(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 8.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 20192, 508] NotebookOptionsPosition[ 19603, 485] NotebookOutlinePosition[ 19946, 500] CellTagsIndexPosition[ 19903, 497] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"(*", RowBox[{ "define", " ", "two", " ", "points", " ", "and", " ", "the", " ", "axis", " ", "vectors"}], "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"xhat", " ", ":=", " ", RowBox[{"{", RowBox[{"1", ",", " ", "0", ",", " ", "0"}], "}"}]}], "\[IndentingNewLine]", RowBox[{"yhat", " ", ":=", " ", RowBox[{"{", RowBox[{"0", ",", " ", "1", ",", " ", "0"}], "}"}]}], "\[IndentingNewLine]", RowBox[{"zhat", " ", ":=", " ", RowBox[{"{", RowBox[{"0", ",", " ", "0", ",", " ", "1"}], "}"}]}], "\[IndentingNewLine]", RowBox[{"ohat", " ", ":=", " ", RowBox[{"{", RowBox[{"0", ",", " ", "0", ",", " ", "0"}], "}"}]}], "\[IndentingNewLine]", RowBox[{"z1", " ", ":=", " ", "1"}], "\[IndentingNewLine]", RowBox[{"m1", " ", ":=", " ", RowBox[{"{", RowBox[{"1", ",", " ", "1", ",", " ", "z1"}], "}"}]}], "\[IndentingNewLine]", RowBox[{"m1p", " ", ":=", " ", RowBox[{"{", RowBox[{"1", ",", " ", "1", ",", " ", "0"}], "}"}]}], "\[IndentingNewLine]", RowBox[{"m2", " ", ":=", " ", RowBox[{"{", RowBox[{"2", ",", " ", "3", ",", " ", "3"}], "}"}]}], "\[IndentingNewLine]", RowBox[{"m2p", " ", ":=", " ", RowBox[{"{", RowBox[{"2", ",", " ", "3", ",", " ", "z1"}], "}"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "This", " ", "stuff", " ", "is", " ", "all", " ", "to", " ", "draw", " ", "a", " ", "circlular", " ", "arc", " ", "in", " ", "the", " ", "plane", " ", "of", " ", "the", " ", "first", " ", "mass"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"h1", " ", ":=", " ", RowBox[{ RowBox[{"(", RowBox[{"m1", " ", ".", " ", "zhat"}], ")"}], " ", "zhat"}]}], "\[IndentingNewLine]", RowBox[{"p1", " ", ":=", " ", RowBox[{"m1", " ", "-", " ", "h1"}]}], "\[IndentingNewLine]", RowBox[{"p1Abs", " ", ":=", " ", RowBox[{"Norm", "[", "p1", "]"}]}], "\[IndentingNewLine]", RowBox[{"p1cap", " ", ":=", " ", RowBox[{"p1", "/", "p1Abs"}]}], "\[IndentingNewLine]", RowBox[{"c1", " ", ":=", " ", RowBox[{ RowBox[{"(", RowBox[{"p1", "+", "m1"}], ")"}], "/", "4"}]}], "\[IndentingNewLine]", RowBox[{"c1Abs", " ", ":=", " ", RowBox[{"Norm", "[", "c1", "]"}]}], "\[IndentingNewLine]", RowBox[{"c1cap", " ", ":=", " ", RowBox[{"c1", " ", "/", " ", "c1Abs"}]}], "\[IndentingNewLine]", RowBox[{"a1", " ", ":=", " ", "0.5"}], "\[IndentingNewLine]", RowBox[{"czp1", " ", ":=", " ", RowBox[{ RowBox[{"(", RowBox[{"zhat", " ", "\[Cross]", " ", "p1cap"}], ")"}], " ", "\[Cross]", " ", "c1cap"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"c1px", "[", "t_", "]"}], " ", ":=", " ", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c1Abs", " ", "+", RowBox[{"a1", " ", RowBox[{"Cos", "[", "t", "]"}]}]}], ")"}], " ", "c1cap"}], " ", "+", " ", RowBox[{"a1", " ", RowBox[{"Sin", "[", "t", "]"}], " ", "czp1"}]}], ")"}], " ", ".", " ", "xhat"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"c1py", "[", "t_", "]"}], " ", ":=", " ", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c1Abs", " ", "+", RowBox[{"a1", " ", RowBox[{"Cos", "[", "t", "]"}]}]}], ")"}], " ", "c1cap"}], " ", "+", " ", RowBox[{"a1", " ", RowBox[{"Sin", "[", "t", "]"}], " ", "czp1"}]}], ")"}], " ", ".", " ", "yhat"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"c1pz", "[", "t_", "]"}], " ", ":=", " ", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c1Abs", " ", "+", RowBox[{"a1", " ", RowBox[{"Cos", "[", "t", "]"}]}]}], ")"}], " ", "c1cap"}], " ", "+", " ", RowBox[{"a1", " ", RowBox[{"Sin", "[", "t", "]"}], " ", "czp1"}]}], ")"}], " ", ".", " ", "zhat"}]}], "\[IndentingNewLine]", RowBox[{"angle1End", " ", ":=", " ", RowBox[{ RowBox[{"Pi", "/", "4"}], " ", "-", "0.1"}]}], "\[IndentingNewLine]", RowBox[{"pts1", " ", ":=", " ", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"c1px", "[", "i", "]"}], ",", " ", RowBox[{"c1py", "[", "i", "]"}], ",", " ", RowBox[{"c1pz", "[", "i", "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"i", ",", " ", RowBox[{ RowBox[{"-", "Pi"}], "/", "5"}], ",", " ", "angle1End", ",", " ", RowBox[{"Pi", "/", "12"}]}], "}"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{"arr1", " ", ":=", " ", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"c1px", "[", "i", "]"}], ",", " ", RowBox[{"c1py", "[", "i", "]"}], ",", " ", RowBox[{"c1pz", "[", "i", "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"i", ",", " ", RowBox[{"angle1End", "-", RowBox[{"Pi", "/", "12"}]}], ",", " ", "angle1End", " ", ",", " ", RowBox[{"Pi", "/", "12"}]}], "}"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{"pa1", " ", ":=", " ", RowBox[{"{", RowBox[{ RowBox[{"c1px", "[", "angle1End", "]"}], ",", " ", RowBox[{"c1py", "[", "angle1End", "]"}], ",", " ", RowBox[{"c1pz", "[", "angle1End", "]"}]}], "}"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{ "This", " ", "stuff", " ", "is", " ", "all", " ", "to", " ", "draw", " ", "a", " ", "circlular", " ", "arc", " ", "in", " ", "the", " ", "plane", " ", "of", " ", "the", " ", "second", " ", "mass"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"h2", " ", ":=", " ", RowBox[{ RowBox[{"(", RowBox[{"m2", " ", ".", " ", "zhat"}], ")"}], " ", "zhat"}]}], "\[IndentingNewLine]", RowBox[{"p2", " ", ":=", " ", RowBox[{"m2", " ", "-", " ", "h2"}]}], "\[IndentingNewLine]", RowBox[{"p2Abs", " ", ":=", " ", RowBox[{"Norm", "[", "p2", "]"}]}], "\[IndentingNewLine]", RowBox[{"p2cap", " ", ":=", " ", RowBox[{"p2", "/", "p2Abs"}]}], "\[IndentingNewLine]", RowBox[{"c2", " ", ":=", " ", RowBox[{ RowBox[{"(", RowBox[{"p2", "+", "m2"}], ")"}], "/", "5"}]}], "\[IndentingNewLine]", RowBox[{"c2Abs", " ", ":=", " ", RowBox[{"Norm", "[", "c2", "]"}]}], "\[IndentingNewLine]", RowBox[{"c2cap", " ", ":=", " ", RowBox[{"c2", " ", "/", " ", "c2Abs"}]}], "\[IndentingNewLine]", RowBox[{"a2", " ", ":=", " ", "0.25"}], "\[IndentingNewLine]", RowBox[{"czp2", " ", ":=", " ", RowBox[{ RowBox[{"(", RowBox[{"zhat", " ", "\[Cross]", " ", "p2cap"}], ")"}], " ", "\[Cross]", " ", "c2cap"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"c2px", "[", "t_", "]"}], " ", ":=", " ", RowBox[{ RowBox[{"(", RowBox[{"m1", " ", "+", " ", RowBox[{ RowBox[{"(", RowBox[{"c2Abs", " ", "+", RowBox[{"a2", " ", RowBox[{"Cos", "[", "t", "]"}]}]}], ")"}], " ", "c2cap"}], " ", "+", " ", RowBox[{"a2", " ", RowBox[{"Sin", "[", "t", "]"}], " ", "czp2"}]}], ")"}], " ", ".", " ", "xhat"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"c2py", "[", "t_", "]"}], " ", ":=", " ", RowBox[{ RowBox[{"(", RowBox[{"m1", " ", "+", " ", RowBox[{ RowBox[{"(", RowBox[{"c2Abs", " ", "+", RowBox[{"a2", " ", RowBox[{"Cos", "[", "t", "]"}]}]}], ")"}], " ", "c2cap"}], " ", "+", " ", RowBox[{"a2", " ", RowBox[{"Sin", "[", "t", "]"}], " ", "czp2"}]}], ")"}], " ", ".", " ", "yhat"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"c2pz", "[", "t_", "]"}], " ", ":=", " ", RowBox[{ RowBox[{"(", RowBox[{"m1", " ", "+", " ", RowBox[{ RowBox[{"(", RowBox[{"c2Abs", " ", "+", RowBox[{"a2", " ", RowBox[{"Cos", "[", "t", "]"}]}]}], ")"}], " ", "c2cap"}], " ", "+", " ", RowBox[{"a2", " ", RowBox[{"Sin", "[", "t", "]"}], " ", "czp2"}]}], ")"}], " ", ".", " ", "zhat"}]}], "\[IndentingNewLine]", RowBox[{"angle2End", " ", ":=", " ", RowBox[{"Pi", "/", "2"}]}], "\[IndentingNewLine]", RowBox[{"pts2", " ", ":=", " ", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"c2px", "[", "i", "]"}], ",", " ", RowBox[{"c2py", "[", "i", "]"}], ",", " ", RowBox[{"c2pz", "[", "i", "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"i", ",", " ", RowBox[{"-", "Pi"}], ",", " ", "angle2End", ",", " ", RowBox[{"Pi", "/", "12"}]}], "}"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{"arr2", " ", ":=", " ", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"c2px", "[", "i", "]"}], ",", " ", RowBox[{"c2py", "[", "i", "]"}], ",", " ", RowBox[{"c2pz", "[", "i", "]"}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{"i", ",", " ", RowBox[{"angle2End", "-", RowBox[{"Pi", "/", "12"}]}], ",", " ", "angle2End", ",", " ", RowBox[{"Pi", "/", "12"}]}], "}"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{"pa2", " ", ":=", " ", RowBox[{"{", RowBox[{ RowBox[{"c2px", "[", "angle2End", "]"}], ",", " ", RowBox[{"c2py", "[", "angle2End", "]"}], ",", " ", RowBox[{"c2pz", "[", "angle2End", "]"}]}], "}"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Okay", ":", " ", RowBox[{ "ready", " ", "to", " ", "plot", " ", "all", " ", "the", " ", "junk", " ", "and", " ", "lable", " ", "it", " ", "all"}]}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{"Graphics3D", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"Arrowheads", "[", ".025", "]"}], ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{"ohat", ",", " ", "xhat"}], " ", "}"}], "]"}], ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{"ohat", ",", " ", "yhat"}], " ", "}"}], "]"}], ",", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{"ohat", ",", " ", "zhat"}], " ", "}"}], "]"}], ",", " ", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{"ohat", ",", " ", "m1"}], "}"}], "]"}], ",", RowBox[{"Arrow", "[", RowBox[{"{", RowBox[{"m1", ",", " ", "m2"}], "}"}], "]"}], ",", " ", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"ohat", ",", " ", "m1", ",", " ", "m1p"}], "}"}], "]"}], ",", " ", RowBox[{"Polygon", "[", RowBox[{"{", RowBox[{"m1", ",", " ", "m2", ",", " ", "m2p"}], "}"}], "]"}], ",", " ", RowBox[{"Text", "[", RowBox[{ RowBox[{"Subscript", "[", RowBox[{"m", ",", " ", "1"}], "]"}], ",", RowBox[{"m1", "+", RowBox[{"{", RowBox[{ RowBox[{"-", "0.1"}], ",", " ", RowBox[{"-", "0.1"}], ",", " ", "0.1"}], "}"}]}]}], "]"}], ",", " ", RowBox[{"Text", "[", RowBox[{ RowBox[{"Subscript", "[", RowBox[{"m", ",", " ", "2"}], "]"}], ",", RowBox[{"m2", "+", RowBox[{"{", RowBox[{ RowBox[{"-", "0.1"}], ",", " ", RowBox[{"-", "0.1"}], ",", " ", "0.1"}], "}"}]}]}], "]"}], ",", " ", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"m1", ",", " ", RowBox[{"m1", "+", RowBox[{"zhat", "/", "2"}]}]}], "}"}], "]"}], ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"Subscript", "[", RowBox[{"\[Theta]", ",", " ", "1"}], "]"}], ",", RowBox[{ RowBox[{"m1", "*", "0.1"}], "+", RowBox[{"0.1", " ", "*", " ", "zhat"}]}]}], "]"}], ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"Subscript", "[", RowBox[{"\[Theta]", ",", " ", "2"}], "]"}], ",", RowBox[{"m1", "+", " ", RowBox[{"m2", "*", "0.03"}], "+", RowBox[{"0.1", " ", "*", " ", "zhat"}]}]}], "]"}], ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"Subscript", "[", RowBox[{"l", ",", " ", "1"}], "]"}], ",", RowBox[{ RowBox[{"m1", "*", "0.5"}], "+", RowBox[{"0.1", " ", "*", " ", "zhat"}]}]}], "]"}], ",", RowBox[{"Text", "[", RowBox[{ RowBox[{"Subscript", "[", RowBox[{"l", ",", " ", "2"}], "]"}], ",", RowBox[{"m1", " ", "+", " ", RowBox[{"m2", "*", "0.3"}], "\[IndentingNewLine]", "+", RowBox[{"0.2", " ", "*", " ", "zhat"}]}]}], "]"}], ",", " ", RowBox[{"BSplineCurve", "[", "pts1", "]"}], ",", " ", RowBox[{"BSplineCurve", "[", "pts2", "]"}], ",", " ", RowBox[{"Arrow", "[", "arr1", "]"}], ",", " ", RowBox[{"Arrow", "[", "arr2", "]"}], ",", " ", RowBox[{"Text", "[", RowBox[{ RowBox[{"Subscript", "[", RowBox[{"j", ",", " ", "2"}], "]"}], ",", " ", "pa2"}], "]"}], ",", " ", RowBox[{"Text", "[", RowBox[{ RowBox[{"Subscript", "[", RowBox[{"j", ",", " ", "1"}], "]"}], ",", " ", "pa1"}], "]"}]}], "}"}], ",", " ", RowBox[{"Boxed", " ", "\[Rule]", " ", "False"}]}], "]"}], "\[IndentingNewLine]"}]}]], "Input", CellChangeTimes->CompressedData[" 1:eJwdzE1I0wEAhvE5bG2EsJaVzhbtUNkYsSyxLNeMPqCtWpPaqHZIMBoOkh2y gqCDDDtYQaBpZBNaZDo6+DGCZhMUA2EMJUOa6VituclcUluEaP9nh5ff5eVR 19+yNIhFItE+YeiJDA8Va5O1N1ORCWx74ZvEl5/3f0V7SzKK7T0DMVy1plMo L8msYbRKfGmr4LGI04aRpn4HFn4feYC6TdNubNz48QkOBs92YavrXA/WaLpe o0Hp9WNwzhhCyzPtFKp738xgZvnaT0yfDKRRuiL9g2JfXWKboGqydQkV2XgW i02uHEoCYdF2wU9HclK0lw7J8fKB6S3ocoWVaEiFd6EuEPNjp001ikHFvRg6 H88n8K/tYAbvVB5aQf3VU1lMHNfm0CH3ykoEL2rOFOFmY3klDnqih/FGb7oG rbur9Bgq09ShOqqz44Xr+g2lgt/8ZjmaVwt3oMQ+vxPbm5J78dVbhRHX4noz ds+t38Xlfx/cuOAJ5h2zTLSh8/yJR+i2Nj7N95o9eWerO8by/+Z3UxhqeD6D 5Q+NX9CkOhpHxZWFRey/r/uFt/vq87ZULOZQZlovUAqe3vNbhh0/irTonR2o QF9fWTUuhaV6NLwvqMVuicmOnSPjDvwPiygfOQ== "]], Cell[BoxData[ Graphics3DBox[ {Arrowheads[0.025], Arrow3DBox[{{0, 0, 0}, {1, 0, 0}}], Arrow3DBox[{{0, 0, 0}, {0, 1, 0}}], Arrow3DBox[{{0, 0, 0}, {0, 0, 1}}], Arrow3DBox[{{0, 0, 0}, {1, 1, 1}}], Arrow3DBox[{{1, 1, 1}, {2, 3, 3}}], Polygon3DBox[{{0, 0, 0}, {1, 1, 1}, {1, 1, 0}}], Polygon3DBox[{{1, 1, 1}, {2, 3, 3}, {2, 3, 1}}], Text3DBox[ SubscriptBox["m", "1"], {0.9, 0.9, 1.1}], Text3DBox[ SubscriptBox["m", "2"], {1.9, 2.9, 3.1}], Line3DBox[ NCache[{{1, 1, 1}, {1, 1, Rational[3, 2]}}, {{1, 1, 1}, {1, 1, 1.5}}]], Text3DBox[ SubscriptBox["\[Theta]", "1"], {0.1, 0.1, 0.2}], Text3DBox[ SubscriptBox["\[Theta]", "2"], {1.06, 1.09, 1.1900000000000002`}], Text3DBox[ SubscriptBox["l", "1"], {0.5, 0.5, 0.6}], Text3DBox[ SubscriptBox["l", "2"], {1.6, 1.9, 2.1}], BSplineCurve3DBox[{{0.7004011751620736, 0.7004011751620736, 0.6619207909141269}, {0.7689594076185005, 0.7689594076185005, 0.5745330092718005}, {0.8191885009221634, 0.8191885009221634, 0.4650288393637567}, {0.8476654253719187, 0.8476654253719187, 0.3408708094050315}, {0.8524495256268587, 0.8524495256268587, 0.21052008395646632`}, {0.8332147731607086, 0.8332147731607086, 0.08285984954262182}}], BSplineCurve3DBox[CompressedData[" 1:eJwB2QEm/iFib1JlAgAAABMAAAADAAAAvuaMZlzA+j8OrelMRRAAQA6t6UxF EPg/bUXT/MKZ+j8j6Dx7pOb/PxZv7VtfEvk/vC4NVIiZ+j8bxhN+TOb/P+aI +ZewHfo/r+yYa7C/+j+DsbJQxA8AQAAsbGQBIPs/ajaOlaEJ+z/QqCowOUcA QDNnxi+3B/w/SEkr1FFy+z/3diBfvZUAQHjsKJEHxfw/ajP9wp7y+z+R5j0S 9/UAQEIyHcQLS/0/vtoSDsqB/D8OJI6KV2EBQI+ZlryhkP0/eRzO+xEW/T9c ldp8jdABQL9TdnwLkf0/qNAkpFul/T99nBu7BDwCQPoW1c5BTP0/e9G8O+Ml /j8dnc1sapwCQPZCvcX0xvw/27pGb+aO/j8kDHXTLOsCQCkHxPE5Cvw/3LIM Mz3Z/j8lhknm7SIDQCWGSebtIvs/LVTGnNb//j8iv5T14D8DQB3ERdfTIPo/ 3WqMRREA/z8nUCn0DEADQE6qOZuCFfk/6qwALunZ/j+vgYDibiMDQDIHx84x E/g/L2MLBPiP/j9kiggD+usCQAHMbAN8K/c/UlBuxUcn/j88vBLUdZ0CQLtG CqIrbvY/Lmac1vqm/T+jTPUgPD0CQPIAFm8n6PU/+nXZLQ== "]], Arrow3DBox[{{0.8523138414039424, 0.8523138414039424, 0.20816802287250247`}, {0.832653255211582, 0.832653255211582, 0.08063759686909183}}], Arrow3DBox[{{1.88458993073893, 