Cell[CellGroupData[{Cell[BoxData[
 RowBox[{"Manipulate", "[", 
  RowBox[{
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"sol", ",", "v"}], "}"}], ",", "
", 
     RowBox[{
      RowBox[{"sol", "=", 
       RowBox[{"First", "[", 
        RowBox[{"v", "/.", 
         RowBox[{"NDSolve", "[", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{
              RowBox[{
               RowBox[{
                RowBox[{"v", "'"}], "[", "t", "]"}], "*", 
               RowBox[{
                RowBox[{
                 RowBox[{"(", 
                  RowBox[{"1", "+", "e"}], ")"}], "^", "2"}], "/", 
                RowBox[{
                 RowBox[{"(", 
                  RowBox[{"1", "+", 
                   RowBox[{
                    RowBox[{"Cos", "[", 
                    RowBox[{"v", "[", "t", "]"}], "]"}], "*", "e"}]}],
                   ")"}], "^", "2"}]}]}], "==", "1"}], ",", 
             RowBox[{
              RowBox[{"v", "[", "0", "]"}], "==", "0"}]}], 
            "}"}], ",", "v", ",", 
           RowBox[{"{", 
            RowBox[{"t", ",", 
             RowBox[{"-", "52"}], ",", "52"}], "}"}]}], "]"}]}], 
        "]"}]}], ";", "
", 
      RowBox[{
       RowBox[{"x", "[", 
        RowBox[{"nn_", ",", "ee_"}], "]"}], ":=", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{"1", "+", "ee"}], ")"}], " ", 
        RowBox[{
         RowBox[{"Cos", "[", 
          RowBox[{"sol", "[", 
           RowBox[{
            RowBox[{"(", 
             RowBox[{"nn", "-", "1"}], ")"}], "/", "10"}], "]"}], 
          "]"}], "/", 
         RowBox[{"(", 
          RowBox[{"1", "+", 
           RowBox[{"ee", " ", 
            RowBox[{"Cos", "[", 
             RowBox[{"sol", "[", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"nn", "-", "1"}], ")"}], "/", "10"}], "]"}], 
             "]"}]}]}], ")"}]}]}]}], ";", "
", 
      RowBox[{
       RowBox[{"y", "[", 
        RowBox[{"nn_", ",", "ee_"}], "]"}], ":=", 
       RowBox[{
        RowBox[{"(", 
         RowBox[{"1", "+", "ee"}], ")"}], " ", 
        RowBox[{
         RowBox[{"Sin", "[", 
          RowBox[{"sol", "[", 
           RowBox[{
            RowBox[{"(", 
             RowBox[{"nn", "-", "1"}], ")"}], "/", "10"}], "]"}], 
          "]"}], "/", 
         RowBox[{"(", 
          RowBox[{"1", "+", 
           RowBox[{"ee", " ", 
            RowBox[{"Cos", "[", 
             RowBox[{"sol", "[", 
              RowBox[{
               RowBox[{"(", 
                RowBox[{"nn", "-", "1"}], ")"}], "/", "10"}], "]"}], 
             "]"}]}]}], ")"}]}]}]}], ";", "
", 
      RowBox[{"Graphics", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{
            RowBox[{"RGBColor", "[", 
             RowBox[{"1", ",", ".8", ",", "0"}], "]"}], ",", 
            RowBox[{"Disk", "[", 
             RowBox[{
              RowBox[{"{", 
               RowBox[{"0", ",", "0"}], "}"}], ",", "0.4"}], "]"}]}], 
           "}"}], ",", 
          RowBox[{"PointSize", "[", ".01", "]"}], ",", 
          RowBox[{"Point", "@", 
           RowBox[{"Table", "[", 
            RowBox[{
             RowBox[{"{", 
              RowBox[{
               RowBox[{"x", "[", 
                RowBox[{"nn", ",", "e"}], "]"}], ",", 
               RowBox[{"y", "[", 
                RowBox[{"nn", ",", "e"}], "]"}]}], "}"}], ",", 
             RowBox[{"{", 
              RowBox[{"nn", ",", 
               RowBox[{"-", "n"}], ",", "n", ",", "4"}], "}"}]}], 
            "]"}]}]}], "}"}], ",", 
        RowBox[{"Axes", "->", "True"}], ",", 
        RowBox[{"PlotRange", "->", 
         RowBox[{"{", 
          RowBox[{
           RowBox[{"{", 
            RowBox[{
             RowBox[{"-", "8"}], ",", "1.5"}], "}"}], ",", 
           RowBox[{"{", 
            RowBox[{
             RowBox[{"-", "4"}], ",", "4"}], "}"}]}], "}"}]}], ",", 
