(* 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[     43001,       1209]
NotebookOptionsPosition[     41313,       1156]
NotebookOutlinePosition[     41870,       1175]
CellTagsIndexPosition[     41827,       1172]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
 StyleBox[
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"NH3", " ", "with", " ", 
     RowBox[{"N", "[", 
      RowBox[{
       RowBox[{"1", "s2", " ", "3", "sp"}], ",", " ", 
       RowBox[{"1", " ", "sp", " ", "LP"}]}], "]"}]}], ",", 
    RowBox[{
     RowBox[{"~", "no"}], " ", "overlap"}], ",", " ", 
    RowBox[{
    "parametrized", " ", "ES", " ", "02.01", ".2013", "\[IndentingNewLine]", 
     RowBox[{"Variables", ":", "\[IndentingNewLine]", "  ", 
      RowBox[{
       RowBox[{"P", " ", "N"}], "-", 
       RowBox[{"core", " ", "radius", "\[IndentingNewLine]", 
        RowBox[{"Q", " ", "N"}]}], "-", 
       RowBox[{
       "H", " ", "cloud", " ", "radius", "\[IndentingNewLine]", "R", " ", 
        "lone", " ", "pair", " ", "radius", "\[IndentingNewLine]", "S", " ", 
        "distance", " ", "proton", " ", "to", " ", "center", " ", "of", " ", 
        "NH", " ", "cloud", "\[IndentingNewLine]", 
        RowBox[{"\[Alpha]", " ", "angle", " ", "lonePair"}]}], "-", "N", "-", 
       RowBox[{
       "H", "\[IndentingNewLine]", "\[Beta]", " ", "angle", " ", "H"}], "-", 
       "N", "-", "H"}]}]}], ",", " ", 
    RowBox[{
     RowBox[{"not", " ", "a", " ", 
      RowBox[{"variable", ":", " ", "cos\[Beta]"}]}], " ", "=", " ", 
     RowBox[{"1.0", "-", 
      RowBox[{"1.5", "*", 
       RowBox[{
        RowBox[{"Sin", "[", "\[Alpha]", "]"}], "^", "2"}]}]}]}]}], " ", 
   "*)"}], "Text",
  FontFamily->"Arial Narrow",
  FontSize->14,
  FontColor->GrayLevel[0]]], "Input",
 CellChangeTimes->{{3.5661428484442425`*^9, 3.5661428783026953`*^9}, {
   3.5661430328053665`*^9, 3.5661430369081736`*^9}, {3.5661430998854847`*^9, 
   3.5661431383537183`*^9}, {3.566143180801393*^9, 3.5661432248645825`*^9}, {
   3.566143288683233*^9, 3.5661432893462706`*^9}, 3.566143344240477*^9, 
   3.566143438043442*^9, 3.566143491551536*^9}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", "wc", "]"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Z", "=", "7.0"}], ";", " ", 
   RowBox[{"w3", "=", 
    RowBox[{"Sqrt", "[", "3", "]"}]}], ";"}], "\[IndentingNewLine]", 
  "\[IndentingNewLine]", 
  RowBox[{"(*", "core", "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Tc", "=", 
   RowBox[{"2.25", "*", 
    RowBox[{"k1", "/", 
     RowBox[{"P", "^", "2"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vnec", "=", 
   RowBox[{
    RowBox[{"-", "3.0"}], "*", 
    RowBox[{"Z", "/", "P"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Veec", "=", 
    RowBox[{"3.0", "*", 
     RowBox[{"s1", "/", "P"}]}]}], ";"}], "\[IndentingNewLine]", 
  "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{"XH", " ", "bond"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Tb", "=", 
   RowBox[{"2.25", "*", 
    RowBox[{"k2", "/", 
     RowBox[{"Q", "^", "2"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vneb", "=", 
   RowBox[{
    RowBox[{"-", "2.0"}], "*", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1.5", "-", 
       RowBox[{"0.5", "*", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"S", "/", "Q"}], ")"}], "^", "2"}]}]}], ")"}], "/", 
     "Q"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Veeb", "=", 
    RowBox[{"3.0", "*", 
     RowBox[{"s2", "/", "Q"}]}]}], ";"}], "\[IndentingNewLine]", 
  "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{"lone", " ", "pair"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Tp", "=", 
   RowBox[{"2.25", "*", 
    RowBox[{"k3", "/", 
     RowBox[{"R", "^", "2"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Veep", "=", 
    RowBox[{"3.0", "*", 
     RowBox[{"s3", "/", "R"}]}]}], ";"}], "\[IndentingNewLine]", 
  "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{"core", "-", "bond"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vnecb", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"-", "2.0"}], "*", 
     RowBox[{"Z", "/", 
      RowBox[{"(", 
       RowBox[{"P", "+", "Q"}], ")"}]}]}], "-", 
    RowBox[{"2", "/", 
     RowBox[{"(", 
      RowBox[{"P", "+", "Q", "+", "S"}], ")"}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Veecb", "=", 
   RowBox[{"4.0", "/", 
    RowBox[{"(", 
     RowBox[{"P", "+", "Q"}], ")"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Vnncb", "=", 
    RowBox[{"Z", "/", 
     RowBox[{"(", 
      RowBox[{"P", "+", "Q", "+", "S"}], ")"}]}]}], ";"}], 
  "\[IndentingNewLine]", "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{"core", "-", 
    RowBox[{"lone", " ", "pair"}]}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vnecp", "=", 
   RowBox[{
    RowBox[{"-", "2.0"}], "*", 
    RowBox[{"Z", "/", 
     RowBox[{"(", 
      RowBox[{"P", "+", "R"}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Veecp", "=", 
    RowBox[{"4.0", "/", 
     RowBox[{"(", 
      RowBox[{"P", "+", "R"}], ")"}]}]}], ";"}], "\[IndentingNewLine]", 
  "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{"bond", "-", "bond"}], "*)"}], "\[IndentingNewLine]", 
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"d1", " ", "w", 
     RowBox[{"(", "NH", ")"}]}], "-", 
    RowBox[{"w", 
     RowBox[{"(", "NH", ")"}]}]}], " ", "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"d1", "=", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"P", "+", "Q"}], ")"}], "*", 
     RowBox[{"Sin", "[", "\[Alpha]", "]"}], "*", "w3"}]}], ";"}], 
  "\[IndentingNewLine]", 