2.3268848961083943`, 1.4018970803921735`}, { 1.8532665618171325`, 2.279899842725699, 1.3691782321257588`}}], Text3DBox[ SubscriptBox["j", "2"], {1.8532665618171325`, 2.279899842725699, 1.3691782321257588`}], Text3DBox[ SubscriptBox["j", "1"], {0.832653255211582, 0.832653255211582, 0.08063759686909183}]}, AutomaticImageSize->True, Boxed->False, ImageSize->{359.99644841651434`, 375.2898579016508}, ViewPoint->{3.3718677297318624`, 0.2574031503521929, -0.11938019677357876`}, ViewVertical->{0.9565875316375587, 0.0502632186286757, 0.7853380441530738}]], "Output", CellChangeTimes->{{3.512781328754222*^9, 3.512781401435379*^9}, { 3.512781638283926*^9, 3.5127816909539385`*^9}, {3.512781721797703*^9, 3.5127817768188496`*^9}, 3.512781878839685*^9, 3.5127819385501003`*^9, 3.5127819815095577`*^9, {3.512782458920864*^9, 3.5127824877095103`*^9}, 3.51278252284552*^9, {3.5127826439464464`*^9, 3.5127826714330187`*^9}, 3.5127827316104608`*^9, 3.512782788955741*^9, 3.5127828683112793`*^9, { 3.5127829410944424`*^9, 3.5127829442826247`*^9}, 3.5127829750813866`*^9, { 3.5127831704775624`*^9, 3.5127832010063086`*^9}, 3.512783255896448*^9, { 3.512783294585661*^9, 3.512783313341734*^9}, {3.512783346771646*^9, 3.5127833685818934`*^9}}] }, Open ]], Cell[BoxData[""], "Input", CellChangeTimes->{{3.5127811662829294`*^9, 3.5127811817588143`*^9}}], Cell[BoxData[""], "Input", CellChangeTimes->{{3.512781183833933*^9, 3.5127811879371676`*^9}}], Cell[BoxData["\"\<\>"], "Input", CellChangeTimes->{3.5127745636242785`*^9}], Cell[BoxData["\[IndentingNewLine]"], "Input", CellChangeTimes->{{3.512774900850567*^9, 3.512774919196616*^9}, { 3.512774960877*^9, 3.5127749781859903`*^9}, {3.512776890216352*^9, 3.5127768912854133`*^9}}], Cell[BoxData[""], "Input", CellChangeTimes->{{3.512776895089631*^9, 3.512776895108632*^9}}], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.512775605373863*^9, 3.512775879095519*^9}, { 3.512775914531546*^9, 3.5127759519936886`*^9}, {3.512775982759448*^9, 3.512776121343375*^9}, {3.5127761554443254`*^9, 3.5127761662519436`*^9}, { 3.512776253840954*^9, 3.512776264935588*^9}, {3.5127763147564373`*^9, 3.5127765080814953`*^9}}], Cell[BoxData[""], "Input", CellChangeTimes->{{3.512776899529885*^9, 3.512776899720896*^9}}] }, WindowSize->{940, 751}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, FrontEndVersion->"8.0 for Microsoft Windows (64-bit) (February 23, 2011)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[579, 22, 14492, 371, 1172, "Input"], Cell[15074, 395, 3434, 59, 390, "Output"] }, Open ]], Cell[18523, 457, 96, 1, 31, "Input"], Cell[18622, 460, 94, 1, 31, "Input"], Cell[18719, 463, 76, 1, 31, "Input"], Cell[18798, 466, 210, 3, 52, "Input"], Cell[19011, 471, 92, 1, 31, "Input"], Cell[19106, 474, 398, 6, 72, "Input"], Cell[19507, 482, 92, 1, 31, "Input"] } ] *) (* End of internal cache information *)