        RowBox[{"ImageSize", "->", 
         RowBox[{"{", 
          RowBox[{"500", ",", "350"}], "}"}]}]}], "]"}]}]}], "]"}], 
   ",", "
", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"n", ",", "220", ",", "\"\<time\>\""}], "}"}], ",", "2",
      ",", "518", ",", "1"}], "}"}], ",", "
", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"e", ",", ".5", ",", "\"\<eccentricity\>\""}], "}"}], 
     ",", "0", ",", "1.4", ",", ".2", ",", 
     RowBox[{"Appearance", "->", "\"\<Labeled\>\""}]}], "}"}], 
   ",", "
", 
   RowBox[{"SynchronousUpdating", "->", "True"}], ",", 
   RowBox[{"TrackedSymbols", ":>", 
    RowBox[{"{", 
     RowBox[{"n", ",", "e"}], "}"}]}]}], "
", 
  "]"}]], "Input",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{
  3.35696210375764*^9, {3.457439010734375*^9, 3.45743901434375*^9}, {
   3.457496573375*^9, 3.45749683896875*^9}, {3.457510163046875*^9, 
   3.457510175796875*^9}, {3.457510206125*^9, 3.457510211515625*^9}, {
   3.45751033075*^9, 3.45751033275*^9}, {3.457583448765625*^9, 
   3.457583518296875*^9}, {3.457585263234375*^9, 
   3.457585273234375*^9}, {3.457585379734375*^9, 
   3.4575854044375*^9}, {3.45758552459375*^9, 3.45758554121875*^9}, {
   3.45758784159375*^9, 3.45758797075*^9}, {3.4575880966875*^9, 
   3.4575881004375*^9}, {3.45758875109375*^9, 3.45758875984375*^9}, {
   3.457588898875*^9, 3.457588908328125*^9}, {3.45758955175*^9, 
   3.457589560109375*^9}, {3.457589612484375*^9, 
   3.457589736015625*^9}, {3.45758979553125*^9, 
   3.457589800984375*^9}, {3.457590240109375*^9, 
   3.457590301359375*^9}, {3.457599315078125*^9, 
   3.457599321171875*^9}, {3.457609139515625*^9, 
   3.457609151265625*^9}, {3.45760924053125*^9, 3.4576092551875*^9}, {
   3.4576093558125*^9, 3.45760936334375*^9}, {3.457614329671875*^9, 
   3.457614352203125*^9}, {3.45761441325*^9, 3.457614464015625*^9}, {
   3.45761478909375*^9, 3.45761480965625*^9}, {3.4576148463125*^9, 
   3.45761488534375*^9}, {3.45761498725*^9, 3.45761499021875*^9}, {
   3.45761507715625*^9, 3.45761508140625*^9}, {3.457615114578125*^9, 
   3.45761518959375*^9}, {3.45761525490625*^9, 
   3.457615294703125*^9}, {3.45761534196875*^9, 3.457615343*^9}, 
   3.457615427328125*^9, {3.45762005134375*^9, 3.45762005728125*^9}, {
   3.457620171765625*^9, 3.45762019678125*^9}, {3.457620530015625*^9, 
   3.457620533234375*^9}, {3.457620782046875*^9, 
   3.4576208078125*^9}, {3.457620858984375*^9, 
   3.457620860484375*^9}, {3.4576211979375*^9, 
   3.457621215578125*^9}, {3.45762154753125*^9, 
   3.457621550984375*^9}, {3.457621979484375*^9, 
   3.4576219954375*^9}, {3.457622198375*^9, 3.45762220934375*^9}, {
   3.457668195234375*^9, 3.4576682040625*^9}, {3.4576682365*^9, 
   3.457668241078125*^9}, {3.457668621375*^9, 3.45766865521875*^9}, 
   3.45766869509375*^9, {3.457668731203125*^9, 3.45766878375*^9}, {
   3.457668838828125*^9, 3.457668857578125*^9}, {3.45766898559375*^9, 
   3.457668991328125*^9}, 3.4576691758125*^9, {3.45767354025*^9, 
   3.457673547078125*^9}, {3.457673737734375*^9, 
   3.457673754109375*^9}, 3.457673788921875*^9, 
   3.457673941171875*^9, {3.457674670046875*^9, 
   3.457674671640625*^9}, {3.457674802890625*^9, 
   3.457674803484375*^9}, {3.457675034890625*^9, 
   3.457675042921875*^9}, {3.45767550790625*^9, 3.457675520046875*^9},
    3.45767565990625*^9, {3.4577190282116804`*^9, 
   3.4577190682586846`*^9}, {3.457719143399198*^9, 
   3.457719158070665*^9}, {3.4577191901398716`*^9, 
   3.4577192068405414`*^9}, {3.4577192813639927`*^9, 
   3.4577192955224085`*^9}, {3.457719573493203*^9, 
   3.457719574142268*^9}, {3.457719606351488*^9, 
   3.4577196377256255`*^9}, {3.4577196864454975`*^9, 
   3.4577197669255447`*^9}, {3.4577198039882503`*^9, 
   3.457719824629314*^9}, {3.457720125879436*^9, 
   3.4577201593647842`*^9}, {3.457723750839628*^9, 