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"d3", " ", "H"}], "-", "H"}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"d3", "=", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "*", 
     RowBox[{"Sin", "[", "\[Alpha]", "]"}], "*", "w3"}]}], ";"}], 
  "\[IndentingNewLine]", 
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{
     RowBox[{"d5", " ", "w", 
      RowBox[{"(", "NH", ")"}]}], "-", "H"}], ",", " ", 
    RowBox[{"\[Beta]", " ", "is", " ", "angle", " ", "HNH"}]}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"cos\[Beta]", "=", 
   RowBox[{"1.0", "-", 
    RowBox[{"1.5", "*", 
     RowBox[{
      RowBox[{"Sin", "[", "\[Alpha]", "]"}], "^", "2"}]}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"d5", "=", 
   RowBox[{"Sqrt", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"(", 
       RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "^", "2"}], "+", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"P", "+", "Q"}], ")"}], "^", "2"}], "-", 
     RowBox[{"2", "*", 
      RowBox[{"(", 
       RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "*", 
      RowBox[{"(", 
       RowBox[{"P", "+", "Q"}], ")"}], "*", "cos\[Beta]"}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Veebb", "=", 
   RowBox[{"4.0", "/", "d1"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vnebb", "=", 
   RowBox[{
    RowBox[{"-", "4.0"}], "/", "d5"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Vnnbb", "=", 
    RowBox[{"1.0", "/", "d3"}]}], ";"}], "\[IndentingNewLine]", 
  "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{"bond", "-", 
    RowBox[{"lone", " ", "pair"}]}], "*)"}], "\[IndentingNewLine]", 
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"d2", " ", "w", 
     RowBox[{"(", "NH", ")"}]}], "-", 
    RowBox[{"w", 
     RowBox[{"(", "LP", ")"}]}]}], " ", "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"d2", "=", 
   RowBox[{"Sqrt", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"(", 
       RowBox[{"P", "+", "Q"}], ")"}], "^", "2"}], "+", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"P", "+", "R"}], ")"}], "^", "2"}], "-", 
     RowBox[{"2", "*", 
      RowBox[{"(", 
       RowBox[{"P", "+", "Q"}], ")"}], "*", 
      RowBox[{"(", 
       RowBox[{"P", "+", "R"}], ")"}], "*", 
      RowBox[{"Cos", "[", "\[Alpha]", "]"}]}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Veebp", " ", "=", " ", 
    RowBox[{"4", "/", "d2"}]}], ";"}], "\[IndentingNewLine]", 
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"d4", " ", "w", 
     RowBox[{"(", "LP", ")"}]}], "-", "H"}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"d4", "=", 
   RowBox[{"Sqrt", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"(", 
       RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "^", "2"}], "+", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"P", "+", "R"}], ")"}], "^", "2"}], "-", 
     RowBox[{"2", "*", 
      RowBox[{"(", 
       RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "*", 
      RowBox[{"(", 
       RowBox[{"P", "+", "R"}], ")"}], "*", 
      RowBox[{"Cos", "[", "\[Alpha]", "]"}]}]}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"Vnebp", " ", "=", 
    RowBox[{
     RowBox[{"-", "2.0"}], "/", "d4"}]}], " ", ";"}], 
  StyleBox["\[IndentingNewLine]", "Text",
   FontFamily->"Arial Narrow"], 
  StyleBox["\[IndentingNewLine]", "Text",
   FontFamily->"Arial Narrow"], 
  StyleBox[
   RowBox[{"(*", 
    RowBox[{
     RowBox[{"lone", " ", "pair"}], "-", 
     RowBox[{"lone", " ", "pair"}]}], "*)"}], "Text",
   FontFamily->"Arial Narrow"], 
  StyleBox["\[IndentingNewLine]",
   FontFamily->"Arial Narrow"], 
  StyleBox[
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{"none", " ", "for", " ", "NH3"}], ",", " ", 
     RowBox[{"but", " ", "for", " ", "H2O", " ", "and", " ", "HF"}]}], " ", 
    "*)"}], "Text",
   FontFamily->"Arial Narrow"], 
  StyleBox["\[IndentingNewLine]",
   FontFamily->"Arial Narrow"], 
  StyleBox[
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{
     "H2O", " ", "has", " ", "two", " ", "independent", " ", "angles", " ", 
      "as", " ", 
      RowBox[{"variables", ":", " ", 
       RowBox[{"H", "-", "O", "-", 
        RowBox[{"H", " ", "and", " ", "LP"}], "-", "O", "-", "LP"}]}]}], ",", 
     " ", 
     RowBox[{
      RowBox[{"or", " ", "LP"}], "-", "O", "-", "H"}]}], " ", "*)"}], "Text",
   FontFamily->"Arial Narrow"], "\[IndentingNewLine]", 
  StyleBox[
   RowBox[{"(*", " ", 
    RowBox[{
     RowBox[{
     "HF", " ", "is", " ", "identical", " ", "to", " ", "NH3", " ", "with", 
      " ", 
      RowBox[{"LP", "/", "bond"}], " ", "reversed"}], ",", " ", 
     RowBox[{"one", " ", "angle"}]}], " ", "*)"}], "Text",
   FontFamily->"Arial Narrow"], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"(*", 
   RowBox[{"sum", " ", "terms"}], "*)"}]}]}], "Input",
 CellChangeTimes->{{3.5661428484442425`*^9, 3.5661428783026953`*^9}, {
   3.5661430328053665`*^9, 3.5661430369081736`*^9}, {3.5661430998854847`*^9, 
   3.5661431383537183`*^9}, {3.566143180801393*^9, 3.5661432248645825`*^9}, {
   3.566143288683233*^9, 3.5661432893462706`*^9}, 3.566143344240477*^9, 
   3.566143438043442*^9}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"T", "=", 
   RowBox[{"Tc", "+", "           ", 
    RowBox[{"3", "*", "Tb"}], "+", "      ", "Tp"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vne", "=", 
   RowBox[{"Vnec", "+", 
    RowBox[{"3", "*", "Vneb"}], "+", "               ", 
    RowBox[{"3", "*", "Vnecb"}], "+", "Vnecp", "+", 
    RowBox[{"3", "*", "Vnebb"}], "+", 
    RowBox[{"3", "*", "Vnebp"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vee", "=", 
