"}], ")"}], "/", "3."}]}], ",", 
           RowBox[{
            RowBox[{"-", 
             RowBox[{"(", 
              RowBox[{"P", " ", "+", " ", "R"}], ")"}]}], "*", 
            RowBox[{"Sqrt", "[", 
             RowBox[{"8.", "/", " ", "9."}], "]"}]}]}], "}"}], ",", "R"}], 
        "]"}], ",", 
       RowBox[{"Disk", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{
            RowBox[{"-", 
             RowBox[{"(", 
              RowBox[{"P", " ", "+", " ", "Q"}], ")"}]}], "-", " ", 
            RowBox[{"p", "*", 
             RowBox[{
              RowBox[{"(", 
               RowBox[{"P", " ", "+", " ", "R"}], ")"}], "/", "3."}]}]}], ",", 
           RowBox[{
            RowBox[{"-", "p"}], "*", 
            RowBox[{"(", 
             RowBox[{"P", " ", "+", " ", "R"}], ")"}], "*", 
            RowBox[{"Sqrt", "[", 
             RowBox[{"8.", "/", " ", "9."}], "]"}]}]}], "}"}], ",", "0.1"}], 
        "]"}], ",", 
       RowBox[{"Circle", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{"P", " ", "+", " ", "Q", " ", "+", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{"P", " ", "+", " ", "R"}], ")"}], "/", "3."}]}], ",", 
           RowBox[{
            RowBox[{"(", 
             RowBox[{"P", " ", "+", " ", "R"}], ")"}], "*", 
            RowBox[{"Sqrt", "[", 
             RowBox[{"8.", "/", " ", "9."}], "]"}]}]}], "}"}], ",", "R"}], 
        "]"}], ",", 
       RowBox[{"Disk", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{
            RowBox[{"(", 
             RowBox[{"P", " ", "+", " ", "Q"}], ")"}], "+", " ", 
            RowBox[{"p", "*", 
             RowBox[{
              RowBox[{"(", 
               RowBox[{"P", " ", "+", " ", "R"}], ")"}], "/", "3."}]}]}], ",", 
           RowBox[{"p", "*", 
            RowBox[{"(", 
             RowBox[{"P", " ", "+", " ", "R"}], ")"}], "*", 
            RowBox[{"Sqrt", "[", 
             RowBox[{"8.", "/", " ", "9."}], "]"}]}]}], "}"}], ",", "0.1"}], 
        "]"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"Dashing", "[", 
          RowBox[{"{", 
           RowBox[{"0.03", ",", "0.03"}], "}"}], "]"}], ",", 
         "\[IndentingNewLine]", 
         RowBox[{"Circle", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{
              RowBox[{"(", 
               RowBox[{"P", " ", "+", " ", "Q"}], ")"}], "+", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "R"}], ")"}], "/", "3."}]}], ",", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "R"}], ")"}]}], "*", 
              RowBox[{"Sqrt", "[", 
               RowBox[{"2.", "/", " ", "9."}], "]"}]}]}], "}"}], ",", "R"}], 
          "]"}], ",", 
         RowBox[{"Disk", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{"P", " ", "+", " ", "Q", " ", "+", " ", 
              RowBox[{"p", "*", 
               RowBox[{
                RowBox[{"(", 
                 RowBox[{"P", " ", "+", " ", "R"}], ")"}], "/", "3."}]}]}], 
             ",", 
             RowBox[{
              RowBox[{"-", "p"}], "*", 
              RowBox[{"(", 
               RowBox[{"P", " ", "+", " ", "R"}], ")"}], "*", 
              RowBox[{
               RowBox[{"Sqrt", "[", "2.", "]"}], "/", "3."}]}]}], "}"}], ",", 
           "0.1"}], "]"}], ",", 
         RowBox[{"Circle", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{
              RowBox[{"-", 
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "Q"}], ")"}]}], "-", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "R"}], ")"}], "/", "3."}]}], ",", 
             RowBox[{
              RowBox[{"(", 
               RowBox[{"P", " ", "+", " ", "R"}], ")"}], "*", 
              RowBox[{"Sqrt", "[", 
               RowBox[{"2.", "/", " ", "9."}], "]"}]}]}], "}"}], ",", "R"}], 
          "]"}], ",", 
         RowBox[{"Disk", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{
              RowBox[{"-", 
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "Q"}], ")"}]}], "-", 
              RowBox[{"p", "*", 
               RowBox[{
