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

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

(* CreatedBy='Mathematica 11.2' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[    139323,       2831]
NotebookOptionsPosition[    134166,       2735]
NotebookOutlinePosition[    134629,       2754]
CellTagsIndexPosition[    134586,       2751]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["Constrained 1d optimal control (Prob. 7.15 / Ex. 7.5)", "Section",
 CellChangeTimes->{{3.51389296222151*^9, 3.5138929763455257`*^9}, {
  3.717328102704728*^9, 3.717328106287125*^9}, {3.7934155082946157`*^9, 
  3.7934155199520197`*^9}},ExpressionUUID->"d4a11a05-61dd-43d1-abc1-\
d7d86bb670c5"],

Cell[TextData[{
 "\[Bullet] revised Oct. 26, 2021\n\t\[Dash] improve text formatting (xdot \
\[Rule] ",
 Cell[BoxData[
  FormBox[
   OverscriptBox["x", "."], TraditionalForm]],
  FormatType->TraditionalForm,ExpressionUUID->
  "c74d1e60-b994-479f-bdef-882c21231532"],
 ") and clean  up other comments"
}], "Text",
 CellChangeTimes->{{3.844263240154601*^9, 3.84426328602067*^9}, {
   3.8442633507004004`*^9, 3.844263362737699*^9}, 3.844263415654808*^9, {
   3.844264009416854*^9, 3.844264018655508*^9}},
 Background->GrayLevel[
  0.85],ExpressionUUID->"db176f9e-4b15-4798-9d93-20e823bd6ce7"],

Cell[BoxData[
 RowBox[{
  RowBox[{"Clear", "[", "\"\<Global`*\>\"", "]"}], ";"}]], "Input",
 CellLabel->
  "In[115]:=",ExpressionUUID->"790608db-906b-4d1e-b79a-0bae31efb231"],

Cell[TextData[{
 StyleBox["Optimal control problem has running cost    ",
  FontSize->16],
 Cell[BoxData[
  FormBox[
   RowBox[{"L", "=", 
    RowBox[{
     RowBox[{
      FractionBox["1", "2"], 
      RowBox[{"(", 
       RowBox[{
        SuperscriptBox["x", "2"], "+", 
        SuperscriptBox["u", "2"]}], ")"}], "    ", "integrated", " ", "over", 
      " ", "t"}], " ", "\[Element]", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"0", ",", "\[Infinity]"}], ")"}], "."}]}]}], TraditionalForm]],
  ExpressionUUID->"f259ed0d-ff5d-440c-a341-5d5e43e532cd"],
 "  \n \tEq. of motion is         ",
 Cell[BoxData[
  FormBox[
   OverscriptBox["x", "."], TraditionalForm]],
  FormatType->TraditionalForm,ExpressionUUID->
  "f1d5276f-45bb-4eeb-bafd-3b2f962c20af"],
 " = -x + u,     x(0) = x0.  "
}], "Text",
 CellChangeTimes->{{3.713776883729083*^9, 3.713776898665091*^9}, {
  3.7137790411607656`*^9, 3.7137790598459263`*^9}, {3.717330081960259*^9, 
  3.7173300849584312`*^9}, {3.717398301192227*^9, 3.717398375758176*^9}, {
  3.717398423675498*^9, 3.717398447695437*^9}, {3.8442632077941027`*^9, 
  3.844263233935171*^9}, {3.844264024093274*^9, 3.844264027291473*^9}},
 Background->GrayLevel[
  0.85],ExpressionUUID->"aaaed593-70f9-463e-8aff-74767b12e258"],

Cell[TextData[{
 StyleBox["Unconstrained case, leads to u(t) = -K* x(t), with K* = ",
  FontSize->16],
 Cell[BoxData[
  SqrtBox["2"]],
  CellChangeTimes->{{3.717329279825513*^9, 3.717329351190675*^9}, {
    3.7173294043030767`*^9, 3.717329418993753*^9}, 3.7173294606284723`*^9, 
    3.717329495545548*^9, 3.7173295404003468`*^9, 3.71732970372895*^9, 
    3.717330092483342*^9, {3.717330300848228*^9, 3.717330353044537*^9}, 
    3.717330759643474*^9, 3.717345330531485*^9, 3.717345461733795*^9, 
    3.717347259782928*^9, 3.717394658141789*^9, 3.717397612076123*^9, {
    3.717397855889676*^9, 3.717397937001588*^9}},ExpressionUUID->
  "ce500129-d6e8-43eb-8473-57581d47c5be"],
 StyleBox["-1.",
  FontSize->16]
}], "Text",
 CellChangeTimes->{{3.713776883729083*^9, 3.713776898665091*^9}, {
  3.7137790411607656`*^9, 3.7137790598459263`*^9}, {3.717330081960259*^9, 
  3.7173300849584312`*^9}, {3.717398378062495*^9, 3.7173984118542843`*^9}, {
  3.844263436469726*^9, 3.844263439569756*^9}},
 Background->GrayLevel[
  0.85],ExpressionUUID->"1b4dc240-c08b-4b8e-a9ef-9fb98fb69786"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"j", "[", 
   RowBox[{"\[Tau]_", ",", "x\[Tau]_"}], "]"}], ":=", 
  RowBox[{"Module", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
     "eq", ",", "init", ",", "x", ",", "\[Lambda]", ",", "t", ",", "xs", ",", 
      "\[Lambda]s", ",", "us", ",", "hs"}], "}"}], ",", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"eq", "=", 
      RowBox[{"{", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{"x", "'"}], "[", "t", "]"}], "\[Equal]", 
         RowBox[{
          RowBox[{"-", " ", 
           RowBox[{"x", "[", "t", "]"}]}], "-", 
          RowBox[{"\[Lambda]", "[", "t", "]"}]}]}], ",", " ", 
        "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{
          RowBox[{"\[Lambda]", "'"}], "[", "t", "]"}], "\[Equal]", "  ", 
         RowBox[{
          RowBox[{"\[Lambda]", "[", "t", "]"}], "-", 
          RowBox[{"x", "[", "t", "]"}]}]}]}], "\[IndentingNewLine]", "}"}]}], 
     ";", "\[IndentingNewLine]", 
     RowBox[{"init", "=", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{
         RowBox[{"x", "[", "\[Tau]", "]"}], "\[Equal]", "x\[Tau]"}], ",", 
        RowBox[{
         RowBox[{"\[Lambda]", "[", "\[Infinity]", "]"}], "\[Equal]", "0"}]}], 
       "}"}]}], ";", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"xs", ",", "\[Lambda]s"}], "}"}], "=", 
      RowBox[{
       RowBox[{"DSolveValue", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"eq", ",", "init"}], "}"}], ",", 
         RowBox[{"{", 
          RowBox[{"x", ",", "\[Lambda]"}], "}"}], ",", "t"}], "]"}], "//", 
       "FullSimplify"}]}], ";", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"us", "[", "t_", "]"}], ":=", 
      RowBox[{"-", 
       RowBox[{"\[Lambda]s", "[", "t", "]"}]}]}], ";", "\[IndentingNewLine]", 
     
     RowBox[{
      RowBox[{"hs", "[", "t_", "]"}], ":=", 
      RowBox[{
       RowBox[{
        RowBox[{
         FractionBox["1", "2"], 
         SuperscriptBox[
          RowBox[{"(", 
           RowBox[{
            RowBox[{"xs", "[", "t", "]"}], "-", 
            RowBox[{"\[Lambda]s", "[", "t", "]"}]}], ")"}], "2"]}], "-", 
        SuperscriptBox[
         RowBox[{"\[Lambda]s", "[", "t", "]"}], "2"]}], "//", 
       "FullSimplify"}]}], ";", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"xs", ",", "\[Lambda]s", ",", "us", ",", "hs"}], "}"}]}]}], 
   "]"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"{", 
    RowBox[{"xu", ",", "\[Lambda]u", ",", "uu", ",", "hu"}], "}"}], "=", 
   RowBox[{"j", "[", 
    RowBox[{"\[Tau]", ",", "x\[Tau]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"Grid", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"{", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"xu", "[", "t", "]"}], ",", 
      RowBox[{"Kstar", "=", 
       RowBox[{
        FractionBox[
         RowBox[{"uu", "[", "t", "]"}], 
         RowBox[{"-", 
          RowBox[{"xu", "[", "t", "]"}]}]], "//", "FullSimplify"}]}]}], 
     "\[IndentingNewLine]", "}"}], "}"}], ",", 
   RowBox[{"Spacings", "\[Rule]", "4"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.717328175401455*^9, 3.717328176143611*^9}, {
  3.717328420060809*^9, 3.7173285465722218`*^9}, {3.717328600901026*^9, 
  3.717328638466007*^9}, {3.717328669434742*^9, 3.717328674335753*^9}, {
  3.717329249483741*^9, 3.717329309092194*^9}, {3.717329398691125*^9, 
  3.71732941826471*^9}, {3.717329456074744*^9, 3.717329519296648*^9}, {
  3.717329560907021*^9, 3.7173296008247147`*^9}, {3.7173296861516047`*^9, 
  3.717329699855158*^9}, {3.717330088018229*^9, 3.717330091961581*^9}, {
  3.7173302943580837`*^9, 3.7173303504221888`*^9}, {3.717330752935425*^9, 
  3.717330758181705*^9}, {3.717345407318966*^9, 3.717345421122452*^9}, {
  3.717397848983923*^9, 3.717397954844194*^9}, {3.7173984705675173`*^9, 
  3.7173984740143023`*^9}, {3.844263670769413*^9, 3.844263673670744*^9}, {
  3.844263735871134*^9, 3.844263738614623*^9}},
 CellLabel->
  "In[116]:=",ExpressionUUID->"95b99ef8-1430-4853-9d51-22af877d3b2c"],