   RowBox[{"Veec", "+", 
    RowBox[{"3", "*", "Veeb"}], "+", " ", "Veep", "+", 
    RowBox[{"3", "*", "Veecb"}], "+", "Veecp", "+", 
    RowBox[{"3", "*", "Veebb"}], "+", 
    RowBox[{"3", "*", "Veebp"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vnn", "=", "                                                 ", 
   RowBox[{
    RowBox[{"3", "*", "Vnncb"}], "+", "                 ", 
    RowBox[{"3", "*", "Vnnbb"}]}]}], ";"}], "\[IndentingNewLine]"}], "Input",
 CellChangeTimes->{{3.5661428484442425`*^9, 3.5661428783026953`*^9}, {
   3.5661430328053665`*^9, 3.5661430369081736`*^9}, {3.5661430998854847`*^9, 
   3.5661431383537183`*^9}, {3.566143180801393*^9, 3.5661432248645825`*^9}, {
   3.566143288683233*^9, 3.5661432893462706`*^9}, 3.566143344240477*^9, {
   3.5661435118159714`*^9, 3.5661435187891836`*^9}, {3.5661470921646585`*^9, 
   3.5661471085134873`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"(*", 
   RowBox[{
    RowBox[{"Parameters", ":", " ", "G3"}], "//", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"6", "-", 
        RowBox[{"311", "G", 
         RowBox[{"(", 
          RowBox[{"d", ",", "p"}], ")"}], " ", "can", " ", "be", " ", "read", 
         " ", "for", " ", "LiH"}]}], " ", "..."}], " ", "HF", 
      "\[IndentingNewLine]", "in", " ", "table", " ", "from", " ", 
      RowBox[{"www", ".", "kimball"}]}], "-", 
     RowBox[{
      RowBox[{
       RowBox[{"model", ".", "org"}], "/", "Kimball"}], "/", 
      RowBox[{"params", ".", "xls"}]}]}]}], " ", "*)"}], 
  "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{"par", "=", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"k1", "\[Rule]", "0.95894892"}], ",", 
      RowBox[{"k2", "\[Rule]", "1.34927913"}], ",", 
      RowBox[{"k3", "\[Rule]", "1.23272312"}], ",", 
      RowBox[{"s1", "\[Rule]", "0.42320792"}], ",", 
      RowBox[{"s2", "\[Rule]", "0.29390809"}], ",", 
      RowBox[{"s3", "\[Rule]", "0.39204779"}]}], "}"}]}], ";"}]}]], "Input",
 CellChangeTimes->{{3.5661428484442425`*^9, 3.5661428783026953`*^9}, {
  3.5661430328053665`*^9, 3.5661430369081736`*^9}, {3.5661430998854847`*^9, 
  3.5661431383537183`*^9}, {3.566143180801393*^9, 3.5661432248645825`*^9}, {
  3.566143288683233*^9, 3.5661432893462706`*^9}, {3.566143344240477*^9, 
  3.566143371150524*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"func", "=", 
   RowBox[{
    RowBox[{"T", "+", "Vne", "+", "Vee", "+", "Vnn"}], "/.", "par"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"t", "=", 
  RowBox[{"FindMinimum", "[", 
   RowBox[{"func", ",", 
    RowBox[{"{", 
     RowBox[{"P", ",", "0.2125"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"Q", ",", "1.12"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"R", ",", " ", "1.355"}], "}"}], ",", 
    RowBox[{"{", 
     RowBox[{"S", ",", "0.58"}], "}"}], ",", " ", 
    RowBox[{"{", 
     RowBox[{"\[Alpha]", ",", "1.97"}], "}"}], ",", 
    RowBox[{"MaxIterations", "\[Rule]", "500"}]}], 
   "]"}]}], "\[IndentingNewLine]"}], "Input",
 CellChangeTimes->{{3.5661428484442425`*^9, 3.5661428783026953`*^9}, {
  3.5661430328053665`*^9, 3.5661430369081736`*^9}, {3.5661430998854847`*^9, 
  3.5661431383537183`*^9}, {3.566143180801393*^9, 3.5661432248645825`*^9}, {
  3.566143288683233*^9, 3.5661432893462706`*^9}, {3.566143344240477*^9, 
  3.5661433819769435`*^9}}],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"-", "56.50693567896597`"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"P", "\[Rule]", "0.21255884296750083`"}], ",", 
     RowBox[{"Q", "\[Rule]", "1.1215796462307126`"}], ",", 
     RowBox[{"R", "\[Rule]", "1.3545219025935082`"}], ",", 
     RowBox[{"S", "\[Rule]", "0.5794206077585493`"}], ",", 
     RowBox[{"\[Alpha]", "\[Rule]", "1.9706412301331597`"}]}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{{3.5661466976555657`*^9, 3.5661467183100023`*^9}, 
   3.566146844592224*^9, 3.566146877617482*^9, 3.566146938785189*^9, 
   3.566146993166885*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"u", "=", 
   RowBox[{"t", "[", 
    RowBox[{"[", "2", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"Vne", "/.", "u"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Vee", "/.", "u"}], "/.", "par"}], "\[IndentingNewLine]", 
 RowBox[{"Vnn", "/.", "u"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{"Vne", "+", "Vee", "+", "Vnn"}], ")"}], "/", "T"}], "/.", "u"}], 
  "/.", "par"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "*", "0.529177"}], "/.", "u"}],
   "\[IndentingNewLine]", 
  RowBox[{"(*", " ", 
   RowBox[{"angle", " ", "HNH"}], " ", "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{
    RowBox[{"180", "/", "\[Pi]"}], "*", 
    RowBox[{"ArcCos", "[", "cos\[Beta]", "]"}]}], "/.", "u"}], 
  "\[IndentingNewLine]", 
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"angle", " ", "LP"}], "-", "N", "-", "H"}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"180", "/", "\[Pi]"}], "*", "\[Alpha]"}], " ", "/.", " ", 
  "u"}], "\[IndentingNewLine]", 
 RowBox[{"d1", " ", "/.", "u"}], "\[IndentingNewLine]", 
 RowBox[{"d3", " ", "/.", "u"}], "\[IndentingNewLine]", 
 RowBox[{"d5", " ", "/.", "u"}], "\[IndentingNewLine]", 
 RowBox[{"d2", " ", "/.", "u"}], "\[IndentingNewLine]", 
 RowBox[{"d4", " ", "/.", "u"}], "\[IndentingNewLine]"}], "Input",
 CellChangeTimes->{{3.5661428484442425`*^9, 3.5661428783026953`*^9}, {
  3.5661430328053665`*^9, 3.5661430369081736`*^9}, {3.5661430998854847`*^9, 
  3.5661431383537183`*^9}, {3.566143180801393*^9, 3.5661432248645825`*^9}, {
  3.566143288683233*^9, 3.5661432893462706`*^9}, {3.566143344240477*^9, 
  3.5661433961729684`*^9}}],

