(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 118072, 3351]*) (*NotebookOutlinePosition[ 118718, 3373]*) (* CellTagsIndexPosition[ 118674, 3369]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[{ \(Clear[p, Uinit, ff1, ff2, FluxFunc, A, FlowLine1, FlowLine2, v, \[Theta], \[Theta]0, \[Theta]1, \[Theta]2, \[Phi], u, xnaught, x, icu, \ icv, t, Vinitial]\), "\[IndentingNewLine]", \(<< Graphics`PlotField`\[IndentingNewLine]\), "\[IndentingNewLine]", \(p[v_] = 2 v^\((\(-2\))\)\), "\[IndentingNewLine]", \(Uinit = {2, 1}\), "\[IndentingNewLine]", \(\[Alpha] = .5\), "\[IndentingNewLine]", \(\[Beta] = .5\[IndentingNewLine]\), "\[IndentingNewLine]", \(FluxFunc[u_, v_] = \({ff1[u_, v_], \ ff2[u_, v_]} = {p[v], \(-u\)}\)\), "\[IndentingNewLine]", \(A = {{\[PartialD]\_u\ ff1[u, v\ ], \[PartialD]\_v\ ff1[u, v]}, {\[PartialD]\_u\ ff2[u, v], \[PartialD]\_v\ ff2[u, v]}}\ \), "\[IndentingNewLine]", \(MatrixForm[A]\[IndentingNewLine]\), "\[IndentingNewLine]", \({EVal1[v_], Eval2[v_]} = Eigenvalues[A]\[IndentingNewLine]\), "\[IndentingNewLine]", \({EVec1[v_], EVec2[v_]} = Eigenvectors[A]\[IndentingNewLine]\), "\[IndentingNewLine]", \(IntegralCurve1[\[Theta]_] = \[Integral]\_0.01\%\[Theta] EVec1[\[Theta]] \[DifferentialD]\[Theta] + Uinit\), "\[IndentingNewLine]", \(IntegralCurve2[\[Theta]1_, \[Theta]2_] = \[Integral]\_0.01\%\[Theta]2 EVec2[\[Theta]] \[DifferentialD]\[Theta] + IntegralCurve1[\[Theta]1]\[IndentingNewLine]\), \ "\[IndentingNewLine]", \(PlotVectorField[ FluxFunc[u, v], {u, 0, 5}, {v, 0, 5}]\), "\[IndentingNewLine]", \(Show[ ParametricPlot[ IntegralCurve1[\[Theta]], {\[Theta], .01, \[Alpha]}], \ \[IndentingNewLine]ParametricPlot[ IntegralCurve2[\[Alpha], \[Theta]], {\[Theta], .01, \[Beta]}]]\)}], \ "Input"], Cell[BoxData[ \(2\/v\^2\)], "Output"], Cell[BoxData[ \({2, 1}\)], "Output"], Cell[BoxData[ \(0.5`\)], "Output"], Cell[BoxData[ \(0.5`\)], "Output"], Cell[BoxData[ \({2\/v\^2, \(-u\)}\)], "Output"], Cell[BoxData[ \({{0, \(-\(4\/v\^3\)\)}, {\(-1\), 0}}\)], "Output"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", \(-\(4\/v\^3\)\)}, {\(-1\), "0"} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"], Cell[BoxData[ \({\(-\(2\/v\^\(3/2\)\)\), 2\/v\^\(3/2\)}\)], "Output"], Cell[BoxData[ \({{2\/v\^\(3/2\), 1}, {\(-\(2\/v\^\(3/2\)\)\), 1}}\)], "Output"], Cell[BoxData[ \({2 + 2\ \((\(-0.01`\) + \[Theta])\)\ If[\[Theta] \[Equal] 0 || Re[\[Theta]] > 0 || Im[\[Theta]] \[NotEqual] 0, 20.`\/\(\(-0.01`\) + \[Theta]\) - 2.`\/\(\((\(-0.01`\) + \[Theta])\)\ \@\[Theta]\), Integrate[ 1\/\((\(\(0.01`\)\(\[InvisibleSpace]\)\) + \[Theta]\ \ \((\(-0.01`\) + \[Theta])\))\)\^\(3/2\), {\[Theta], 0, 1}, Assumptions \[Rule] \(! 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