Cell[BoxData[
 TagBox[GridBox[{
    {
     RowBox[{
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{
        RowBox[{
         RowBox[{"-", 
          SqrtBox["2"]}], " ", "t"}], "+", 
        RowBox[{
         SqrtBox["2"], " ", "\[Tau]"}]}]], " ", "x\[Tau]"}], 
     RowBox[{
      RowBox[{"-", "1"}], "+", 
      SqrtBox["2"]}]}
   },
   AutoDelete->False,
   GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
   GridBoxSpacings->{"Columns" -> {{4}}}],
  "Grid"]], "Output",
 CellChangeTimes->{{3.717329279825513*^9, 3.717329351190675*^9}, {
   3.7173294043030767`*^9, 3.717329418993753*^9}, 3.7173294606284723`*^9, 
   3.717329495545548*^9, 3.7173295404003468`*^9, 3.71732970372895*^9, 
   3.717330092483342*^9, {3.717330300848228*^9, 3.717330353044537*^9}, 
   3.717330759643474*^9, 3.717345330531485*^9, 3.717345461733795*^9, 
   3.717347259782928*^9, 3.717394658141789*^9, 3.717397612076123*^9, {
   3.717397855889676*^9, 3.717397937001588*^9}, 3.71739847478529*^9, 
   3.717406951010892*^9, 3.7174150217089033`*^9, 3.793905752277104*^9, {
   3.79390580760301*^9, 3.793905818440427*^9}, 3.7939075769393063`*^9, {
   3.793907738260029*^9, 3.7939077602795277`*^9}, {3.793907853651252*^9, 
   3.793907868040987*^9}, 3.823229365053393*^9, 3.844263478458413*^9, 
   3.8442636768434753`*^9, 3.844263741229219*^9, 3.844263950084683*^9, 
   3.8442640453557777`*^9, 3.848356249077745*^9, 3.8483565122847967`*^9},
 CellLabel->
  "Out[118]=",ExpressionUUID->"ea65d8d1-d334-40da-bae9-1b5c4014dcee"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{"xu", "[", "t", "]"}], ",", 
      RowBox[{"\[Lambda]u", "[", "t", "]"}], ",", 
      RowBox[{"uu", "[", "t", "]"}]}], "}"}], "/.", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"\[Tau]", "\[Rule]", "1"}], ",", 
      RowBox[{"x\[Tau]", "\[Rule]", "1"}]}], "}"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"t", ",", "0", ",", "10"}], "}"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7173285515044117`*^9, 3.717328580980174*^9}, {
  3.71732864388236*^9, 3.717328653281889*^9}, {3.717328694159494*^9, 
  3.7173287223613663`*^9}, {3.717329358762452*^9, 3.717329388793722*^9}, {
  3.717329502025976*^9, 3.717329514401091*^9}, {3.7173295472579737`*^9, 
  3.717329548847609*^9}, {3.7173297212922564`*^9, 3.717329726212079*^9}, {
  3.7173303624553633`*^9, 3.717330363565127*^9}, {3.717345422995018*^9, 
  3.717345426074855*^9}},
 CellLabel->
  "In[119]:=",ExpressionUUID->"e5da61f0-dcc7-4f1e-a250-1006a2edb58d"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwVV3c4148Tt7Oy9/x8fHzJiFKk1PtOogjZVPbIloomDYSsJCENFCGjEmVl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       "]], 
      LineBox[CompressedData["
1:eJwVV3k01t8Ttu9l37fX+wqhVKSNzwwKSWSXRJaiSFJKUnwjQpaQrZAQpShL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       "]], LineBox[CompressedData["
1:eJwVV3k0lm8TtmUv+7693lcIpVJK4RkpJBHZkshSKhJKSYpfRJElZCsklFKU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       "]]},
     Annotation[#, "Charting`Private`Tag$48445#1"]& ]}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{All, All},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.717328559979665*^9, 3.717328581422954*^9}, {
   3.7173286458512487`*^9, 3.717328654109706*^9}, {3.7173287045565968`*^9, 
   3.717328723009028*^9}, 3.717328800354147*^9, {3.717329297699938*^9, 
   3.717329312363666*^9}, {3.717329364241433*^9, 3.717329406710894*^9}, 
   3.7173294629159193`*^9, {3.7173294979213743`*^9, 3.71732954974821*^9}, {
   3.717329706372404*^9, 3.7173297275524817`*^9}, 3.717330095275113*^9, 
   3.7173303643387947`*^9, 3.717345330782772*^9, {3.717345457945983*^9, 
   3.717345464212594*^9}, 3.717347265366398*^9, 3.7173946584382763`*^9, 
   3.71739761235614*^9, 3.717406954761183*^9, 3.717415021984788*^9, 
   3.7939057524054823`*^9, {3.793905807737121*^9, 3.7939058185739098`*^9}, 
   3.793907577068549*^9, {3.793907738393031*^9, 3.793907760405367*^9}, {
   3.793907853773752*^9, 3.793907868171547*^9}, 3.82322936519014*^9, 
   3.844263478828094*^9, 3.844263676871272*^9, 3.844263741347385*^9, 
   3.8442639501963987`*^9, 3.844264045467651*^9, 3.848356249340469*^9, 
   3.848356512396867*^9},
 CellLabel->
  "Out[119]=",ExpressionUUID->"cd669a3a-edc1-4f74-9e17-40200c409f2b"]
}, Open  ]],