Cell[BoxData[
 RowBox[{"-", "156.31115252225578`"}]], "Output",
 CellChangeTimes->{{3.5661466976555657`*^9, 3.566146718325602*^9}, 
   3.5661468446078243`*^9, 3.566146877617482*^9, 3.5661469388007894`*^9, 
   3.5661469931824846`*^9}],

Cell[BoxData["31.340309455040384`"], "Output",
 CellChangeTimes->{{3.5661466976555657`*^9, 3.566146718325602*^9}, 
   3.5661468446078243`*^9, 3.566146877617482*^9, 3.5661469388007894`*^9, 
   3.5661469931824846`*^9}],

Cell[BoxData["11.956971691023773`"], "Output",
 CellChangeTimes->{{3.5661466976555657`*^9, 3.566146718325602*^9}, 
   3.5661468446078243`*^9, 3.566146877617482*^9, 3.5661469388007894`*^9, 
   3.5661469931824846`*^9}],

Cell[BoxData[
 RowBox[{"-", "1.999999999676859`"}]], "Output",
 CellChangeTimes->{{3.5661466976555657`*^9, 3.566146718325602*^9}, 
   3.5661468446078243`*^9, 3.566146877617482*^9, 3.5661469388007894`*^9, 
   3.5661469931824846`*^9}],

Cell[BoxData["1.0126114622502889`"], "Output",
 CellChangeTimes->{{3.5661466976555657`*^9, 3.566146718325602*^9}, 
   3.5661468446078243`*^9, 3.566146877617482*^9, 3.5661469388007894`*^9, 
   3.5661469931824846`*^9}],

Cell[BoxData["105.8248111138388`"], "Output",
 CellChangeTimes->{{3.5661466976555657`*^9, 3.566146718325602*^9}, 
   3.5661468446078243`*^9, 3.566146877617482*^9, 3.5661469388007894`*^9, 
   3.5661469931824846`*^9}],

Cell[BoxData["112.90942542109883`"], "Output",
 CellChangeTimes->{{3.5661466976555657`*^9, 3.566146718325602*^9}, 
   3.5661468446078243`*^9, 3.566146877617482*^9, 3.5661469388007894`*^9, 
   3.5661469931824846`*^9}],

Cell[BoxData["2.128523276784143`"], "Output",
 CellChangeTimes->{{3.5661466976555657`*^9, 3.566146718325602*^9}, 
   3.5661468446078243`*^9, 3.566146877617482*^9, 3.5661469388007894`*^9, 
   3.566146993198085*^9}],

Cell[BoxData["3.0529477354501084`"], "Output",
 CellChangeTimes->{{3.5661466976555657`*^9, 3.566146718325602*^9}, 
   3.5661468446078243`*^9, 3.566146877617482*^9, 3.5661469388007894`*^9, 
   3.566146993198085*^9}],

Cell[BoxData["2.6141917600677806`"], "Output",
 CellChangeTimes->{{3.5661466976555657`*^9, 3.566146718325602*^9}, 
   3.5661468446078243`*^9, 3.566146877617482*^9, 3.5661469388007894`*^9, 
   3.566146993198085*^9}],

Cell[BoxData["2.421443002175422`"], "Output",
 CellChangeTimes->{{3.5661466976555657`*^9, 3.566146718325602*^9}, 
   3.5661468446078243`*^9, 3.566146877617482*^9, 3.5661469388007894`*^9, 
   3.566146993198085*^9}],

Cell[BoxData["2.9072482741647896`"], "Output",
 CellChangeTimes->{{3.5661466976555657`*^9, 3.566146718325602*^9}, 
   3.5661468446078243`*^9, 3.566146877617482*^9, 3.5661469388007894`*^9, 
   3.566146993198085*^9}]
}, Open  ]],