                RowBox[{"(", 
                 RowBox[{"P", " ", "+", " ", "R"}], ")"}], "/", "3."}]}]}], 
             ",", 
             RowBox[{"p", "*", 
              RowBox[{"(", 
               RowBox[{"P", " ", "+", " ", "R"}], ")"}], "*", 
              RowBox[{
               RowBox[{"Sqrt", "[", "2.", "]"}], "/", "3."}]}]}], "}"}], ",", 
           "0.1"}], "]"}]}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"Thickness", "[", "0.01", "]"}], ",", 
         RowBox[{"Line", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "Q"}], ")"}]}], ",", "0"}], "}"}],
             ",", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{"P", " ", "+", " ", "Q"}], ",", "0"}], "}"}]}], "}"}], 
          "]"}], ",", 
         RowBox[{"Line", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{
              RowBox[{"P", " ", "+", " ", "Q"}], ",", "0"}], "}"}], ",", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{"P", " ", "+", " ", "Q", " ", "+", " ", 
               RowBox[{"p", "*", 
                RowBox[{
                 RowBox[{"(", 
                  RowBox[{"P", " ", "+", " ", "R"}], ")"}], "/", "3."}]}]}], 
              ",", 
              RowBox[{"p", "*", 
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "R"}], ")"}], "*", 
               RowBox[{"Sqrt", "[", 
                RowBox[{"8.", "/", " ", "9."}], "]"}]}]}], "}"}]}], "}"}], 
          "]"}], ",", 
         RowBox[{"Line", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{
              RowBox[{"-", 
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "Q"}], ")"}]}], ",", "0"}], "}"}],
             ",", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{
               RowBox[{"-", 
                RowBox[{"(", 
                 RowBox[{"P", " ", "+", " ", "Q"}], ")"}]}], "-", " ", 
               RowBox[{"p", "*", 
                RowBox[{
                 RowBox[{"(", 
                  RowBox[{"P", " ", "+", " ", "R"}], ")"}], "/", "3."}]}]}], 
              ",", 
              RowBox[{
               RowBox[{"-", "p"}], "*", 
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "R"}], ")"}], "*", 
               RowBox[{"Sqrt", "[", 
                RowBox[{"8.", "/", " ", "9."}], "]"}]}]}], "}"}]}], "}"}], 
          "]"}], ",", "\[IndentingNewLine]", 
         RowBox[{"{", 
          RowBox[{
           RowBox[{"Dashing", "[", 
            RowBox[{"{", 
             RowBox[{"0.01", ",", "0.01"}], "}"}], "]"}], ",", 
           "\[IndentingNewLine]", 
           RowBox[{"Line", "[", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{"{", 
               RowBox[{
                RowBox[{"P", " ", "+", " ", "Q"}], ",", "0"}], "}"}], ",", 
              RowBox[{"{", 
               RowBox[{
                RowBox[{"P", " ", "+", " ", "Q", " ", "+", " ", 
                 RowBox[{"p", "*", 
                  RowBox[{
                   RowBox[{"(", 
                    RowBox[{"P", " ", "+", " ", "R"}], ")"}], "/", "3."}]}]}],
                 ",", 
                RowBox[{
                 RowBox[{"-", "p"}], "*", 
                 RowBox[{"(", 
                  RowBox[{"P", " ", "+", " ", "R"}], ")"}], "*", 
                 RowBox[{"Sqrt", "[", 
                  RowBox[{"2.", "/", " ", "9."}], "]"}]}]}], "}"}]}], "}"}], 
            "]"}], ",", "\[IndentingNewLine]", 
           RowBox[{"Line", "[", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{"{", 
               RowBox[{
                RowBox[{"-", 
                 RowBox[{"(", 
                  RowBox[{"P", " ", "+", " ", "Q"}], ")"}]}], ",", "0"}], 
               "}"}], ",", 
              RowBox[{"{", 
               RowBox[{
                RowBox[{
                 RowBox[{"-", 
                  RowBox[{"(", 
                   RowBox[{"P", " ", "+", " ", "Q"}], ")"}]}], " ", "-", " ", 
                 RowBox[{"p", "*", 
                  RowBox[{
                   RowBox[{"(", 
                    RowBox[{"P", " ", "+", " ", "R"}], ")"}], "/", "3."}]}]}],