Cell[TextData[StyleBox["Constrained case",
 FontSize->16]], "Text",
 CellChangeTimes->{{3.713776883729083*^9, 3.713776898665091*^9}, {
  3.7137790411607656`*^9, 3.7137790598459263`*^9}, {3.717330081960259*^9, 
  3.717330101143979*^9}},
 Background->GrayLevel[
  0.85],ExpressionUUID->"adab4b9b-193c-46c1-b3ef-917f524634a0"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"jc", "[", 
   RowBox[{"\[Tau]_", ",", "x0_"}], "]"}], ":=", 
  RowBox[{"Module", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
     "eqx", ",", "initx", ",", "eq\[Lambda]", ",", "init\[Lambda]", ",", "x", 
      ",", "\[Lambda]", ",", "t", ",", "xs", ",", "\[Lambda]s", ",", "us", 
      ",", "hs"}], "}"}], ",", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"eqx", "=", 
      RowBox[{
       RowBox[{
        RowBox[{"x", "'"}], "[", "t", "]"}], "\[Equal]", 
       RowBox[{
        RowBox[{"-", " ", 
         RowBox[{"x", "[", "t", "]"}]}], "-", "1"}]}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"initx", "=", 
      RowBox[{
       RowBox[{"x", "[", "0", "]"}], "\[Equal]", "x0"}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"xs", "=", 
      RowBox[{"DSolveValue", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"eqx", ",", "initx"}], "}"}], ",", "x", ",", "t"}], "]"}]}], 
     ";", "\[IndentingNewLine]", "\[IndentingNewLine]", 
     RowBox[{"eq\[Lambda]", "=", 
      RowBox[{
       RowBox[{
        RowBox[{"\[Lambda]", "'"}], "[", "t", "]"}], "\[Equal]", "  ", 
       RowBox[{
        RowBox[{"\[Lambda]", "[", "t", "]"}], "-", 
        RowBox[{"xs", "[", "t", "]"}]}]}]}], ";", "\[IndentingNewLine]", 
     RowBox[{"init\[Lambda]", "=", 
      RowBox[{
       RowBox[{"\[Lambda]", "[", "\[Tau]", "]"}], "\[Equal]", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          SqrtBox["2"], "-", "1"}], ")"}], 
        RowBox[{"xs", "[", "\[Tau]", "]"}]}]}]}], ";", "  ", 
     RowBox[{"(*", " ", 
      RowBox[{"wrong", " ", "condition", 
       RowBox[{"??", "  ", 
        RowBox[{"\[Lambda]", " ", "not", " ", 
         RowBox[{"continuous", " ", "?"}]}]}]}], "  ", "*)"}], 
     "\[IndentingNewLine]", 
     RowBox[{"\[Lambda]s", "=", 
      RowBox[{
       RowBox[{"DSolveValue", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"eq\[Lambda]", ",", "init\[Lambda]"}], "}"}], ",", 
         "\[Lambda]", ",", "t"}], "]"}], "//", "FullSimplify"}]}], ";", 
     "\[IndentingNewLine]", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"us", "[", "t_", "]"}], ":=", 
      RowBox[{"-", "1"}]}], ";", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"hs", "[", "t_", "]"}], ":=", 
      RowBox[{
       RowBox[{
        RowBox[{
         FractionBox["1", "2"], 
         RowBox[{"(", 
          RowBox[{
           SuperscriptBox[
            RowBox[{"xs", "[", "t", "]"}], "2"], "+", "1"}], ")"}]}], "-", 
        RowBox[{
         RowBox[{"\[Lambda]s", "[", "t", "]"}], 
         RowBox[{"xs", "[", "t", "]"}]}], "-", 
        RowBox[{"\[Lambda]s", "[", "t", "]"}]}], "//", "FullSimplify"}]}], 
     ";", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"xs", ",", "\[Lambda]s", ",", "us", ",", "hs"}], "}"}]}]}], 
   "]"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"{", 
    RowBox[{"xc", ",", "\[Lambda]c", ",", "uc", ",", "hc"}], "}"}], "=", 
   RowBox[{"jc", "[", 
    RowBox[{"\[Tau]", ",", "x0"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"{", 
   RowBox[{
    RowBox[{"xc", "[", "t", "]"}], ",", 
    RowBox[{"\[Lambda]c", "[", "t", "]"}], ",", 
    RowBox[{"uc", "[", "t", "]"}], ",", 
    RowBox[{"hc", "[", "t", "]"}]}], "}"}], "  ", 
  RowBox[{"(*", " ", 
   RowBox[{
    RowBox[{"solution", " ", "for", " ", "\[Lambda]", 
     RowBox[{"(", "t", ")"}], " ", "is", " ", "probably", " ", "wrong"}], ",",
     " ", 
    RowBox[{
    "since", " ", "final", " ", "condition", " ", "may", " ", "be", " ", 
     "wrong"}], ",", " ", 
    RowBox[{"but", " ", "important", " ", "part", " ", "is", " ", "ok"}]}], 
   " ", "*)"}]}], "\[IndentingNewLine]"}], "Input",
 CellChangeTimes->{{3.717330113148654*^9, 3.717330244912578*^9}, {
   3.717330370823106*^9, 3.717330580425313*^9}, {3.7173306171736298`*^9, 
   3.71733064246672*^9}, 3.7173306940942287`*^9, {3.717330766021762*^9, 
   3.7173308420992823`*^9}, {3.717330878210096*^9, 3.7173308787441607`*^9}, {
   3.717331006726824*^9, 3.717331009363298*^9}, {3.717345303552827*^9, 
   3.7173453184875927`*^9}, 3.717347281481401*^9, {3.717394672235299*^9, 
   3.717394693706148*^9}, {3.717395221325636*^9, 3.717395226282857*^9}, {
   3.717397831432582*^9, 3.717397833237953*^9}, {3.717398254232073*^9, 
   3.7173982753979197`*^9}, {3.717398499053525*^9, 3.7173985228861713`*^9}, {
   3.717406700743691*^9, 3.717406714470572*^9}, {3.7174070634034653`*^9, 
   3.7174070681029577`*^9}, {3.793907841014102*^9, 3.793907862032744*^9}},
 CellLabel->
  "In[120]:=",ExpressionUUID->"4e5b696b-05aa-4fd5-b0e1-9323909c7294"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{
    RowBox[{"-", 
     SuperscriptBox["\[ExponentialE]", 
      RowBox[{"-", "t"}]]}], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", "1"}], "+", 
      SuperscriptBox["\[ExponentialE]", "t"], "-", "x0"}], ")"}]}], ",", 
   RowBox[{
    RowBox[{"-", 
     FractionBox["1", "2"]}], " ", 
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{
      RowBox[{"-", "t"}], "-", 
      RowBox[{"2", " ", "\[Tau]"}]}]], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"3", " ", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{"2", " ", "t"}]]}], "-", 
      RowBox[{"2", " ", 
       SqrtBox["2"], " ", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{"2", " ", "t"}]]}], "-", 
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{"2", " ", "\[Tau]"}]], "-", 
      RowBox[{"4", " ", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"2", " ", "t"}], "+", "\[Tau]"}]]}], "+", 
      RowBox[{"2", " ", 
       SqrtBox["2"], " ", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{
         RowBox[{"2", " ", "t"}], "+", "\[Tau]"}]]}], "+", 
      RowBox[{"2", " ", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{"t", "+", 
         RowBox[{"2", " ", "\[Tau]"}]}]]}], "+", 
      RowBox[{"3", " ", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{"2", " ", "t"}]], " ", "x0"}], "-", 
      RowBox[{"2", " ", 
       SqrtBox["2"], " ", 
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{"2", " ", "t"}]], " ", "x0"}], "-", 
      RowBox[{
       SuperscriptBox["\[ExponentialE]", 
        RowBox[{"2", " ", "\[Tau]"}]], " ", "x0"}]}], ")"}]}], ",", 
   RowBox[{"-", "1"}], ",", 
   RowBox[{"1", "+", 
    RowBox[{
     FractionBox["1", "2"], " ", 
     SuperscriptBox["\[ExponentialE]", 
      RowBox[{
       RowBox[{"-", "2"}], " ", "\[Tau]"}]], " ", 
     RowBox[{"(", 
      RowBox[{"1", "+", "x0"}], ")"}], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"2", " ", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"-", "2"}], "+", 
          SqrtBox["2"]}], ")"}], " ", 
        SuperscriptBox["\[ExponentialE]", "\[Tau]"]}], "-", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          RowBox[{"-", "3"}], "+", 
          RowBox[{"2", " ", 
           SqrtBox["2"]}]}], ")"}], " ", 
        RowBox[{"(", 
         RowBox[{"1", "+", "x0"}], ")"}]}]}], ")"}]}]}]}], "}"}]], "Output",
 CellChangeTimes->{{3.717330236328618*^9, 3.7173302455335197`*^9}, {
   3.7173304098693933`*^9, 3.717330419138184*^9}, 3.717330644144805*^9, {
   3.717330694789019*^9, 3.717330699378633*^9}, 3.717330772743012*^9, {
   3.7173308352869177`*^9, 3.717330842725851*^9}, {3.717330879281927*^9, 
   3.7173308823113813`*^9}, 3.717331010508452*^9, 3.717345327094132*^9, 
   3.717345383132056*^9, 3.717345479250423*^9, 3.717349857645793*^9, 
   3.717394659403887*^9, 3.717394722909844*^9, 3.717395227379086*^9, 
   3.717397612868877*^9, {3.7173978144049807`*^9, 3.717397833682288*^9}, 
   3.717406958989955*^9, 3.717407077089994*^9, 3.717415022432081*^9, 
   3.793905752744483*^9, {3.793905807791297*^9, 3.7939058186269712`*^9}, 
   3.7939075771244907`*^9, {3.793907738447974*^9, 3.793907760460849*^9}, {
   3.793907853831521*^9, 3.793907868224464*^9}, 3.823229365561886*^9, 
   3.844263479214201*^9, 3.844263676959737*^9, 3.844263741436152*^9, 
   3.84426395047059*^9, 3.844264045559119*^9, 3.8483562497669697`*^9, 
   3.848356512685095*^9},
 CellLabel->
  "Out[122]=",ExpressionUUID->"595eb70f-9367-4765-8b1f-3bf4f955d904"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"hc1", "=", 
   RowBox[{
    RowBox[{"hc", "[", "t", "]"}], "/.", 
    RowBox[{"x0", "\[Rule]", "5"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"Plot", "[", 
  RowBox[{"hc1", ",", 
   RowBox[{"{", 
    RowBox[{"\[Tau]", ",", "0", ",", "2"}], "}"}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.7174076227707987`*^9, 3.7174077159302053`*^9}},
 CellLabel->
  "In[123]:=",ExpressionUUID->"3e497900-0913-4b1a-85d0-32b1df1ef2ea"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwV13c41e8fx/GjVFpSSUaKsvopVEZU54UUGWVGqMyMlhUqZUt2oQhlh+xR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       "]]},
     Annotation[#, "Charting`Private`Tag$48960#1"]& ]}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0, 2}, {0., 0.580898947360676}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.717407624334036*^9, 3.717407716421907*^9}, 
   3.717415022540372*^9, 3.793905752781229*^9, {3.793905807836681*^9, 
   3.793905818673114*^9}, 3.793907577162901*^9, {3.793907738495203*^9, 
   3.793907760504717*^9}, {3.793907853882284*^9, 3.793907868269562*^9}, 
   3.823229365592943*^9, 3.844263479244513*^9, 3.84426367698606*^9, 
   3.844263741465591*^9, 3.8442639504992228`*^9, 3.844264045596182*^9, 
   3.848356249856998*^9, 3.848356512715629*^9},
 CellLabel->
  "Out[124]=",ExpressionUUID->"bb4b6e6d-40a6-4b97-8193-92b310568429"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FindMinimum", "[", 
  RowBox[{"hc1", ",", 
   RowBox[{"{", 
    RowBox[{"\[Tau]", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7174077444450903`*^9, 3.717407755103365*^9}},
 CellLabel->
  "In[125]:=",ExpressionUUID->"3559b54d-2072-4170-be3a-995135a6e3ae"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"-", "6.661338147750939`*^-16"}], ",", 
   RowBox[{"{", 
    RowBox[{"\[Tau]", "\[Rule]", "0.5638122915929182`"}], "}"}]}], 
  "}"}]], "Output",
 CellChangeTimes->{
  3.717407755568686*^9, 3.717415022654619*^9, 3.793905752796022*^9, {
   3.7939058078720427`*^9, 3.79390581870927*^9}, 3.793907577178174*^9, {
   3.79390773852822*^9, 3.793907760533942*^9}, {3.793907853913208*^9, 
   3.793907868303018*^9}, 3.823229365613751*^9, 3.844263479271471*^9, 
   3.844263676996315*^9, 3.844263741476906*^9, 3.8442639505096693`*^9, 
   3.844264045608116*^9, 3.848356249908265*^9, 3.8483565127361107`*^9},
 CellLabel->
  "Out[125]=",ExpressionUUID->"89df2495-5241-4660-82b2-cff25ed3c302"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"FindRoot", "[", 
  RowBox[{"hc1", ",", 
   RowBox[{"{", 
    RowBox[{"\[Tau]", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7174080430512323`*^9, 3.717408043533704*^9}},
 CellLabel->
  "In[126]:=",ExpressionUUID->"cc056b4a-1cbe-4278-a5cd-b8a64c9e949a"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"\[Tau]", "\[Rule]", "0.5638123200211512`"}], "}"}]], "Output",
 CellChangeTimes->{
  3.717408046764287*^9, 3.717415022889119*^9, 3.7939057528203363`*^9, {
   3.7939058079084473`*^9, 3.793905818745146*^9}, 3.7939075772030354`*^9, {
   3.793907738560073*^9, 3.7939077605441217`*^9}, {3.7939078539445677`*^9, 
   3.793907868312831*^9}, 3.823229365636245*^9, 3.84426347929356*^9, 
   3.844263677013084*^9, 3.8442637414968653`*^9, 3.844263950526655*^9, 
   3.8442640456290407`*^9, 3.848356249929392*^9, 3.8483565127421*^9},
 CellLabel->
  "Out[126]=",ExpressionUUID->"56aeb2c4-5394-4960-90c7-d6a79c963c12"]
}, Open  ]],