Cell[BoxData[{
 RowBox[{
  RowBox[{"wd", " ", "=", " ", 
   RowBox[{
    RowBox[{"Sin", "[", "\[Alpha]", "]"}], " ", "/.", " ", "u"}]}], ";", "  ", 
  RowBox[{"wc", "=", 
   RowBox[{
    RowBox[{"Cos", "[", "\[Alpha]", "]"}], " ", "/.", " ", "u"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"Projection", " ", "onto", " ", "HHH"}], "-", "plane"}], " ", 
   "*)"}]}]}], "Input",
 CellChangeTimes->{{3.5661428484442425`*^9, 3.5661428783026953`*^9}, {
  3.5661430328053665`*^9, 3.5661430369081736`*^9}, {3.5661430998854847`*^9, 
  3.5661431383537183`*^9}, {3.566143180801393*^9, 3.5661432248645825`*^9}, {
  3.566143288683233*^9, 3.5661432893462706`*^9}, {3.566143344240477*^9, 
  3.566143410119393*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"plot1", "=", 
   RowBox[{
    RowBox[{"Graphics", "[", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"Circle", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"0", ",", "0"}], "}"}], ",", "P"}], "]"}], ",", 
       RowBox[{"Disk", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"0", ",", "0"}], "}"}], ",", "0.1"}], "]"}], ",", 
       RowBox[{"Circle", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"0", ",", "0"}], "}"}], ",", "R"}], "]"}], ",", 
       RowBox[{"Circle", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{
            RowBox[{"-", "wd"}], "*", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{"P", "+", "Q"}], ")"}], "/", "2"}]}], ",", 
           RowBox[{"wd", "*", "w3", "*", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{"P", "+", "Q"}], ")"}], "/", "2"}]}]}], "}"}], ",", 
         "Q"}], "]"}], ",", 
       RowBox[{"Circle", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{
            RowBox[{"-", "wd"}], "*", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{"P", "+", "Q"}], ")"}], "/", "2"}]}], ",", 
           RowBox[{
            RowBox[{"-", "wd"}], "*", "w3", "*", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{"P", "+", "Q"}], ")"}], "/", "2"}]}]}], "}"}], ",", 
         "Q"}], "]"}], ",", 
       RowBox[{"Circle", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{"wd", "*", 
            RowBox[{"(", 
             RowBox[{"P", "+", "Q"}], ")"}]}], ",", "0"}], "}"}], ",", "Q"}], 
        "]"}], ",", 
       RowBox[{"Disk", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{
            RowBox[{"-", "wd"}], "*", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "/", "2"}]}], ",", 
           RowBox[{"wd", "*", "w3", "*", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "/", "2"}]}]}], "}"}],
          ",", "0.1"}], "]"}], ",", 
       RowBox[{"Disk", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{
            RowBox[{"-", "wd"}], "*", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "/", "2"}]}], ",", 
           RowBox[{
            RowBox[{"-", "wd"}], "*", "w3", "*", 
            RowBox[{
             RowBox[{"(", 
              RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "/", "2"}]}]}], "}"}],
          ",", "0.1"}], "]"}], ",", 
       RowBox[{"Disk", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{
           RowBox[{"wd", "*", 
            RowBox[{"(", 
             RowBox[{"P", "+", "Q", "+", "S"}], ")"}]}], ",", "0"}], "}"}], 
         ",", "0.1"}], "]"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"Thickness", "[", "0.012", "]"}], ",", 
         RowBox[{"Line", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{"0", ",", "0"}], "}"}], ",", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{"wd", "*", 
               RowBox[{"(", 
                RowBox[{"P", "+", "Q", "+", "S"}], ")"}]}], ",", "0"}], 
             "}"}]}], "}"}], "]"}], ",", 
         RowBox[{"Line", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{"0", ",", "0"}], "}"}], ",", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{
               RowBox[{"-", "wd"}], "*", 
               RowBox[{
                RowBox[{"(", 
                 RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "/", "2"}]}], ",", 
              RowBox[{"wd", "*", "w3", "*", 
               RowBox[{
                RowBox[{"(", 
                 RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "/", "2"}]}]}], 
             "}"}]}], "}"}], "]"}], ",", 
         RowBox[{"Line", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{"0", ",", "0"}], "}"}], ",", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{
               RowBox[{"-", "wd"}], "*", 
               RowBox[{
                RowBox[{"(", 
                 RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "/", "2"}]}], ",", 
              RowBox[{
               RowBox[{"-", "wd"}], "*", "w3", "*", 
               RowBox[{
                RowBox[{"(", 
                 RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "/", "2"}]}]}], 
             "}"}]}], "}"}], "]"}]}], "}"}]}], "}"}], "]"}], "/.", "u"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"Show", "[", 
  RowBox[{"plot1", ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"AspectRatio", "\[Rule]", "Automatic"}], ",", 
     RowBox[{"PlotRange", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"-", "3"}], ",", "3"}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"-", "3"}], ",", "3"}], "}"}]}], "}"}]}], ",", 
     RowBox[{"Axes", "\[Rule]", "True"}], ",", 
     RowBox[{"GridLines", "\[Rule]", "Automatic"}], ",", 
     RowBox[{"Frame", "\[Rule]", "True"}]}], "}"}]}], 
  "]"}], "\[IndentingNewLine]"}], "Input",
 CellChangeTimes->{{3.5661428484442425`*^9, 3.5661428783026953`*^9}, {
  3.5661430328053665`*^9, 3.5661430369081736`*^9}, {3.5661430998854847`*^9, 
  3.5661431383537183`*^9}, {3.566143180801393*^9, 3.5661432248645825`*^9}, {
  3.566143288683233*^9, 3.5661432893462706`*^9}, {3.566143344240477*^9, 
  3.566143410119393*^9}}],

