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0, Rational[1, 2]}, {{ Hold[$CellContext`\[Phi]$$], Rational[1, 3] Pi, "latitude"}, 0, Rational[1, 2] Pi}, {{ Hold[$CellContext`t1$$], 0, "time"}, 0, 60 Pi}}, Typeset`size$$ = { 375., {185., 190.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`\[Omega]$1155277$$ = 0, $CellContext`\[CapitalOmega]$1155278$$ = 0, $CellContext`\[Phi]$1155279$$ = 0, $CellContext`t1$1155280$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`t1$$ = 0, $CellContext`\[Phi]$$ = Rational[1, 3] Pi, $CellContext`\[Omega]$$ = 1, $CellContext`\[CapitalOmega]$$ = Rational[1, 16]}, "ControllerVariables" :> { Hold[$CellContext`\[Omega]$$, $CellContext`\[Omega]$1155277$$, 0], Hold[$CellContext`\[CapitalOmega]$$, \ $CellContext`\[CapitalOmega]$1155278$$, 0], Hold[$CellContext`\[Phi]$$, $CellContext`\[Phi]$1155279$$, 0], Hold[$CellContext`t1$$, $CellContext`t1$1155280$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`fde = { Derivative[ 2][$CellContext`x][$CellContext`t] == (-$CellContext`\[Omega]$$^2) \ $CellContext`x[$CellContext`t] + ((2 $CellContext`\[CapitalOmega]$$) Sin[$CellContext`\[Phi]$$]) Derivative[1][$CellContext`y][$CellContext`t], Derivative[ 2][$CellContext`y][$CellContext`t] == (-$CellContext`\[Omega]$$^2) \ $CellContext`y[$CellContext`t] - ((2 $CellContext`\[CapitalOmega]$$) Sin[$CellContext`\[Phi]$$]) Derivative[1][$CellContext`x][$CellContext`t]}; $CellContext`sol = NDSolve[ Join[$CellContext`fde, {$CellContext`x[0] == 2, $CellContext`y[0] == 2, Derivative[1][$CellContext`x][0] == 0, Derivative[1][$CellContext`y][0] == 0}], { $CellContext`x[$CellContext`t], $CellContext`y[$CellContext`t]}, {$CellContext`t, 0, 64 Pi}, MaxSteps -> Infinity]; Graphics3D[{ Part[ ParametricPlot3D[ $CellContext`pendelPos[ ReplaceAll[{ $CellContext`x[$CellContext`t], $CellContext`y[$CellContext`t]}, Part[$CellContext`sol, 1]]], {$CellContext`t, $CellContext`t1$$, $CellContext`t1$$ + 4 Pi}, PlotStyle -> { Thickness[0.007], RGBColor[1, 0.47, 0]}], 1], Part[ ParametricPlot3D[ ReplaceAll[{ $CellContext`x[$CellContext`t], $CellContext`y[$CellContext`t], -4}, Part[$CellContext`sol, 1]], {$CellContext`t, 0, 64 Pi}, PlotPoints -> 1024], 1], $CellContext`pendel[$CellContext`t1$$, $CellContext`sol]}, PlotRange -> {{-3, 3}, {-3, 3}, {-4, 0}}, ImageSize -> {375, 375}]), "Specifications" :> {{{$CellContext`\[Omega]$$, 1, "pendulum frequency"}, 0.1, 10, ImageSize -> Tiny}, {{$CellContext`\[CapitalOmega]$$, Rational[1, 16], "Earth rotation frequency"}, 0, Rational[1, 2], ImageSize -> Tiny}, {{$CellContext`\[Phi]$$, Rational[1, 3] Pi, "latitude"}, 0, Rational[1, 2] Pi, ImageSize -> Tiny}, {{$CellContext`t1$$, 0, "time"}, 0, 60 Pi, ImageSize -> Tiny}}, "Options" :> { TrackedSymbols :> Manipulate, ControlPlacement -> Left, SynchronousUpdating -> False}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{621., {212., 217.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>(({$CellContext`fde = { Derivative[ 2][$CellContext`x][$CellContext`t] == (-0.010000000000000002`) \ $CellContext`x[$CellContext`t] + (Sqrt[3] Derivative[1][$CellContext`y][$CellContext`t])/16, Derivative[ 2][$CellContext`y][$CellContext`t] == (-0.010000000000000002`) \ $CellContext`y[$CellContext`t] - (Sqrt[3] Derivative[1][$CellContext`x][$CellContext`t])/16}, Attributes[Derivative] = { NHoldAll, ReadProtected}, $CellContext`sol = {{$CellContext`x[$CellContext`t] -> InterpolatingFunction[{{0., 201.06192982974676`}}, { 3, 3, 2, {235}, {4}, 0, 0, 0, 0}, CompressedData[" 1:eJxFiAk0FYgChq1XSp5soWcn2WVJN+r+15IlyXItl+u6+73oVVrsKjRZRlkH g5S1MSqtZKkZS6UpKstkmWp0ayhLG64kvXfem3Ped85/vvN/uqz9flwJMTEx 8f9sSuz/8OdExhUuwaT/WfC340i7RfFnY2xS//4ZpNH5m5zVjrUk7//2q6RL 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The pendulum demonstrates the \ motion of a mathematical pendulum under the influence of the rotation of the \ Earth. One of the most popular installations of a real Foucault's pendulum is \ located at Mus\[EAcute]e des arts et m\[EAcute]tiers in Paris, France. 