Cell[TextData[StyleBox["Compute overall cost function jtot",
 FontSize->16]], "Text",
 CellChangeTimes->{{3.713776883729083*^9, 3.713776898665091*^9}, {
  3.7137790411607656`*^9, 3.7137790598459263`*^9}, {3.717330081960259*^9, 
  3.717330101143979*^9}, {3.717397794543202*^9, 3.717397806653232*^9}},
 Background->GrayLevel[
  0.85],ExpressionUUID->"a8c9d8a0-6a26-42b0-9f32-2deb764d0399"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"j1", "[", "\[Tau]_", "]"}], ":=", 
   RowBox[{
    RowBox[{
     RowBox[{"Integrate", "[", 
      RowBox[{
       RowBox[{
        FractionBox["1", "2"], 
        SuperscriptBox[
         RowBox[{"xc", "[", "t", "]"}], "2"]}], ",", 
       RowBox[{"{", 
        RowBox[{"t", ",", "0", ",", "\[Tau]"}], "}"}]}], "]"}], "+", 
     FractionBox["\[Tau]", "2"]}], "//", "FullSimplify"}]}], ";", 
  RowBox[{"j1", "[", "\[Tau]", "]"}]}]], "Input",
 CellChangeTimes->{{3.717395623589875*^9, 3.717395704610016*^9}, {
  3.717395751850662*^9, 3.717395778177391*^9}, {3.717397364802083*^9, 
  3.717397372320272*^9}},
 CellLabel->
  "In[127]:=",ExpressionUUID->"3939753f-503f-4534-9495-fafff80e4ca3"],

Cell[BoxData[
 RowBox[{
  FractionBox["1", "4"], " ", 
  RowBox[{"(", 
   RowBox[{
    RowBox[{"-", "3"}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "2"}], "+", "x0"}], ")"}], " ", "x0"}], "+", 
    RowBox[{"4", " ", 
     SuperscriptBox["\[ExponentialE]", 
      RowBox[{"-", "\[Tau]"}]], " ", 
     RowBox[{"(", 
      RowBox[{"1", "+", "x0"}], ")"}]}], "-", 
    RowBox[{
     SuperscriptBox["\[ExponentialE]", 
      RowBox[{
       RowBox[{"-", "2"}], " ", "\[Tau]"}]], " ", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"1", "+", "x0"}], ")"}], "2"]}], "+", 
    RowBox[{"4", " ", "\[Tau]"}]}], ")"}]}]], "Output",
 CellChangeTimes->{{3.717397366483968*^9, 3.717397373192608*^9}, 
   3.717397613948403*^9, 3.717415024021392*^9, 3.793905753404464*^9, {
   3.7939058084560337`*^9, 3.793905819301181*^9}, 3.793907577789205*^9, {
   3.793907739111918*^9, 3.7939077611003857`*^9}, {3.793907854506217*^9, 
   3.7939078688637123`*^9}, 3.8232293662390203`*^9, 3.844263479848091*^9, 
   3.844263677519814*^9, 3.844263742013069*^9, 3.844263951052677*^9, 
   3.8442640461629057`*^9, 3.8483562505025587`*^9, 3.848356513255723*^9},
 CellLabel->
  "Out[127]=",ExpressionUUID->"a20aa417-3271-408b-a89d-718a6875808d"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   FractionBox["1", "2"], 
   RowBox[{"(", 
    RowBox[{"1", "+", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{
        RowBox[{"-", "1"}], "+", 
        SqrtBox["2"]}], ")"}], "2"]}], ")"}]}], "//", "Simplify"}]], "Input",
 CellLabel->
  "In[128]:=",ExpressionUUID->"0bb30ede-2d77-4f6d-baa6-20f09e79ea73"],