Cell[BoxData[
 GraphicsBox[{CircleBox[{0, 0}, 0.21255884296750083`], DiskBox[{0, 0}, 0.1], 
   CircleBox[{0, 0}, 1.3545219025935082`], 
   CircleBox[{-0.6144517434138547, 1.0642616383920716`}, 1.1215796462307126`],
    CircleBox[{-0.6144517434138547, -1.0642616383920716`}, 
    1.1215796462307126`], 
   CircleBox[{1.2289034868277093`, 0}, 1.1215796462307126`], 
   DiskBox[{-0.8813100984419893, 1.5264738677250542`}, 0.1], 
   DiskBox[{-0.8813100984419893, -1.5264738677250542`}, 0.1], 
   DiskBox[{1.7626201968839785`, 0}, 0.1], 
   {Thickness[0.012], LineBox[{{0, 0}, {1.7626201968839785`, 0}}], 
    LineBox[{{0, 0}, {-0.8813100984419893, 1.5264738677250542`}}], 
    LineBox[{{0, 0}, {-0.8813100984419893, -1.5264738677250542`}}]}},
  AspectRatio->Automatic,
  Axes->True,
  Frame->True,
  GridLines->Automatic,
  PlotRange->{{-3, 3}, {-3, 3}}]], "Output",
 CellChangeTimes->{{3.566146697702366*^9, 3.566146718356802*^9}, 
   3.566146844639024*^9, 3.566146877648682*^9, 3.5661469388319893`*^9, 
   3.566146993213685*^9}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"plot3", " ", "=", " ", 
   RowBox[{
    RowBox[{"Graphics3D", "[", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"Sphere", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", " ", "P"}], "]"}], 
       ",", 
       RowBox[{"Sphere", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"0", ",", "0", ",", "0"}], "}"}], ",", " ", "0.1"}], "]"}], 
       ",", " ", 
       RowBox[{"Sphere", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"0", ",", "0", ",", 
           RowBox[{"P", "+", "R"}]}], "}"}], ",", " ", "R"}], "]"}], ",", " ",
        "\[IndentingNewLine]", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"Opacity", "[", "0.5", "]"}], ",", 
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{
              RowBox[{"-", "wd"}], "*", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "Q"}], ")"}], "/", "2"}]}], ",", 
             " ", 
             RowBox[{"wd", "*", "w3", "*", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "Q"}], ")"}], "/", "2"}]}], ",", 
             RowBox[{"wc", "*", 
              RowBox[{"(", 
               RowBox[{"P", "+", "Q"}], ")"}]}]}], "}"}], ",", " ", "Q"}], 
          "]"}], ",", " ", "\[IndentingNewLine]", 
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{
              RowBox[{"-", "wd"}], "*", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "Q"}], ")"}], "/", "2"}]}], ",", 
             " ", 
             RowBox[{
              RowBox[{"-", "wd"}], "*", "w3", "*", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "Q"}], ")"}], "/", "2"}]}], ",", 
             RowBox[{"wc", "*", 
              RowBox[{"(", 
               RowBox[{"P", "+", "Q"}], ")"}]}]}], "}"}], ",", " ", "Q"}], 
          "]"}], ",", " ", 
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{"wd", "*", 
              RowBox[{"(", 
               RowBox[{"P", " ", "+", " ", "Q"}], ")"}]}], ",", " ", "0", ",", 
             RowBox[{"wc", "*", 
              RowBox[{"(", 
               RowBox[{"P", "+", "Q"}], ")"}]}]}], "}"}], ",", " ", "Q"}], 
          "]"}]}], "}"}], ",", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"Darker", "[", "Red", "]"}], ",", "\[IndentingNewLine]", 
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{
              RowBox[{"-", "wd"}], "*", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "Q", " ", "+", " ", "S"}], ")"}], 
               "/", "2"}]}], ",", " ", 
             RowBox[{"wd", "*", "w3", "*", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "Q", " ", "+", " ", "S"}], ")"}], 
               "/", "2"}]}], ",", 
             RowBox[{"wc", "*", 
              RowBox[{"(", 
               RowBox[{"P", "+", "Q", "+", "S"}], ")"}]}]}], "}"}], ",", " ", 
           "0.1"}], "]"}], ",", "\[IndentingNewLine]", 
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{
              RowBox[{"-", "wd"}], "*", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "Q", " ", "+", " ", "S"}], ")"}], 
               "/", "2"}]}], ",", " ", 
             RowBox[{
              RowBox[{"-", "wd"}], "*", "w3", "*", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"P", " ", "+", " ", "Q", " ", "+", " ", "S"}], ")"}], 
               "/", "2"}]}], ",", 
             RowBox[{"wc", "*", 
              RowBox[{"(", 
               RowBox[{"P", "+", "Q", "+", "S"}], ")"}]}]}], "}"}], ",", " ", 
           "0.1"}], "]"}], ",", "\[IndentingNewLine]", 
         RowBox[{"Sphere", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{"wd", "*", 
              RowBox[{"(", 
               RowBox[{"P", " ", "+", " ", "Q", " ", "+", " ", "S"}], ")"}]}],
              ",", " ", "0", ",", 
             RowBox[{"wc", "*", 
              RowBox[{"(", 
               RowBox[{"P", "+", "Q", "+", "S"}], ")"}]}]}], "}"}], ",", " ", 
           "0.1"}], "]"}]}], "}"}]}], "}"}], "]"}], " ", "/.", " ", "u"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"Show", "[", 
  RowBox[{"plot3", ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"AspectRatio", " ", "->", " ", "Automatic"}], ",", " ", 
     RowBox[{"Boxed", " ", "\[Rule]", " ", "False"}]}], "}"}]}], 
  "]"}]}], "Input",
 CellChangeTimes->{{3.5661464147646685`*^9, 3.566146439287912*^9}, {
   3.566146505400828*^9, 3.566146609468611*^9}, 3.5661466450210733`*^9, {
   3.5661467117267904`*^9, 3.5661467122883916`*^9}, {3.566146817869377*^9, 
   3.5661468378998117`*^9}, {3.5661468705194693`*^9, 
   3.5661468715646715`*^9}, {3.5661469228107615`*^9, 
   3.5661469312971764`*^9}, {3.5661469641976337`*^9, 3.5661469774888573`*^9}}],

