(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 33073, 662] NotebookOptionsPosition[ 16219, 361] NotebookOutlinePosition[ 33159, 664] CellTagsIndexPosition[ 33116, 661] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`dia$$ = 0.02, $CellContext`size$$ = 1.3, $CellContext`t$$ = 1.2, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`t$$], 1.2, Style["t", RGBColor[0, 0, 1], 13, Bold]}, 0, 2, 0.1}, {{ Hold[$CellContext`size$$], 1.3, Style["Scale", 13, Bold]}, 0.5, 2, 0.2}, {{ Hold[$CellContext`dia$$], 0.02, Style["Tube", 13, Bold]}, 0.01, 0.5}, { Hold[ Dynamic[ Column[{"", "", "", "", Style[" r(t) = {Cos(t), Sin(t), t}", 20], Null, Null, Null, Null, Labeled[ Framed[ Round[ $CellContext`Tn[$CellContext`t$$], 0.1]], Style["Unit Tangent", Green, 20], Top], Null, Labeled[ Framed[ Round[ $CellContext`Nr[$CellContext`t$$], 0.1]], Style["Unit Inward Normal", Red, 20], Top], Null, Labeled[ Framed[ Round[ $CellContext`Bn[$CellContext`t$$], 0.1]], Style["Binormal", Blue, 20], Top], Null, Null, Null, Null, Row[{ Style["Osculating ", Green, 20], Style["Plane ", Red, 20]}], Framed[ Row[{$CellContext`A1 "X" + $CellContext`B1 "Y" + $CellContext`C1 "Z", " = ", $CellContext`w1}]], Null, Row[{ Style["Rectifying ", Green, 20], Style["Plane", Blue, 20]}], Framed[ Row[{$CellContext`A2 "X" + $CellContext`B2 "Y" + $CellContext`C2 "Z", " = ", $CellContext`w2}]], Null, Row[{ Style["Binormal ", Blue, 20], Style["Plane ", Red, 20]}], Framed[ Row[{$CellContext`A3 "X" + $CellContext`B3 "Y" + $CellContext`C3 "Z", " = ", $CellContext`w3}]]}, Center]]], Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = { 600., {297.5, 302.5}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`t$4562$$ = 0, $CellContext`size$4563$$ = 0, $CellContext`dia$4564$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`dia$$ = 0.02, $CellContext`size$$ = 1.3, $CellContext`t$$ = 1.2}, "ControllerVariables" :> { Hold[$CellContext`t$$, $CellContext`t$4562$$, 0], Hold[$CellContext`size$$, $CellContext`size$4563$$, 0], Hold[$CellContext`dia$$, $CellContext`dia$4564$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Pane[$CellContext`W1 = Round[Norm[ $CellContext`Nr[$CellContext`t$$]] Norm[ Derivative[1][$CellContext`r][$CellContext`t$$]] (Part[ $CellContext`r[$CellContext`t$$], 1] Part[ $CellContext`Bn[$CellContext`t$$], 1] + Part[ $CellContext`r[$CellContext`t$$], 2] Part[ $CellContext`Bn[$CellContext`t$$], 2] + Part[ $CellContext`r[$CellContext`t$$], 3] Part[ $CellContext`Bn[$CellContext`t$$], 3]), 0.1]; {$CellContext`a1, $CellContext`b1, $CellContext`c1} = Round[Norm[ $CellContext`Nr[$CellContext`t$$]] Norm[ Derivative[ 1][$CellContext`r][$CellContext`t$$]] \ $CellContext`Bn[$CellContext`t$$], 0.1]; If[$CellContext`a1 != 0, {$CellContext`A1, $CellContext`B1, $CellContext`C1, \ $CellContext`w1} = Round[{$CellContext`a1, $CellContext`b1, $CellContext`c1, \ $CellContext`W1}/$CellContext`a1, 0.1], If[$CellContext`b1 != 0, {$CellContext`A1, $CellContext`B1, $CellContext`C1, \ $CellContext`w1} = Round[{$CellContext`a1, $CellContext`b1, $CellContext`c1, \ $CellContext`W1}/$CellContext`b1, 0.1], {$CellContext`A1, $CellContext`B1, $CellContext`C1, \ $CellContext`w1} = Round[{$CellContext`a1, $CellContext`b1, $CellContext`c1, \ $CellContext`W1}/$CellContext`c1, 0.1]]]; $CellContext`W2 = Round[Norm[ $CellContext`Nr[$CellContext`t$$]] (Part[ $CellContext`r[$CellContext`t$$], 1] Part[ $CellContext`Nr[$CellContext`t$$], 1] + Part[ $CellContext`r[$CellContext`t$$], 2] Part[ $CellContext`Nr[$CellContext`t$$], 2] + Part[ $CellContext`r[$CellContext`t$$], 3] Part[ $CellContext`Nr[$CellContext`t$$], 3]), 0.1]; {$CellContext`a2, $CellContext`b2, $CellContext`c2} = Round[Norm[ $CellContext`Nr[$CellContext`t$$]] \ $CellContext`Nr[$CellContext`t$$], 0.1]; If[$CellContext`a2 != 0, {$CellContext`A2, $CellContext`B2, $CellContext`C2, \ $CellContext`w2} = Round[{$CellContext`a2, $CellContext`b2, $CellContext`c2, \ $CellContext`W2}/$CellContext`a2, 0.1], If[$CellContext`b2 != 0, {$CellContext`A2, $CellContext`B2, $CellContext`C2, \ $CellContext`w2} = Round[{$CellContext`a2, $CellContext`b2, $CellContext`c2, \ $CellContext`W2}/$CellContext`b2, 0.1], {$CellContext`A2, $CellContext`B2, $CellContext`C2, \ $CellContext`w2} = Round[{$CellContext`a2, $CellContext`b2, $CellContext`c2, \ $CellContext`W2}/$CellContext`c2, 0.1]]]; $CellContext`W3 = Round[Norm[ Derivative[1][$CellContext`r][$CellContext`t$$]] (Part[ $CellContext`r[$CellContext`t$$], 1] Part[ $CellContext`Tn[$CellContext`t$$], 1] + Part[ $CellContext`r[$CellContext`t$$], 2] Part[ $CellContext`Tn[$CellContext`t$$], 2] + Part[ $CellContext`r[$CellContext`t$$], 3] Part[ $CellContext`Tn[$CellContext`t$$], 3]), 0.1]; {$CellContext`a3, $CellContext`b3, $CellContext`c3} = Round[Norm[ Derivative[ 1][$CellContext`r][$CellContext`t$$]] \ $CellContext`Tn[$CellContext`t$$], 0.1]; If[$CellContext`a3 != 0, {$CellContext`A3, $CellContext`B3, $CellContext`C3, \ $CellContext`w3} = Round[{$CellContext`a3, $CellContext`b3, $CellContext`c3, \ $CellContext`W3}/$CellContext`a3, 0.1], If[$CellContext`b3 != 0, {$CellContext`A3, $CellContext`B3, $CellContext`C3, \ $CellContext`w3} = Round[{$CellContext`a3, $CellContext`b3, $CellContext`c3, \ $CellContext`W3}/$CellContext`b3, 0.1], {$CellContext`A3, $CellContext`B3, $CellContext`C3, \ $CellContext`w3} = Round[{$CellContext`a3, $CellContext`b3, $CellContext`c3, \ $CellContext`W3}/$CellContext`c3, 0.1]]]; Framed[ Show[ ParametricPlot3D[ $CellContext`r[$CellContext`s], {$CellContext`s, 0, 2}, PlotStyle -> {Cyan, Tube[$CellContext`dia$$]}, PlotRange -> {{-2, 2}, {-2, 2}, {-2, 8}}], ParametricPlot3D[ Tooltip[ $CellContext`OscPl[$CellContext`u, $CellContext`v, \ $CellContext`t$$], "Osculating"], {$CellContext`u, 0, $CellContext`size$$}, {$CellContext`v, 0, $CellContext`size$$}, PlotRange -> {{-2, 2}, {-2, 2}, {-2, 8}}], ParametricPlot3D[ Tooltip[ $CellContext`RecPl[$CellContext`u, $CellContext`v, \ $CellContext`t$$], "Rectifying"], {$CellContext`u, 0, $CellContext`size$$}, {$CellContext`v, 0, $CellContext`size$$}, PlotRange -> {{-2, 2}, {-2, 2}, {-2, 8}}], ParametricPlot3D[ Tooltip[ $CellContext`NorPl[$CellContext`u, $CellContext`v, \ $CellContext`t$$], "Binormal"], {$CellContext`u, 0, $CellContext`size$$}, {$CellContext`v, 0, $CellContext`size$$}, PlotRange -> {{-2, 2}, {-2, 2}, {-2, 8}}], Graphics3D[{Green, Arrow[{ $CellContext`r[$CellContext`t$$], \ $CellContext`r[$CellContext`t$$] + 2 $CellContext`size$$ $CellContext`Tn[$CellContext`t$$]}]}], Graphics3D[{Red, Arrow[{ $CellContext`r[$CellContext`t$$], \ $CellContext`r[$CellContext`t$$] + 2 $CellContext`size$$ $CellContext`Nr[$CellContext`t$$]}]}], Graphics3D[{Blue, Arrow[{ $CellContext`r[$CellContext`t$$], \ $CellContext`r[$CellContext`t$$] + 2 $CellContext`size$$ $CellContext`Bn[$CellContext`t$$]}]}], Graphics3D[{ RGBColor[1, 0, 1], PointSize[0.03], Point[ $CellContext`r[$CellContext`t$$]]}], PlotRange -> All, ImageSize -> {590, 590}, Axes -> True, AxesLabel -> {"X", "Y", "Z"}, ViewPoint -> {1.3, -2.4, 1.}]], ImageSize -> {600, 600}, Alignment -> {Center, Center}], "Specifications" :> {{{$CellContext`t$$, 1.2, Style["t", RGBColor[0, 0, 1], 13, Bold]}, 0, 2, 0.1}, Delimiter, {{$CellContext`size$$, 1.3, Style["Scale", 13, Bold]}, 0.5, 2, 0.2}, {{$CellContext`dia$$, 0.02, Style["Tube", 13, Bold]}, 0.01, 0.5}, Dynamic[ Column[{"", "", "", "", Style[" r(t) = {Cos(t), Sin(t), t}", 20], Null, Null, Null, Null, Labeled[ Framed[ Round[ $CellContext`Tn[$CellContext`t$$], 0.1]], Style["Unit Tangent", Green, 20], Top], Null, Labeled[ Framed[ Round[ $CellContext`Nr[$CellContext`t$$], 0.1]], Style["Unit Inward Normal", Red, 20], Top], Null, Labeled[ Framed[ Round[ $CellContext`Bn[$CellContext`t$$], 0.1]], Style["Binormal", Blue, 20], Top], Null, Null, Null, Null, Row[{ Style["Osculating ", Green, 20], Style["Plane ", Red, 20]}], Framed[ Row[{$CellContext`A1 "X" + $CellContext`B1 "Y" + $CellContext`C1 "Z", " = ", $CellContext`w1}]], Null, Row[{ Style["Rectifying ", Green, 20], Style["Plane", Blue, 20]}], Framed[ Row[{$CellContext`A2 "X" + $CellContext`B2 "Y" + $CellContext`C2 "Z", " = ", $CellContext`w2}]], Null, Row[{ Style["Binormal ", Blue, 20], Style["Plane ", Red, 20]}], Framed[ Row[{$CellContext`A3 "X" + $CellContext`B3 "Y" + $CellContext`C3 "Z", " = ", $CellContext`w3}]]}, Center]]}, "Options" :> { ControlPlacement -> Left, FrameLabel -> { "\!\(\*\nStyleBox[\"\[Copyright]\",\nFontSize->14]\)\!\(\*\n\ StyleBox[\" \",\nFontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"N\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\".\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"Bykov\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\",\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"SJ\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"Delta\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"College\",\n\ FontColor->RGBColor[0, 0, 1]]\)"}}, "DefaultOptions" :> {}], ImageSizeCache->{900., {341., 346.