Cell[BoxData[
 RowBox[{"2", "-", 
  SqrtBox["2"]}]], "Output",
 CellChangeTimes->{
  3.7173973356917963`*^9, 3.717397614254902*^9, 3.717415024195438*^9, 
   3.793905753498043*^9, {3.793905808560999*^9, 3.7939058194053583`*^9}, 
   3.7939075778110523`*^9, {3.793907739210784*^9, 3.793907761123728*^9}, {
   3.793907854624107*^9, 3.793907868888735*^9}, 3.823229366355433*^9, 
   3.844263479932938*^9, 3.8442636775256367`*^9, 3.844263742018214*^9, 
   3.844263951100758*^9, 3.844264046168038*^9, 3.848356250564967*^9, 
   3.84835651329583*^9},
 CellLabel->
  "Out[128]=",ExpressionUUID->"15ca43cd-0564-4f0e-a275-744c60436fbc"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"xc", "[", "\[Tau]", "]"}]], "Input",
 CellChangeTimes->{{3.717398001263749*^9, 3.717398004412529*^9}},
 CellLabel->
  "In[129]:=",ExpressionUUID->"cd799536-73c4-44c3-a0fe-98df452d00ef"],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{"-", "\[Tau]"}]]}], " ", 
  RowBox[{"(", 
   RowBox[{
    RowBox[{"-", "1"}], "+", 
    SuperscriptBox["\[ExponentialE]", "\[Tau]"], "-", "x0"}], 
   ")"}]}]], "Output",
 CellChangeTimes->{
  3.717398005025896*^9, 3.7174150243056383`*^9, 3.793905753506494*^9, {
   3.793905808568519*^9, 3.79390581941469*^9}, 3.7939075779381943`*^9, {
   3.7939077392186203`*^9, 3.7939077612245083`*^9}, {3.793907854630837*^9, 
   3.793907869011365*^9}, 3.823229366362554*^9, 3.844263479938312*^9, 
   3.844263677542004*^9, 3.844263742037436*^9, 3.8442639511071033`*^9, 
   3.8442640461868*^9, 3.848356250572136*^9, 3.848356513302248*^9},
 CellLabel->
  "Out[129]=",ExpressionUUID->"fa0ba084-95ff-4a5d-9b43-15ae394313ab"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"j2", "[", "\[Tau]_", "]"}], ":=", 
   RowBox[{
    RowBox[{"Integrate", "[", 
     RowBox[{
      RowBox[{
       RowBox[{
        RowBox[{"(", 
         RowBox[{"2", "-", 
          SqrtBox["2"]}], ")"}], 
        SuperscriptBox[
         RowBox[{"xu", "[", "t", "]"}], "2"]}], "/.", 
       RowBox[{"x\[Tau]", "\[Rule]", 
        RowBox[{"xc", "[", "\[Tau]", "]"}]}]}], ",", 
      RowBox[{"{", 
       RowBox[{"t", ",", "\[Tau]", ",", "\[Infinity]"}], "}"}]}], "]"}], "//",
     "Simplify"}]}], ";", "  ", 
  RowBox[{"j2", "[", "\[Tau]", "]"}]}]], "Input",
 CellChangeTimes->{{3.717395727109515*^9, 3.7173957431613407`*^9}, {
   3.717395830283972*^9, 3.717395875498472*^9}, {3.717396213570225*^9, 
   3.7173962616768436`*^9}, 3.717396399724082*^9, {3.717397329402767*^9, 
   3.717397354392705*^9}, 3.717397389329647*^9, {3.717397478593897*^9, 
   3.717397489616897*^9}, {3.717398015207714*^9, 3.7173980161592007`*^9}, {
   3.717398800422529*^9, 3.7173988048064003`*^9}},
 CellLabel->
  "In[130]:=",ExpressionUUID->"3e35a4ef-6447-45e7-b83a-0515224099e7"],

Cell[BoxData[
 RowBox[{
  FractionBox["1", "2"], " ", 
  RowBox[{"(", 
   RowBox[{
    RowBox[{"-", "1"}], "+", 
    SqrtBox["2"]}], ")"}], " ", 
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{
    RowBox[{"-", "2"}], " ", "\[Tau]"}]], " ", 
  SuperscriptBox[
   RowBox[{"(", 
    RowBox[{"1", "-", 
     SuperscriptBox["\[ExponentialE]", "\[Tau]"], "+", "x0"}], ")"}], 
   "2"]}]], "Output",
 CellChangeTimes->{
  3.717397355614828*^9, 3.717397391392207*^9, 3.7173974914010487`*^9, 
   3.717397614887624*^9, {3.717398011937645*^9, 3.7173980175135098`*^9}, 
   3.7173988065431623`*^9, 3.7174150250600853`*^9, 3.79390575354639*^9, {
   3.7939058092562933`*^9, 3.79390582006396*^9}, 3.79390757863463*^9, {
   3.793907739879387*^9, 3.793907761890483*^9}, {3.793907855291396*^9, 
   3.793907869673867*^9}, 3.823229366400544*^9, 3.8442634799929237`*^9, 
   3.8442636776674013`*^9, 3.844263742745413*^9, 3.844263951790957*^9, 
   3.844264046836912*^9, 3.848356250664551*^9, 3.848356513984928*^9},
 CellLabel->
  "Out[130]=",ExpressionUUID->"22ede937-5af9-4c1e-996d-2190af07b929"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"jtot", "[", "\[Tau]_", "]"}], ":=", 
   RowBox[{
    RowBox[{
     RowBox[{"j1", "[", "\[Tau]", "]"}], "+", 
     RowBox[{"j2", "[", "\[Tau]", "]"}]}], "//", "Simplify"}]}], ";", 
  RowBox[{"jtot", "[", "\[Tau]", "]"}]}]], "Input",
 CellChangeTimes->{{3.717395883014604*^9, 3.7173959189529333`*^9}, {
  3.717397406530208*^9, 3.717397429882262*^9}},
 CellLabel->
  "In[131]:=",ExpressionUUID->"ee9b5c81-200e-4218-951c-fa93db7576b3"],

Cell[BoxData[
 RowBox[{
  FractionBox["1", "4"], " ", 
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{
    RowBox[{"-", "2"}], " ", "\[Tau]"}]], " ", 
  RowBox[{"(", 
   RowBox[{
    RowBox[{
     RowBox[{"-", "4"}], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "2"}], "+", 
       SqrtBox["2"]}], ")"}], " ", 
     SuperscriptBox["\[ExponentialE]", "\[Tau]"], " ", 
     RowBox[{"(", 
      RowBox[{"1", "+", "x0"}], ")"}]}], "+", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "3"}], "+", 
       RowBox[{"2", " ", 
        SqrtBox["2"]}]}], ")"}], " ", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"1", "+", "x0"}], ")"}], "2"]}], "+", 
    RowBox[{
     SuperscriptBox["\[ExponentialE]", 
      RowBox[{"2", " ", "\[Tau]"}]], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "5"}], "+", 
       RowBox[{"2", " ", 
        SqrtBox["2"]}], "-", 
       RowBox[{"2", " ", "x0"}], "+", 
       SuperscriptBox["x0", "2"], "+", 
       RowBox[{"4", " ", "\[Tau]"}]}], ")"}]}]}], ")"}]}]], "Output",
 CellChangeTimes->{{3.7173974090222597`*^9, 3.717397430577848*^9}, 
   3.717397510023423*^9, 3.7173976152760143`*^9, 3.717398812965094*^9, 
   3.717415025823943*^9, 3.793905753662643*^9, {3.793905809607194*^9, 
   3.793905820409561*^9}, 3.793907579022901*^9, {3.793907740268525*^9, 
   3.7939077622307*^9}, {3.793907855648838*^9, 3.7939078700402946`*^9}, 
   3.823229366519822*^9, 3.8442634800638533`*^9, 3.844263677766756*^9, 
   3.844263743092424*^9, 3.844263952093618*^9, 3.844264047166502*^9, 
   3.848356250735157*^9, 3.848356514282851*^9},
 CellLabel->
  "Out[131]=",ExpressionUUID->"59f89cfe-4ebf-4c2b-8bb6-be664ba608d8"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"jtot1", "=", 
  RowBox[{
   RowBox[{
    RowBox[{"jtot", "[", "\[Tau]", "]"}], "/.", 
    RowBox[{"x0", "\[Rule]", "5"}]}], "//", "FullSimplify"}]}]], "Input",
 CellChangeTimes->{{3.7173959560527554`*^9, 3.717396012482664*^9}, 
   3.717396048017111*^9, {3.7173974143941317`*^9, 3.7173974151434917`*^9}},
 CellLabel->
  "In[132]:=",ExpressionUUID->"928d1d81-73b3-4e15-ac59-b4217f3cc30e"],