                 ",", 
                RowBox[{"p", "*", 
                 RowBox[{"(", 
                  RowBox[{"P", " ", "+", " ", "R"}], ")"}], "*", 
                 RowBox[{"Sqrt", "[", 
                  RowBox[{"2.", "/", " ", "9."}], "]"}]}]}], "}"}]}], "}"}], 
            "]"}]}], "}"}]}], "}"}]}], "}"}], "]"}], " ", "/.", " ", "u"}]}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.5666538505009747`*^9, 3.566653909687478*^9}, {
  3.566654101131015*^9, 3.5666541287742634`*^9}, {3.5666542228892283`*^9, 
  3.566654230143241*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{"plot1", ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"AspectRatio", " ", "->", " ", "Automatic"}], ",", 
     RowBox[{"PlotRange", " ", "->", " ", "All"}], ",", 
     RowBox[{"Axes", " ", "->", " ", "True"}], ",", 
     RowBox[{"GridLines", " ", "->", " ", "Automatic"}], ",", 
     RowBox[{"Frame", " ", "->", " ", "True"}]}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.5666538505009747`*^9, 3.566653909687478*^9}, {
  3.566654101131015*^9, 3.566654120194248*^9}}],

Cell[BoxData[
 GraphicsBox[{CircleBox[{-1.439652178651659, 0}, 0.26141206364711966`], 
   DiskBox[{-1.439652178651659, 0}, 0.1], 
   CircleBox[{1.439652178651659, 0}, 0.26141206364711966`], 
   DiskBox[{1.439652178651659, 0}, 0.1], 
   CircleBox[{0, 0}, 1.1782401150045392`], 
   CircleBox[{-1.9504470307597088`, -1.444746014883127}, 1.27097249267703], 
   DiskBox[{-2.1330943167282523`, -1.9613505527778305`}, 0.1], 
   CircleBox[{1.9504470307597088`, 1.444746014883127}, 1.27097249267703], 
   DiskBox[{2.1330943167282523`, 1.9613505527778305`}, 0.1], 
   {Dashing[{0.03, 0.03}], 
    CircleBox[{1.9504470307597088`, -0.7223730074415635}, 1.27097249267703], 
    DiskBox[{2.1330943167282523`, -0.9806752763889153}, 0.1], 
    CircleBox[{-1.9504470307597088`, 0.7223730074415635}, 1.27097249267703], 
    DiskBox[{-2.1330943167282523`, 0.9806752763889153}, 0.1]}, 
   {Thickness[0.01], 
    LineBox[{{-1.439652178651659, 0}, {1.439652178651659, 0}}], 
    LineBox[{{1.439652178651659, 0}, {2.1330943167282523`, 
      1.9613505527778305`}}], 
    LineBox[{{-1.439652178651659, 
       0}, {-2.1330943167282523`, -1.9613505527778305`}}], 
    {Dashing[{0.01, 0.01}], 
     LineBox[{{1.439652178651659, 0}, {
       2.1330943167282523`, -0.9806752763889153}}], 
     LineBox[{{-1.439652178651659, 0}, {-2.1330943167282523`, 
       0.9806752763889153}}]}}},
  AspectRatio->Automatic,
  Axes->True,
  Frame->True,
  GridLines->Automatic,
  PlotRange->All]], "Output",
 CellChangeTimes->{3.566654634963952*^9}]
}, Open  ]],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.5666538505009747`*^9, 3.566653909687478*^9}}]
},
WindowSize->{896, 740},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
PrintingCopies->1,
PrintingPageRange->{Automatic, Automatic},
PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> False}},
FrontEndVersion->"9.0 for Microsoft Windows (64-bit) (November 20, 2012)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[557, 20, 2455, 65, 152, "Input"],
Cell[3015, 87, 2411, 71, 172, "Input"],
Cell[5429, 160, 3319, 95, 192, "Input"],
Cell[8751, 257, 1556, 45, 112, "Input"],
Cell[CellGroupData[{
Cell[10332, 306, 1468, 39, 172, "Input"],
Cell[11803, 347, 424, 11, 31, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[12264, 363, 2229, 68, 232, "Input"],
Cell[14496, 433, 104, 2, 31, "Output"],
Cell[14603, 437, 87, 1, 31, "Output"],
Cell[14693, 440, 87, 1, 31, "Output"],
Cell[14783, 443, 88, 1, 31, "Output"],
Cell[14874, 446, 87, 1, 31, "Output"],
Cell[14964, 449, 88, 1, 31, "Output"],
Cell[15055, 452, 87, 1, 31, "Output"]
}, Open  ]],
Cell[15157, 456, 94, 1, 31, "Input"],
Cell[15254, 459, 10872, 302, 352, "Input"],
Cell[CellGroupData[{
Cell[26151, 765, 522, 11, 52, "Input"],
Cell[26676, 778, 1507, 31, 323, "Output"]
}, Open  ]],
Cell[28198, 812, 94, 1, 31, "Input"]
}
]
*)

(* End of internal cache information *)