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({{$CellContext`W1 = -11.8, $CellContext`Nr[ Pattern[$CellContext`s, Blank[]]] := {-Sin[Pi $CellContext`s], -Cos[Pi $CellContext`s], 0}, Attributes[Derivative] = { NHoldAll, ReadProtected}, $CellContext`r[ Pattern[$CellContext`s, Blank[]]] := { Sin[Pi $CellContext`s], Cos[Pi $CellContext`s], Pi $CellContext`s}, $CellContext`Bn[ Pattern[$CellContext`s, Blank[]]] := { Cos[Pi $CellContext`s]/Sqrt[ 2], -(Sin[Pi $CellContext`s]/Sqrt[2]), -(1/Sqrt[ 2])}, $CellContext`a1 = -2.5, $CellContext`b1 = 1.8, $CellContext`c1 = -3.1, $CellContext`A1 = 1., $CellContext`B1 = -0.7000000000000001, $CellContext`C1 = 1.2000000000000002`, $CellContext`w1 = 4.7, $CellContext`W2 = -1., $CellContext`a2 = 0.6000000000000001, $CellContext`b2 = 0.8, $CellContext`c2 = 0, $CellContext`A2 = 1., $CellContext`B2 = 1.3, $CellContext`C2 = 0, $CellContext`w2 = -1.7000000000000002`, $CellContext`W3 = 11.8, $CellContext`Tn[ Pattern[$CellContext`s, Blank[]]] := { Cos[Pi $CellContext`s]/Sqrt[2], -(Sin[Pi $CellContext`s]/Sqrt[2]), 1/Sqrt[2]}, $CellContext`a3 = -2.5, $CellContext`b3 = 1.8, $CellContext`c3 = 3.1, $CellContext`A3 = 1., $CellContext`B3 = -0.7000000000000001, $CellContext`C3 = \ -1.2000000000000002`, $CellContext`w3 = -4.7, $CellContext`OscPl[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`h, Blank[]], Pattern[$CellContext`s, Blank[]]] := {($CellContext`p Cos[Pi $CellContext`s])/Sqrt[2] + Sin[Pi $CellContext`s] - $CellContext`h Sin[Pi $CellContext`s], Cos[Pi $CellContext`s] - $CellContext`h Cos[Pi $CellContext`s] - ($CellContext`p Sin[Pi $CellContext`s])/ Sqrt[2], $CellContext`p/Sqrt[2] + Pi $CellContext`s}, $CellContext`RecPl[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`h, Blank[]], Pattern[$CellContext`s, Blank[]]] := {($CellContext`h Cos[Pi $CellContext`s])/Sqrt[ 2] + ($CellContext`p Cos[Pi $CellContext`s])/Sqrt[2] + Sin[Pi $CellContext`s], Cos[Pi $CellContext`s] - ($CellContext`h Sin[Pi $CellContext`s])/ Sqrt[2] - ($CellContext`p Sin[Pi $CellContext`s])/Sqrt[ 2], -($CellContext`h/Sqrt[2]) + $CellContext`p/Sqrt[2] + Pi $CellContext`s}, $CellContext`NorPl[ Pattern[$CellContext`p, Blank[]], Pattern[$CellContext`h, Blank[]], Pattern[$CellContext`s, Blank[]]] := {($CellContext`h Cos[Pi $CellContext`s])/Sqrt[2] + Sin[Pi $CellContext`s] - $CellContext`p Sin[Pi $CellContext`s], Cos[Pi $CellContext`s] - $CellContext`p Cos[Pi $CellContext`s] - ($CellContext`h Sin[Pi $CellContext`s])/ Sqrt[2], -($CellContext`h/Sqrt[2]) + Pi $CellContext`s}}; {Null}}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.469993999875*^9}] }, WindowSize->{1272, 922}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, DockedCells->FEPrivate`If[ 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