Cell[BoxData[
 RowBox[{
  FractionBox["5", "2"], "+", 
  FractionBox["1", 
   SqrtBox["2"]], "+", 
  RowBox[{
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{
     RowBox[{"-", "2"}], " ", "\[Tau]"}]], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"9", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"-", "3"}], "+", 
        RowBox[{"2", " ", 
         SqrtBox["2"]}]}], ")"}]}], "-", 
     RowBox[{"6", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"-", "2"}], "+", 
        SqrtBox["2"]}], ")"}], " ", 
      SuperscriptBox["\[ExponentialE]", "\[Tau]"]}]}], ")"}]}], "+", 
  "\[Tau]"}]], "Output",
 CellChangeTimes->{{3.717395977699731*^9, 3.717396014147008*^9}, 
   3.7173960496088953`*^9, 3.717396272551271*^9, 3.717397435535513*^9, {
   3.717397515807724*^9, 3.717397518869529*^9}, 3.7173976163514967`*^9, 
   3.7173980346359577`*^9, 3.717398818339531*^9, 3.7174150267389927`*^9, 
   3.793905753822913*^9, {3.793905810250949*^9, 3.793905821030664*^9}, 
   3.793907579672336*^9, {3.7939077409441233`*^9, 3.7939077628486423`*^9}, {
   3.79390785626792*^9, 3.7939078706534224`*^9}, 3.823229366696888*^9, 
   3.844263480197328*^9, 3.8442636781594477`*^9, 3.844263743603263*^9, 
   3.844263952605702*^9, 3.844264047610592*^9, 3.8483562508694963`*^9, 
   3.848356514835104*^9},
 CellLabel->
  "Out[132]=",ExpressionUUID->"4aa6d169-d17d-43ed-864a-b775ee7fee8e"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Grid", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"Plot", "[", 
       RowBox[{"jtot1", ",", 
        RowBox[{"{", 
         RowBox[{"\[Tau]", ",", "0.55", ",", "0.58"}], "}"}]}], "]"}], ",", 
      RowBox[{
       RowBox[{"Log", "[", 
        FractionBox[
         RowBox[{"1", "+", "5"}], 
         RowBox[{"2", "+", 
          SqrtBox["2"]}]], "]"}], "//", "N"}], ",", 
      RowBox[{"FindMinimum", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"jtot1", ",", 
          RowBox[{"\[Tau]", "\[GreaterEqual]", "0.5"}]}], "}"}], ",", 
        RowBox[{"{", 
         RowBox[{"\[Tau]", ",", "1"}], "}"}]}], "]"}]}], "}"}], "}"}], ",", 
   RowBox[{"Spacings", "\[Rule]", "2"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7173959263738956`*^9, 3.717395939392333*^9}, 
   3.7173959879630527`*^9, {3.7173960221873007`*^9, 3.717396054025165*^9}, {
   3.717396874239414*^9, 3.717396927292704*^9}, {3.7173975432955837`*^9, 
   3.717397543613328*^9}, {3.717397592027175*^9, 3.717397601362858*^9}, {
   3.717398873126705*^9, 3.7173988920874023`*^9}, {3.717399053286146*^9, 
   3.7173991322165613`*^9}, {3.717415010812557*^9, 3.717415019428589*^9}},
 CellLabel->
  "In[133]:=",ExpressionUUID->"e0785b5f-a269-4fa6-83ef-04d014cd0920"],

Cell[BoxData[
 TagBox[GridBox[{
    {
     GraphicsBox[{{{}, {}, 
        TagBox[
         {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
          Opacity[1.], LineBox[CompressedData["
1:eJwl0nkw3FccAPCNa9FgByt1VISU7bKpuiPqK+iRg7hDhpkwSVDbEkKoZMSs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           "]]},
         Annotation[#, "Charting`Private`Tag$54618#1"]& ]}, {}},
      AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
      Axes->{True, True},
      AxesLabel->{None, None},
      AxesOrigin->{0.55, 5.270918185590109},
      DisplayFunction->Identity,
      Frame->{{False, False}, {False, False}},
      FrameLabel->{{None, None}, {None, None}},
      FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
      GridLines->{None, None},
      GridLinesStyle->Directive[
        GrayLevel[0.5, 0.4]],
      ImagePadding->All,
      Method->{
       "DefaultBoundaryStyle" -> Automatic, 
        "DefaultGraphicsInteraction" -> {
         "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
          "Effects" -> {
           "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
            "Droplines" -> {
             "freeformCursorMode" -> True, 
              "placement" -> {"x" -> "All", "y" -> "None"}}}}, 
        "DefaultMeshStyle" -> AbsolutePointSize[6], "ScalingFunctions" -> 
        None, "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
            (Identity[#]& )[
             Part[#, 1]], 
            (Identity[#]& )[
             Part[#, 2]]}& ), "CopiedValueFunction" -> ({
            (Identity[#]& )[
             Part[#, 1]], 
            (Identity[#]& )[
             Part[#, 2]]}& )}},
      PlotRange->{{0.55, 0.58}, {5.270918185590109, 5.270920470029928}},
      PlotRangeClipping->True,
      PlotRangePadding->{{
         Scaled[0.02], 
         Scaled[0.02]}, {
         Scaled[0.05], 
         Scaled[0.05]}},
      Ticks->{Automatic, Automatic}], "0.5638122919285393`", 
     RowBox[{"{", 
      RowBox[{"5.270919073837447`", ",", 
       RowBox[{"{", 
        RowBox[{"\[Tau]", "\[Rule]", "0.5651067825305714`"}], "}"}]}], "}"}]}
   },
   AutoDelete->False,
   GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}},
   GridBoxSpacings->{"Columns" -> {{2}}}],
  "Grid"]], "Output",
 CellChangeTimes->{{3.7173990584379587`*^9, 3.7173991327484903`*^9}, {
   3.7174150155488377`*^9, 3.717415027271131*^9}, 3.7939057565830603`*^9, {
   3.793905810335868*^9, 3.793905821113119*^9}, 3.793907579732216*^9, {
   3.793907741046424*^9, 3.793907762924458*^9}, {3.793907856343685*^9, 
   3.7939078707286587`*^9}, 3.823229370424437*^9, 3.8442634817202387`*^9, 
   3.844263679864257*^9, 3.844263743761756*^9, 3.8442639526527767`*^9, 
   3.844264047665782*^9, 3.848356252727458*^9, 3.848356514975219*^9},
 CellLabel->
  "Out[133]=",ExpressionUUID->"526649b3-0daa-4e58-8c17-28dddc9ad6c9"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Simplify", "/@", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{
     SubscriptBox["\[PartialD]", "\[Tau]"], "jtot1"}], ",", " ", 
    RowBox[{
     RowBox[{
      SubscriptBox["\[PartialD]", "\[Tau]"], "jtot1"}], "/.", 
     RowBox[{"\[Tau]", "->", 
      RowBox[{"Log", "[", 
       FractionBox[
        RowBox[{"1", "+", "5"}], 
        RowBox[{"2", "+", 
         SqrtBox["2"]}]], "]"}]}]}]}], "}"}], "  ", 
  RowBox[{"(*", " ", 
   RowBox[{"check", " ", "the", " ", "minimization"}], " ", "*)"}]}]], "Input",\

 CellChangeTimes->{{3.793905785004353*^9, 3.793905831460438*^9}, {
  3.793906121598167*^9, 3.793906151485733*^9}, {3.793907661386538*^9, 
  3.793907757244627*^9}},
 CellLabel->
  "In[134]:=",ExpressionUUID->"8109c1b1-8440-4d6a-8cee-ce43b23dd136"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{
    SuperscriptBox["\[ExponentialE]", 
     RowBox[{
      RowBox[{"-", "2"}], " ", "\[Tau]"}]], " ", 
    RowBox[{"(", 
     RowBox[{"54", "-", 
      RowBox[{"36", " ", 
       SqrtBox["2"]}], "+", 
      RowBox[{"6", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "2"}], "+", 
         SqrtBox["2"]}], ")"}], " ", 
       SuperscriptBox["\[ExponentialE]", "\[Tau]"]}], "+", 
      SuperscriptBox["\[ExponentialE]", 
       RowBox[{"2", " ", "\[Tau]"}]]}], ")"}]}], ",", "0"}], "}"}]], "Output",\

 CellChangeTimes->{{3.793905787366702*^9, 3.7939058320372887`*^9}, {
   3.793906122152203*^9, 3.793906151842516*^9}, 3.793907579809127*^9, {
   3.7939076746099873`*^9, 3.7939077629572268`*^9}, {3.793907856375976*^9, 
   3.7939078707604113`*^9}, 3.823229370637486*^9, 3.844263481823843*^9, 
   3.844263680216632*^9, 3.8442637438531*^9, 3.844263952680257*^9, 
   3.844264047694858*^9, 3.8483562528363323`*^9, 3.848356515006268*^9},
 CellLabel->
  "Out[134]=",ExpressionUUID->"d36f916f-4589-4e14-8cb7-f70e1ddca2fe"]
}, Open  ]],

Cell[TextData[StyleBox["So the minimum (inflection pt., actually) occurs just \
at the crossover point where u = \[Dash]1, \nas one might expect.",
 FontSize->16]], "Text",
 CellChangeTimes->{{3.713776883729083*^9, 3.713776898665091*^9}, {
  3.7137790411607656`*^9, 3.7137790598459263`*^9}, {3.717330081960259*^9, 
  3.717330101143979*^9}, {3.717397794543202*^9, 3.717397806653232*^9}, {
  3.7173980453093643`*^9, 3.7173982407239637`*^9}, {3.717398867311322*^9, 
  3.717398869405738*^9}, {3.71739918029784*^9, 3.717399225848094*^9}, {
  3.844263871685652*^9, 3.844263880922172*^9}},
 Background->GrayLevel[
  0.85],ExpressionUUID->"c17b264c-41de-4307-8e44-d1cc20498357"],