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Starting the drag near the center \ tumbles\\nthe graphic; starting near a corner turns it parallel to the plane \ of the screen.\\nHold down \"", FrameBox[ "Ctrl", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" (or \"", FrameBox[ "Cmd", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" on Mac) and drag up and down to zoom.\""}], LabelStyle->{ FontFamily -> "Verdana", FontSize -> 10, FontColor -> GrayLevel[0.35], Background -> GrayLevel[0.98]}]]], StyleBox["\[NonBreakingSpace]\[FilledVerySmallSquare]\[NonBreakingSpace]", FontColor->RGBColor[0.928786, 0.43122, 0.104662]], Cell[BoxData[ TooltipBox[ PaneSelectorBox[{False->Cell[TextData[StyleBox["Slider Zoom", FontFamily->"Verdana"]]], True->Cell[TextData[StyleBox["Slider Zoom", FontFamily->"Verdana", FontColor->GrayLevel[0.5]]]]}, Dynamic[ CurrentValue["MouseOver"]]], RowBox[{"\"Hold down the \"", FrameBox[ "Alt", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" key while moving a slider to make fine adjustments in the slider \ value.\\nHold \"", FrameBox[ "Ctrl", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" and/or \"", FrameBox[ "Shift", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" at the same time as \"", FrameBox[ "Alt", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" to make ever finer adjustments.\""}], LabelStyle->{ FontFamily -> "Verdana", FontSize -> 10, FontColor -> GrayLevel[0.35], Background -> GrayLevel[0.98]}]]], StyleBox["\[NonBreakingSpace]\[FilledVerySmallSquare]\[NonBreakingSpace]", FontColor->RGBColor[0.928786, 0.43122, 0.104662]], Cell[BoxData[ TooltipBox[ PaneSelectorBox[{False->Cell[TextData[StyleBox["Automatic Animation", FontFamily->"Verdana"]]], True->Cell[TextData[StyleBox[ "Automatic Animation", FontFamily->"Verdana", FontColor->GrayLevel[0.5]]]]}, Dynamic[ CurrentValue["MouseOver"]]], RowBox[{"\"Animate a slider in this Demonstration by clicking the\"", AdjustmentBox[ Cell[ GraphicsData[ "CompressedBitmap", "eJzzTSzJSM1NLMlMTlRwL0osyMhMLlZwyy8CCjEzMjAwcIKwAgOI/R/IhBKc\n\ /4EAyGAG0f+nTZsGwgysIJIRKsWKLAXGIHFmEpUgLADxWUAkI24jZs+eTaEt\n\ IG+wQKRmzJgBlYf5lhEA30OqWA=="], "Graphics", ImageSize -> {9, 9}, ImageMargins -> 0], BoxBaselineShift -> 0.1839080459770115, BoxMargins -> {{0., 0.}, {-0.1839080459770115, 0.1839080459770115}}], "\"button\\nnext to the slider, and then clicking the play button that \ appears.\\nAnimate all controls by selecting \"", StyleBox["Autorun", FontWeight -> "Bold"], "\" from the\"", AdjustmentBox[ Cell[ GraphicsData[ "CompressedBitmap", "eJyNULENwyAQfEySIlMwTVJlCGRFsosokeNtqBmDBagoaZjAI1C8/8GUUUC6\n\ 57h7cQ8PvU7Pl17nUav7oj/TPH7V7b2QJAUAXBkKmCPRowxICy64bRvGGNF7\n\ X8CctGoDSN4xhIDGGDhzFXwUh3/ClBKrDQPmnGXtI6u0OOd+tZBVUqy1xSaH\n\ UqiK6pPe4XdEdAz6563tx/gejuORGMxJaz8mdpJn7hc="], "Graphics", ImageSize -> {10, 10}, ImageMargins -> 0], BoxBaselineShift -> 0.1839080459770115, BoxMargins -> {{0., 0.}, {-0.1839080459770115, 0.1839080459770115}}], "\"menu.