Cell[BoxData[
 Graphics3DBox[{SphereBox[{0, 0, 0}, 0.21255884296750083`], 
   SphereBox[{0, 0, 0}, 0.1], 
   SphereBox[{0, 0, 1.5670807455610092`}, 1.3545219025935082`], 
   {Opacity[0.5], 
    SphereBox[{-0.6144517434138547, 1.0642616383920716`, -0.5193474062925403},
      1.1215796462307126`], 
    SphereBox[{-0.6144517434138547, -1.0642616383920716`, \
-0.5193474062925403}, 1.1215796462307126`], 
    SphereBox[{1.2289034868277093`, 0, -0.5193474062925403}, 
     1.1215796462307126`]}, 
   {RGBColor[
     NCache[
      Rational[2, 3], 0.6666666666666666], 0, 0], 
    SphereBox[{-0.8813100984419893, 1.5264738677250542`, -0.744901643898485}, 
     0.1], SphereBox[{-0.8813100984419893, -1.5264738677250542`, \
-0.744901643898485}, 0.1], 
    SphereBox[{1.7626201968839785`, 0, -0.744901643898485}, 0.1]}},
  AspectRatio->Automatic,
  AutomaticImageSize->True,
  Boxed->False,
  ImageSize->{380.8575719117401, 345.1860297507955},
  ViewPoint->{-2.1981426235710373`, 2.549462380819429, 0.34410837715284837`},
  ViewVertical->{-0.4042312862442738, 0.3715799874092275, 
   0.8614825214204245}]], "Output",
 CellChangeTimes->{3.566146877679882*^9, 3.5661469388475895`*^9, 
  3.566146993244885*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{"(*", " ", 
  RowBox[{
   RowBox[{"Projection", " ", "onto", " ", "LP"}], "-", "HH", "-", "plane"}], 
  " ", "*)"}]], "Input",
 CellChangeTimes->{{3.5661428484442425`*^9, 3.5661428783026953`*^9}, {
  3.5661430328053665`*^9, 3.5661430369081736`*^9}, {3.5661430998854847`*^9, 
  3.5661431383537183`*^9}, {3.566143180801393*^9, 3.5661432248645825`*^9}, {
  3.566143288683233*^9, 3.5661432893462706`*^9}, {3.566143344240477*^9, 
  3.5661434217882133`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"plot2", "=", 
    RowBox[{
     RowBox[{"Graphics", "[", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"Circle", "[", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"0", ",", "0"}], "}"}], ",", "P"}], "]"}], ",", 
        RowBox[{"Disk", "[", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"0", ",", "0"}], "}"}], ",", "0.1"}], "]"}], ",", 
        RowBox[{"Circle", "[", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"0", ",", 
            RowBox[{"P", "+", "R"}]}], "}"}], ",", "R"}], "]"}], ",", 
        RowBox[{"Circle", "[", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"0", ",", 
            RowBox[{"P", "+", "R"}]}], "}"}], ",", "0.08"}], "]"}], ",", 
        RowBox[{"Circle", "[", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{
            RowBox[{"wd", "*", 
             RowBox[{"(", 
              RowBox[{"P", "+", "Q"}], ")"}]}], ",", 
            RowBox[{"wc", "*", 
             RowBox[{"(", 
              RowBox[{"P", "+", "Q"}], ")"}]}]}], "}"}], ",", "Q"}], "]"}], 
        ",", 
        RowBox[{"Disk", "[", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{
            RowBox[{"wd", "*", 
             RowBox[{"(", 
              RowBox[{"P", "+", "Q", "+", "S"}], ")"}]}], ",", 
            RowBox[{"wc", "*", 
             RowBox[{"(", 
              RowBox[{"P", "+", "Q", "+", "S"}], ")"}]}]}], "}"}], ",", 
          "0.1"}], "]"}], ",", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Dashing", "[", 
           RowBox[{"{", "0.02", "}"}], "]"}], ",", 
          RowBox[{"Circle", "[", 
           RowBox[{
            RowBox[{"{", 
             RowBox[{
              RowBox[{
               RowBox[{"-", "wd"}], "*", 
               RowBox[{
                RowBox[{"(", 
                 RowBox[{"P", "+", "Q"}], ")"}], "/", "2"}]}], ",", 
              RowBox[{"wc", "*", 
               RowBox[{"(", 
                RowBox[{"P", "+", "Q"}], ")"}]}]}], "}"}], ",", "Q"}], 
           "]"}]}], "}"}], ",", 
        RowBox[{"Disk", "[", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{
            RowBox[{
             RowBox[{"-", "wd"}], "*", 
             RowBox[{
              RowBox[{"(", 
               RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "/", "2"}]}], ",", 
            RowBox[{"wc", "*", 
             RowBox[{"(", 
              RowBox[{"P", "+", "Q", "+", "S"}], ")"}]}]}], "}"}], ",", 
          "0.1"}], "]"}], ",", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Thickness", "[", "0.012", "]"}], ",", 
          RowBox[{"Line", "[", 
           RowBox[{"{", 
            RowBox[{
             RowBox[{"{", 
              RowBox[{"0", ",", "0"}], "}"}], ",", 
             RowBox[{"{", 
              RowBox[{
               RowBox[{"wd", "*", 
                RowBox[{"(", 
                 RowBox[{"P", "+", "Q", "+", "S"}], ")"}]}], ",", 
               RowBox[{"wc", "*", 
                RowBox[{"(", 
                 RowBox[{"P", "+", "Q", "+", "S"}], ")"}]}]}], "}"}]}], "}"}],
            "]"}], ",", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"Dashing", "[", 
             RowBox[{"{", "0.02", "}"}], "]"}], ",", 
            RowBox[{"Line", "[", 
             RowBox[{"{", 
              RowBox[{
               RowBox[{"{", 
                RowBox[{"0", ",", "0"}], "}"}], ",", 
               RowBox[{"{", 
                RowBox[{
                 RowBox[{
                  RowBox[{"-", "wd"}], "*", 
                  RowBox[{
                   RowBox[{"(", 
                    RowBox[{"P", "+", "Q", "+", "S"}], ")"}], "/", "2"}]}], 
                 ",", 
                 RowBox[{"wc", "*", 
                  RowBox[{"(", 
                   RowBox[{"P", "+", "Q", "+", "S"}], ")"}]}]}], "}"}]}], 
              "}"}], "]"}]}], "}"}], ",", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{"Dashing", "[", 
             RowBox[{"{", 
              RowBox[{"0.02", ",", "0.04"}], "}"}], "]"}], ",", 
            RowBox[{"Line", "[", 
             RowBox[{"{", 
              RowBox[{
               RowBox[{"{", 
                RowBox[{"0", ",", "0"}], "}"}], ",", 
               RowBox[{"{", 
                RowBox[{"0", ",", 
                 RowBox[{"P", "+", "R"}]}], "}"}]}], "}"}], "]"}]}], "}"}]}], 
         " ", "}"}]}], "}"}], "]"}], "/.", "u"}]}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{"Show", "[", 
  RowBox[{"plot2", ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"AspectRatio", "\[Rule]", "Automatic"}], ",", 
     RowBox[{"PlotRange", "\[Rule]", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"-", "3"}], ",", "3"}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"-", "3"}], ",", "3"}], "}"}]}], "}"}]}], ",", 
     RowBox[{"Axes", "\[Rule]", "True"}], ",", 
     RowBox[{"GridLines", "\[Rule]", "Automatic"}], ",", 
     RowBox[{"Frame", "\[Rule]", "True"}]}], "}"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.5661428484442425`*^9, 3.5661428783026953`*^9}, {
  3.5661430328053665`*^9, 3.5661430369081736`*^9}, {3.5661430998854847`*^9, 
  3.5661431383537183`*^9}, {3.566143180801393*^9, 3.5661432248645825`*^9}, {
  3.566143288683233*^9, 3.5661432893462706`*^9}, {3.566143344240477*^9, 
  3.5661434217882133`*^9}}],