Cell[TextData[StyleBox["Now do it numerically the \
\[OpenCurlyDoubleQuote]right\[CloseCurlyDoubleQuote] way, with a single \
equation, using u = -Clip[\[Lambda]].  \nUnfortunately, as DSolveValue does \
not seem to work with the piecewise ODE \n(although it claims it can...), I \
do it numerically.  \nBut the numerical solution confirms the above analysis.",
 FontSize->16]], "Text",
 CellChangeTimes->{{3.713776883729083*^9, 3.713776898665091*^9}, {
  3.7137790411607656`*^9, 3.7137790598459263`*^9}, {3.717330081960259*^9, 
  3.7173300849584312`*^9}, {3.717398301192227*^9, 3.717398375758176*^9}, {
  3.717398423675498*^9, 3.717398447695437*^9}, {3.717408102652858*^9, 
  3.717408157939961*^9}, {3.793415611420127*^9, 3.793415639314148*^9}, {
  3.844263886202601*^9, 3.8442639086227627`*^9}},
 Background->GrayLevel[
  0.85],ExpressionUUID->"4ccbd125-b8f4-4619-99ae-1e74c6f9a3eb"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"j3", "[", "x0_", "]"}], ":=", 
  RowBox[{"Module", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
     "eq", ",", "init", ",", "x", ",", "\[Lambda]", ",", "t", ",", "xs", ",", 
      "\[Lambda]s", ",", "us", ",", "\[Tau]"}], "}"}], ",", 
    "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"\[Tau]", "=", "10"}], ";", "\[IndentingNewLine]", 
     RowBox[{"eq", "=", 
      RowBox[{"{", "\[IndentingNewLine]", 
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{"x", "'"}], "[", "t", "]"}], "\[Equal]", 
         RowBox[{
          RowBox[{"-", " ", 
           RowBox[{"x", "[", "t", "]"}]}], "-", 
          RowBox[{"Clip", "[", 
           RowBox[{"\[Lambda]", "[", "t", "]"}], "]"}]}]}], ",", "   ", 
        RowBox[{"(*", " ", 
         RowBox[{
          RowBox[{"value", " ", "between"}], " ", "\[PlusMinus]", "1"}], " ", 
         "*)"}], "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{
          RowBox[{"\[Lambda]", "'"}], "[", "t", "]"}], "\[Equal]", "  ", 
         RowBox[{
          RowBox[{"\[Lambda]", "[", "t", "]"}], "-", 
          RowBox[{"x", "[", "t", "]"}]}]}]}], "\[IndentingNewLine]", "}"}]}], 
     ";", "\[IndentingNewLine]", 
     RowBox[{"init", "=", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{
         RowBox[{"x", "[", "0", "]"}], "\[Equal]", "x0"}], ",", 
        RowBox[{
         RowBox[{"\[Lambda]", "[", "\[Tau]", "]"}], "\[Equal]", "0"}]}], 
       "}"}]}], ";", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"xs", ",", "\[Lambda]s"}], "}"}], "=", 
      RowBox[{
       RowBox[{"NDSolveValue", "[", 
        RowBox[{
         RowBox[{"{", 
          RowBox[{"eq", ",", "init"}], "}"}], ",", 
         RowBox[{"{", 
          RowBox[{"x", ",", "\[Lambda]"}], "}"}], ",", 
         RowBox[{"{", 
          RowBox[{"t", ",", "0", ",", "\[Tau]"}], "}"}]}], "]"}], "//", 
       "FullSimplify"}]}], ";", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"us", "[", "t_", "]"}], ":=", 
      RowBox[{"-", 
       RowBox[{"Clip", "[", 
        RowBox[{"\[Lambda]s", "[", "t", "]"}], "]"}]}]}], ";", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{"xs", ",", "\[Lambda]s", ",", "us"}], "}"}]}]}], 
   "]"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"{", 
    RowBox[{"x", ",", "\[Lambda]", ",", "u"}], "}"}], "=", 
   RowBox[{"j3", "[", "5", "]"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.717408171133328*^9, 3.7174081840842047`*^9}},
 CellLabel->
  "In[135]:=",ExpressionUUID->"5b3d29d1-2169-45ec-83b2-5e067f237fca"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"x", "[", "t", "]"}], ",", 
     RowBox[{"\[Lambda]", "[", "t", "]"}], ",", 
     RowBox[{"u", "[", "t", "]"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"t", ",", "0", ",", "10"}], "}"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", "All"}]}], "]"}]], "Input",
 CellLabel->
  "In[137]:=",ExpressionUUID->"a6d4da12-8e86-4534-8979-3ea18c9e1d99"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwVV3c01+8Xt3f29sHH52OFiKRU3vfaI1EyIpEVEpVSiiQqChnJKkopRZEi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       "]]},
     Annotation[#, "Charting`Private`Tag$55009#1"]& ], 
    TagBox[
     {RGBColor[0.880722, 0.611041, 0.142051], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwVVnc01w8XNrL33nyNKERJovS5F6VIskNSJDuzQlRCIUQIUSKzgZR+Etmy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       "]]},
     Annotation[#, "Charting`Private`Tag$55009#2"]& ], 
    TagBox[
     {RGBColor[0.560181, 0.691569, 0.194885], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[{{2.0408163265306121`*^-7, -1.}, {
       0.09814340804846831, -1.}, {0.19628661201530398`, -1.}, {
       0.40908357085458646`, -1.}, {0.4587573870663201, -1.}, {
       0.5084312032780537, -1.}, {0.5332681113839205, -1.}, {
       0.5581050194897873, -1.}, {0.5612096330030207, -1.}, {
       0.5640857785397008, -1.}}], LineBox[CompressedData["
1:eJwVVnc4148Tt7P3np8PohAlifLtfShFkh2SItmZFZVKKCoihCglRAORkuh9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       "]]},
     Annotation[#, "Charting`Private`Tag$55009#3"]& ], {}}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0, 0},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{All, All},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{
  3.717408192191861*^9, 3.717415027736083*^9, 3.793905756989246*^9, {
   3.7939058106035337`*^9, 3.7939058213792067`*^9}, 3.793907580046103*^9, {
   3.7939077413197412`*^9, 3.793907763181622*^9}, {3.7939078566012087`*^9, 
   3.7939078709838047`*^9}, 3.823229370878286*^9, 3.844263482137596*^9, 
   3.844263680409461*^9, 3.844263744047279*^9, 3.84426395289544*^9, 
   3.844264047891362*^9, 3.848356253255473*^9, 3.848356515206675*^9},
 CellLabel->
  "Out[137]=",ExpressionUUID->"a0e682b1-1154-4748-a895-aaae29e97eeb"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"hc", "[", "\[Tau]", "]"}], "/.", 
   RowBox[{"\[Tau]", "\[Rule]", 
    RowBox[{"Log", "[", 
     FractionBox[
      RowBox[{"1", "+", "x0"}], 
      RowBox[{"2", "+", 
       SqrtBox["2"]}]], "]"}]}]}], "//", "Simplify"}]], "Input",
 CellChangeTimes->{{3.717414163072012*^9, 3.7174142371457653`*^9}},
 CellLabel->
  "In[138]:=",ExpressionUUID->"ad6b7644-4b54-43d2-8b92-d16148cf974a"],

Cell[BoxData["0"], "Output",
 CellChangeTimes->{{3.717414166882975*^9, 3.7174141968775454`*^9}, {
   3.717414232203536*^9, 3.717414237684002*^9}, 3.717415028170312*^9, 
   3.793905757245798*^9, {3.7939058108450613`*^9, 3.793905821624131*^9}, 
   3.7939075803570213`*^9, {3.79390774162178*^9, 3.793907763421557*^9}, {
   3.793907856847948*^9, 3.793907871224101*^9}, 3.823229371147649*^9, 
   3.844263482380167*^9, 3.844263680629732*^9, 3.8442637442696323`*^9, 
   3.844263953134572*^9, 3.8442640481280327`*^9, 3.848356253452179*^9, 
   3.848356515420274*^9},
 CellLabel->
  "Out[138]=",ExpressionUUID->"d82802d7-4932-434d-8f25-380e163e64ec"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     FractionBox["3", "2"], "-", 
     SqrtBox["2"]}], ")"}], 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{"2", "+", 
      SqrtBox["2"]}], ")"}], "2"]}], "//", "Simplify"}]], "Input",
 CellChangeTimes->{{3.7174144410473623`*^9, 3.7174144707256403`*^9}},
 CellLabel->
  "In[139]:=",ExpressionUUID->"90de7123-e3e7-456c-bf76-5b357dd9db78"],