   3.4577238064971933`*^9}, {3.4577238389804416`*^9, 
   3.45772385416696*^9}, {3.457723973299872*^9, 
   3.4577242852090597`*^9}, {3.457785759648726*^9, 
   3.457785763199634*^9}, {3.457786050917913*^9, 
   3.4577860801603003`*^9}, 3.457786114481928*^9, {
   3.457786155427203*^9, 3.457786187169847*^9}, {3.457786297526808*^9,
    3.457786320483213*^9}, {3.4577863607429237`*^9, 
   3.4577863618899927`*^9}, {3.457786424852816*^9, 
   3.457786431027405*^9}, {3.4577864968528214`*^9, 
   3.457786529844969*^9}, 3.760736804509104*^9},
 CellID->10264207],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`e$$ = 0., $CellContext`n$$ = 456, 
    Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, 
    Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, 
    Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", 
    Typeset`specs$$ = {{{
       Hold[$CellContext`n$$], 456, "time"}, 2, 518, 1}, {{
       Hold[$CellContext`e$$], 0., "eccentricity"}, 0, 1.4, 0.2}}, 
    Typeset`size$$ = {500., {173., 177.}}, Typeset`update$$ = 0, 
    Typeset`initDone$$, Typeset`skipInitDone$$ = 
    True, $CellContext`n$39758$$ = 0, $CellContext`e$39759$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`e$$ = 0., $CellContext`n$$ = 456}, 
      "ControllerVariables" :> {
        Hold[$CellContext`n$$, $CellContext`n$39758$$, 0], 
        Hold[$CellContext`e$$, $CellContext`e$39759$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$,
         Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, 
        Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> 
      Module[{$CellContext`sol$, $CellContext`v$}, $CellContext`sol$ = 
         First[
           ReplaceAll[$CellContext`v$, 
            
            NDSolve[{
             Derivative[
                1][$CellContext`v$][$CellContext`t] ((
                  1 + $CellContext`e$$)^2/(1 + Cos[
                    $CellContext`v$[$CellContext`t]] \
$CellContext`e$$)^2) == 1, $CellContext`v$[0] == 
              0}, $CellContext`v$, {$CellContext`t, -52, 
              52}]]]; $CellContext`x[
           Pattern[$CellContext`nn$, 
            Blank[]], 
           Pattern[$CellContext`ee$, 
            Blank[]]] := (1 + $CellContext`ee$) (Cos[
             $CellContext`sol$[($CellContext`nn$ - 1)/10]]/(
           1 + $CellContext`ee$ Cos[
              $CellContext`sol$[($CellContext`nn$ - 1)/
               10]])); $CellContext`y[
           Pattern[$CellContext`nn$, 
            Blank[]], 
           Pattern[$CellContext`ee$, 
            Blank[]]] := (1 + $CellContext`ee$) (Sin[
             $CellContext`sol$[($CellContext`nn$ - 1)/10]]/(
           1 + $CellContext`ee$ Cos[
              $CellContext`sol$[($CellContext`nn$ - 1)/10]])); 
        Graphics[{{
            RGBColor[1, 0.8, 0], 
            Disk[{0, 0}, 0.4]}, 
           PointSize[0.01], 
           Point[
            Table[{
              $CellContext`x[$CellContext`nn, $CellContext`e$$], 
              $CellContext`y[$CellContext`nn, $CellContext`e$$]}, \
{$CellContext`nn, -$CellContext`n$$, $CellContext`n$$, 4}]]}, Axes -> 
          True, PlotRange -> {{-8, 1.5}, {-4, 4}}, 
          ImageSize -> {500, 350}]], 
      "Specifications" :> {{{$CellContext`n$$, 456, "time"}, 2, 518, 
         1}, {{$CellContext`e$$, 0., "eccentricity"}, 0, 1.4, 0.2, 
         Appearance -> "Labeled"}}, 
      "Options" :> {
       SynchronousUpdating -> True, 
        TrackedSymbols :> {$CellContext`n$$, $CellContext`e$$}}, 
      "DefaultOptions" :> {ControllerLinking -> True}],
     ImageSizeCache->{545., {232., 238.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    SynchronousInitialization->True,
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellGroupingRules->{"GroupTogetherGrouping", 10000.},
 CellChangeTimes->{3.7607368045093718`*^9},
 CellID->637255294]
}, {2}]]