Cell[BoxData[
 GraphicsBox[{CircleBox[{0, 0}, 0.21255884296750083`], DiskBox[{0, 0}, 0.1], 
   CircleBox[{0, 1.5670807455610092`}, 1.3545219025935082`], 
   CircleBox[{0, 1.5670807455610092`}, 0.08], 
   CircleBox[{1.2289034868277093`, -0.5193474062925403}, 1.1215796462307126`],
    DiskBox[{1.7626201968839785`, -0.744901643898485}, 0.1], 
   {Dashing[{0.02}], 
    CircleBox[{-0.6144517434138547, -0.5193474062925403}, 
     1.1215796462307126`]}, 
   DiskBox[{-0.8813100984419893, -0.744901643898485}, 0.1], 
   {Thickness[0.012], 
    LineBox[{{0, 0}, {1.7626201968839785`, -0.744901643898485}}], 
    {Dashing[{0.02}], 
     LineBox[{{0, 0}, {-0.8813100984419893, -0.744901643898485}}]}, 
    {Dashing[{0.02, 0.04}], LineBox[{{0, 0}, {0, 1.5670807455610092`}}]}}},
  AspectRatio->Automatic,
  Axes->True,
  Frame->True,
  GridLines->Automatic,
  PlotRange->{{-3, 3}, {-3, 3}}]], "Output",
 CellChangeTimes->{{3.5661466978895664`*^9, 3.5661467184192023`*^9}, 
   3.5661468448574247`*^9, 3.5661468777266817`*^9, 3.5661469388943896`*^9, 
   3.566146993276085*^9}]
}, Open  ]]
},
WindowSize->{757, 847},
WindowMargins->{{Automatic, 360}, {21, Automatic}},
PrintingCopies->1,
PrintingPageRange->{Automatic, Automatic},
PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> False}},
FrontEndVersion->"9.0 for Microsoft Windows (64-bit) (November 20, 2012)",
StyleDefinitions->FrontEnd`FileName[{"Utility"}, "Notepad.nb", 
  CharacterEncoding -> "WindowsANSI"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[557, 20, 1850, 42, 194, "Input"],
Cell[2410, 64, 8899, 285, 1052, "Input"],
Cell[11312, 351, 1365, 30, 112, "Input"],
Cell[12680, 383, 1388, 34, 92, "Input"],
Cell[CellGroupData[{
Cell[14093, 421, 1006, 25, 92, "Input"],
Cell[15102, 448, 615, 14, 30, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[15754, 467, 1786, 46, 332, "Input"],
Cell[17543, 515, 233, 4, 30, "Output"],
Cell[17779, 521, 216, 3, 30, "Output"],
Cell[17998, 526, 216, 3, 30, "Output"],
Cell[18217, 531, 232, 4, 30, "Output"],
Cell[18452, 537, 216, 3, 30, "Output"],
Cell[18671, 542, 215, 3, 30, "Output"],
Cell[18889, 547, 216, 3, 30, "Output"],
Cell[19108, 552, 213, 3, 30, "Output"],
Cell[19324, 557, 214, 3, 30, "Output"],
Cell[19541, 562, 214, 3, 30, "Output"],
Cell[19758, 567, 213, 3, 30, "Output"],
Cell[19974, 572, 214, 3, 30, "Output"]
}, Open  ]],
Cell[20203, 578, 751, 18, 52, "Input"],
Cell[CellGroupData[{
Cell[20979, 600, 5711, 165, 252, "Input"],
Cell[26693, 767, 1026, 20, 379, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[27756, 792, 5320, 141, 172, "Input"],
Cell[33079, 935, 1200, 26, 360, "Output"]
}, Open  ]],
Cell[34294, 964, 475, 9, 31, "Input"],
Cell[CellGroupData[{
Cell[34794, 977, 5434, 152, 252, "Input"],
Cell[40231, 1131, 1066, 22, 379, "Output"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)