Cell[BoxData["1"], "Output",
 CellChangeTimes->{{3.7174144676677*^9, 3.717414471300582*^9}, 
   3.7174150283303547`*^9, 3.793905757251691*^9, {3.793905810957382*^9, 
   3.7939058217419033`*^9}, 3.79390758036275*^9, {3.793907741627652*^9, 
   3.7939077635371313`*^9}, {3.793907856940754*^9, 3.7939078713127937`*^9}, 
   3.823229371152813*^9, 3.844263482385549*^9, 3.844263680634816*^9, 
   3.84426374427573*^9, 3.8442639531734324`*^9, 3.844264048134439*^9, 
   3.8483562534572973`*^9, 3.848356515479631*^9},
 CellLabel->
  "Out[139]=",ExpressionUUID->"f2244423-bef6-4133-b8fe-c82af9784552"]
}, Open  ]]
}, Open  ]]
},
WindowSize->{808, 751},
WindowMargins->{{68, Automatic}, {Automatic, 0}},
DockedCells->{},
PrintingCopies->1,
PrintingPageRange->{1, Automatic},
FrontEndVersion->"12.3 for Mac OS X x86 (64-bit) (June 19, 2021)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"f87aa257-093a-4087-b819-be4845659131"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 298, 4, 67, "Section",ExpressionUUID->"d4a11a05-61dd-43d1-abc1-d7d86bb670c5"],
Cell[881, 28, 589, 14, 74, "Text",ExpressionUUID->"db176f9e-4b15-4798-9d93-20e823bd6ce7"],
Cell[1473, 44, 174, 4, 30, "Input",ExpressionUUID->"790608db-906b-4d1e-b79a-0bae31efb231"],
Cell[1650, 50, 1253, 32, 79, "Text",ExpressionUUID->"aaaed593-70f9-463e-8aff-74767b12e258"],
Cell[2906, 84, 1075, 21, 52, "Text",ExpressionUUID->"1b4dc240-c08b-4b8e-a9ef-9fb98fb69786"],
Cell[CellGroupData[{
Cell[4006, 109, 4064, 103, 369, "Input",ExpressionUUID->"95b99ef8-1430-4853-9d51-22af877d3b2c"],
Cell[8073, 214, 1523, 33, 37, "Output",ExpressionUUID->"ea65d8d1-d334-40da-bae9-1b5c4014dcee"]
}, Open  ]],
Cell[CellGroupData[{
Cell[9633, 252, 1055, 24, 30, "Input",ExpressionUUID->"e5da61f0-dcc7-4f1e-a250-1006a2edb58d"],
Cell[10691, 278, 40571, 686, 241, "Output",ExpressionUUID->"cd669a3a-edc1-4f74-9e17-40200c409f2b"]
}, Open  ]],
Cell[51277, 967, 323, 6, 52, "Text",ExpressionUUID->"adab4b9b-193c-46c1-b3ef-917f524634a0"],
Cell[CellGroupData[{
Cell[51625, 977, 4620, 115, 384, "Input",ExpressionUUID->"4e5b696b-05aa-4fd5-b0e1-9323909c7294"],
Cell[56248, 1094, 3574, 93, 116, "Output",ExpressionUUID->"595eb70f-9367-4765-8b1f-3bf4f955d904"]
}, Open  ]],
Cell[CellGroupData[{
Cell[59859, 1192, 459, 12, 52, "Input",ExpressionUUID->"3e497900-0913-4b1a-85d0-32b1df1ef2ea"],
Cell[60321, 1206, 7992, 150, 241, "Output",ExpressionUUID->"bb4b6e6d-40a6-4b97-8193-92b310568429"]
}, Open  ]],
Cell[CellGroupData[{
Cell[68350, 1361, 294, 7, 30, "Input",ExpressionUUID->"3559b54d-2072-4170-be3a-995135a6e3ae"],
Cell[68647, 1370, 727, 15, 37, "Output",ExpressionUUID->"89df2495-5241-4660-82b2-cff25ed3c302"]
}, Open  ]],
Cell[CellGroupData[{
Cell[69411, 1390, 291, 7, 30, "Input",ExpressionUUID->"cc056b4a-1cbe-4278-a5cd-b8a64c9e949a"],
Cell[69705, 1399, 641, 11, 34, "Output",ExpressionUUID->"56aeb2c4-5394-4960-90c7-d6a79c963c12"]
}, Open  ]],
Cell[70361, 1413, 387, 6, 52, "Text",ExpressionUUID->"a8c9d8a0-6a26-42b0-9f32-2deb764d0399"],
Cell[CellGroupData[{
Cell[70773, 1423, 734, 20, 47, "Input",ExpressionUUID->"3939753f-503f-4534-9495-fafff80e4ca3"],
Cell[71510, 1445, 1249, 31, 50, "Output",ExpressionUUID->"a20aa417-3271-408b-a89d-718a6875808d"]
}, Open  ]],
Cell[CellGroupData[{
Cell[72796, 1481, 353, 12, 47, "Input",ExpressionUUID->"0bb30ede-2d77-4f6d-baa6-20f09e79ea73"],
Cell[73152, 1495, 623, 12, 35, "Output",ExpressionUUID->"15ca43cd-0564-4f0e-a275-744c60436fbc"]
}, Open  ]],
Cell[CellGroupData[{
Cell[73812, 1512, 209, 4, 30, "Input",ExpressionUUID->"cd799536-73c4-44c3-a0fe-98df452d00ef"],
Cell[74024, 1518, 794, 18, 34, "Output",ExpressionUUID->"fa0ba084-95ff-4a5d-9b43-15ae394313ab"]
}, Open  ]],
Cell[CellGroupData[{
Cell[74855, 1541, 1103, 27, 59, "Input",ExpressionUUID->"3e35a4ef-6447-45e7-b83a-0515224099e7"],
Cell[75961, 1570, 1074, 25, 50, "Output",ExpressionUUID->"22ede937-5af9-4c1e-996d-2190af07b929"]
}, Open  ]],
Cell[CellGroupData[{
Cell[77072, 1600, 478, 12, 30, "Input",ExpressionUUID->"ee9b5c81-200e-4218-951c-fa93db7576b3"],
Cell[77553, 1614, 1685, 46, 50, "Output",ExpressionUUID->"59f89cfe-4ebf-4c2b-8bb6-be664ba608d8"]
}, Open  ]],
Cell[CellGroupData[{
Cell[79275, 1665, 410, 9, 30, "Input",ExpressionUUID->"928d1d81-73b3-4e15-ac59-b4217f3cc30e"],
Cell[79688, 1676, 1388, 35, 54, "Output",ExpressionUUID->"4aa6d169-d17d-43ed-864a-b775ee7fee8e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[81113, 1716, 1293, 31, 112, "Input",ExpressionUUID->"e0785b5f-a269-4fa6-83ef-04d014cd0920"],
Cell[82409, 1749, 4307, 90, 117, "Output",ExpressionUUID->"526649b3-0daa-4e58-8c17-28dddc9ad6c9"]
}, Open  ]],
Cell[CellGroupData[{
Cell[86753, 1844, 780, 22, 53, "Input",ExpressionUUID->"8109c1b1-8440-4d6a-8cee-ce43b23dd136"],
Cell[87536, 1868, 1083, 27, 38, "Output",ExpressionUUID->"d36f916f-4589-4e14-8cb7-f70e1ddca2fe"]
}, Open  ]],
Cell[88634, 1898, 670, 10, 76, "Text",ExpressionUUID->"c17b264c-41de-4307-8e44-d1cc20498357"],
Cell[89307, 1910, 885, 13, 124, "Text",ExpressionUUID->"4ccbd125-b8f4-4619-99ae-1e74c6f9a3eb"],
Cell[90195, 1925, 2590, 71, 241, "Input",ExpressionUUID->"5b3d29d1-2169-45ec-83b2-5e067f237fca"],
Cell[CellGroupData[{
Cell[92810, 2000, 433, 12, 30, "Input",ExpressionUUID->"a6d4da12-8e86-4534-8979-3ea18c9e1d99"],
Cell[93246, 2014, 38745, 659, 236, "Output",ExpressionUUID->"a0e682b1-1154-4748-a895-aaae29e97eeb"]
}, Open  ]],
Cell[CellGroupData[{
Cell[132028, 2678, 430, 12, 53, "Input",ExpressionUUID->"ad6b7644-4b54-43d2-8b92-d16148cf974a"],
Cell[132461, 2692, 640, 10, 34, "Output",ExpressionUUID->"d82802d7-4932-434d-8f25-380e163e64ec"]
}, Open  ]],
Cell[CellGroupData[{
Cell[133138, 2707, 408, 13, 47, "Input",ExpressionUUID->"90de7123-e3e7-456c-bf76-5b357dd9db78"],
Cell[133549, 2722, 589, 9, 57, "Output",ExpressionUUID->"f2244423-bef6-4133-b8fe-c82af9784552"]
}, Open  ]]
}, Open  ]]
}
]
*)