\""}], LabelStyle->{ FontFamily -> "Verdana", FontSize -> 10, FontColor -> GrayLevel[0.35], Background -> GrayLevel[0.98]}]]] }], "ManipulateCaption", CellMargins->{{Inherited, Inherited}, {0, 0}}, Deployed->True, FontFamily->"Verdana", CellTags->"ControlSuggestions"], Cell["DETAILS", "DetailsSection"], Cell["\<\ The Coriolis force causes the pendulum to change its oscillation plane. On \ the equator (latitude = 0) the Coriolis force is zero and the pendulum will \ behave there like an ordinary pendulum. On a pole the Coriolis force attains \ its maximum. The control for the latitude ranges over [0, \[Pi]/2].\ \>", "DetailNotes", CellID->8379850], Cell["RELATED LINKS", "RelatedLinksSection"], Cell[TextData[{ ButtonBox["Coriolis Acceleration", BaseStyle->"Hyperlink", ButtonData->{ URL["http://scienceworld.wolfram.com/physics/CoriolisAcceleration.html"], None}], " (", StyleBox[ButtonBox["ScienceWorld", BaseStyle->"SiteLink", ButtonData->{ URL["http://scienceworld.wolfram.com/"], None}, ButtonNote->"http://scienceworld.wolfram.com/"], FontSlant->"Italic"], ")" }], "RelatedLinks", CellID->11395330], Cell[TextData[{ ButtonBox["Foucault Pendulum", BaseStyle->"Hyperlink", ButtonData->{ URL["http://scienceworld.wolfram.com/physics/FoucaultPendulum.html"], None}], " (", StyleBox[ButtonBox["ScienceWorld", BaseStyle->"SiteLink", ButtonData->{ URL["http://scienceworld.wolfram.com/"], None}, ButtonNote->"http://scienceworld.wolfram.com/"], FontSlant->"Italic"], ")" }], "RelatedLinks", CellID->461730571], Cell[TextData[StyleBox[ButtonBox["DOWNLOAD DEMONSTRATION SOURCE CODE \ \[RightGuillemet]", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/versions/source.jsp?id=\ FoucaultsPendulum&version=0012"], None}, ButtonNote-> "http://demonstrations.wolfram.com/FoucaultsPendulum/FoucaultsPendulum-\ source.nb"], FontWeight->"Bold", FontColor->RGBColor[0.928786, 0.43122, 0.104662]]], "ShowSource", FontSize->10], Cell["PERMANENT CITATION DATA", "CitationSection"], Cell[TextData[{ "\"", ButtonBox["Foucault's Pendulum", BaseStyle->"SiteLink", ButtonData->{ URL["http://demonstrations.wolfram.com/FoucaultsPendulum/"], None}, ButtonNote->"http://demonstrations.wolfram.com/FoucaultsPendulum/"], "\"", " from ", ButtonBox["The Wolfram Demonstrations Project", BaseStyle->"SiteLink", ButtonData->{ URL["http://demonstrations.wolfram.com/"], None}, ButtonNote->"http://demonstrations.wolfram.com/"], "\[ParagraphSeparator]\[NonBreakingSpace]", ButtonBox["http://demonstrations.wolfram.com/FoucaultsPendulum/", BaseStyle->"SiteLink", ButtonData->{ URL["http://demonstrations.wolfram.com/FoucaultsPendulum/"], None}, ButtonNote->"http://demonstrations.wolfram.com/FoucaultsPendulum/"] }], "Citations"], Cell[" ", "AuthorSection"], Cell[TextData[{ "Contributed by: ", ButtonBox["Jens-Peer Kuska", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/author.html?author=Jens-Peer+\ Kuska"], None}, ButtonNote-> "http://demonstrations.wolfram.com/author.html?author=Jens-Peer+Kuska"] }], "Author", FontColor->GrayLevel[0.6]], Cell[TextData[{ "Additional contributions by: ", ButtonBox["Jeff Bryant", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/author.html?author=Jeff+Bryant"], None}, ButtonNote-> "http://demonstrations.wolfram.com/author.html?author=Jeff+Bryant"] }], "Author", FontColor->GrayLevel[0.6], CellID->40340620], Cell[TextData[{ "\[Copyright] ", StyleBox[ButtonBox["The Wolfram Demonstrations Project & Contributors", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/"], None}, ButtonNote->"http://demonstrations.wolfram.com/"], FontColor->GrayLevel[0.6]], "\[ThickSpace]\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]\ \[ThickSpace]", StyleBox[ButtonBox["Terms of Use", BaseStyle->"Hyperlink", ButtonData->{ URL["http://demonstrations.wolfram.com/termsofuse.html"], None}, ButtonNote->"http://demonstrations.wolfram.com/termsofuse.html"], FontColor->GrayLevel[0.6]] }], "Text", CellFrame->{{0, 0}, {0, 0.5}}, CellMargins->{{48, 48}, {20, 50}}, CellFrameColor->GrayLevel[0.45098], FontFamily->"Verdana", FontSize->9, FontColor->GrayLevel[0.6], CellTags->"Copyright"] }, Editable->False, Saveable->False, ScreenStyleEnvironment->"Working", CellGrouping->Manual, WindowSize->{750, 650}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, WindowElements->{ "StatusArea", "MemoryMonitor", "MagnificationPopUp", "VerticalScrollBar", "MenuBar"}, WindowTitle->"Foucault's Pendulum", DockedCells->{}, CellContext->Notebook, FrontEndVersion->"6.0 for Microsoft Windows (32-bit) (May 21, 2008)", StyleDefinitions->Notebook[{ Cell[ CellGroupData[{ Cell[ "Demonstration Styles", "Title", CellChangeTimes -> { 3.3509184553711*^9, {3.36928902713192*^9, 3.36928902738193*^9}, { 3.3754479092466917`*^9, 3.3754479095123196`*^9}, { 3.375558447161495*^9, 3.375558447395873*^9}, {3.37572892702972*^9, 3.375728927639103*^9}}], Cell[ StyleData[StyleDefinitions -> "Default.nb"]], Cell[ CellGroupData[{ Cell[ "Style Environment Names", "Section", CellChangeTimes -> {{3.369277974278112*^9, 3.369277974396138*^9}}], Cell[ StyleData[All, "Working"], ShowCellBracket -> False]}, Closed]], Cell[ CellGroupData[{ Cell[ "Notebook Options", "Section", CellChangeTimes -> {{3.374865264950812*^9, 3.374865265419568*^9}}], Cell[ " The options defined for the style below will be used at the \ Notebook level. ", "Text"], Cell[ StyleData["Notebook"], Editable -> True, PageHeaders -> {{None, None, None}, {None, None, None}}, PageFooters -> {{None, None, None}, {None, None, None}}, PageHeaderLines -> {False, False}, PageFooterLines -> {False, False}, PrintingOptions -> { "FacingPages" -> False, "FirstPageFooter" -> False, "RestPagesFooter" -> False}, CreateCellID -> True, CellFrameLabelMargins -> 6, DefaultNewInlineCellStyle -> "InlineMath", DefaultInlineFormatType -> "DefaultTextInlineFormatType", TrackCellChangeTimes -> False, ShowStringCharacters -> True, CacheGraphics -> False, StyleMenuListing -> None]}, Closed]], Cell[ CellGroupData[{ Cell[ "Input/Output", "Section", CellChangeTimes -> {{3.3756313297791014`*^9, 3.3756313299509783`*^9}}], Cell[ "The cells in this section define styles used for input and output \ to the kernel. Be careful when modifying, renaming, or removing these \ styles, because the front end associates special meanings with these style \ names. 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CellGroupData[{ Cell[ "Basic Styles", "Section", CellChangeTimes -> {{3.34971724802035*^9, 3.34971724966638*^9}, { 3.35091840608065*^9, 3.35091840781999*^9}, {3.35091845122987*^9, 3.35091845356607*^9}, {3.35686681885432*^9, 3.35686681945788*^9}, { 3.375657418186455*^9, 3.375657418452083*^9}}], Cell[ StyleData["Hyperlink"], StyleMenuListing -> None, FontColor -> GrayLevel[0]], Cell[ StyleData["SiteLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontColor -> GrayLevel[0.45098], ButtonBoxOptions -> { Active -> True, ButtonFrame -> "None", ButtonFunction :> (FrontEndExecute[{ NotebookLocate[#2]}]& ), ButtonNote -> ButtonData}], Cell[ StyleData["Link"], FontColor -> GrayLevel[0.45098]], Cell[ CellGroupData[{ Cell[ StyleData["DemoNotes"], CellFrame -> True, CellMargins -> {{0, 0}, {0, 0}}, ReturnCreatesNewCell -> True, CellFrameMargins -> {{48, 48}, {4, 4}}, CellFrameColor -> GrayLevel[0.99], StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 10, FontColor -> GrayLevel[0.45098]], Cell[ StyleData["DemoNotes", "Printout"], CellMargins -> {{24, 0}, {0, 10}}, FontSize -> 9]}, Closed]], Cell[ StyleData["SnapshotsSection"], CellFrame -> {{0, 0}, {0, 2}}, ShowCellBracket -> False, ShowGroupOpener -> True, CellMargins -> {{48, 48}, {10, 30}}, PrivateCellOptions -> {"DefaultCellGroupOpen" -> False}, CellGroupingRules -> {"SectionGrouping", 30}, CellFrameMargins -> {{8, 8}, {8, 2}}, CellFrameColor -> RGBColor[0.870588, 0.521569, 0.121569], DefaultNewCellStyle -> "SnapshotCaption", StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 12, FontColor -> GrayLevel[0.45098]], Cell[ StyleData[ "SnapshotCaption", StyleDefinitions -> StyleData["DemoNotes"]], ShowCellBracket -> False], Cell[ CellGroupData[{ Cell[ StyleData["SnapshotOutput"], ShowCellBracket -> False, CellMargins -> {{48, 10}, {5, 7}}, Evaluatable -> True, CellGroupingRules -> "InputGrouping", StripStyleOnPaste -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, DefaultFormatType -> DefaultInputFormatType, ShowAutoStyles -> True, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, AutoItalicWords -> {}, LanguageCategory -> "Mathematica", FormatType -> InputForm, NumberMarks -> True, LinebreakAdjustments -> {0.85, 2, 10, 0, 1}, CounterIncrements -> "Input", MenuPosition -> 1500, MenuCommandKey -> "9"], Cell[ StyleData["SnapshotOuput", "Printout"], CellMargins -> {{39, 0}, {4, 6}}, LinebreakAdjustments -> {0.85, 2, 10, 1, 1}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DemoTitle"], Deletable -> False, ShowCellBracket -> False, CellMargins -> {{48, 48}, {22, 10}}, CellGroupingRules -> {"SectionGrouping", 20}, StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 20, FontWeight -> "Bold", Background -> GrayLevel[1]], Cell[ StyleData["DemoName", "Printout"], CellMargins -> {{24, 8}, {8, 27}}, HyphenationOptions -> {"HyphenationCharacter" -> "-"}, FontSize -> 16]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DetailsSection"], CellFrame -> {{0, 0}, {0, 1}}, ShowCellBracket -> False, CellMargins -> {{48, 48}, {8, 28}}, CellGroupingRules -> {"SectionGrouping", 25}, CellFrameMargins -> {{48, 48}, {6, 8}}, CellFrameColor -> RGBColor[0.691905, 0.790311, 0.300252], StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 10, FontWeight -> "Bold", FontColor -> RGBColor[0.691905, 0.790311, 0.300252]], Cell[ StyleData["DetailsSection", "Printout"], CellMargins -> {{12, 0}, {0, 16}}, PageBreakBelow -> False, FontSize -> 12]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DemoSection"], CellFrame -> {{0, 0}, {0, 1}}, ShowCellBracket -> False, CellMargins -> {{48, 48}, {8, 28}}, CellGroupingRules -> {"SectionGrouping", 30}, CellFrameMargins -> {{48, 48}, {6, 8}}, CellFrameColor -> RGBColor[ 0.6950942244602121, 0.7903257801174944, 0.29706263828488594`], StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 10, FontWeight -> "Bold", FontSlant -> "Plain", FontColor -> RGBColor[ 0.6950942244602121, 0.7903257801174944, 0.29706263828488594`]], Cell[ StyleData["DemoSection", "Printout"], CellMargins -> {{12, 0}, {0, 16}}, PageBreakBelow -> False, FontSize -> 12]}, Closed]], Cell[ StyleData["ManipulateSection"], CellFrame -> {{0, 0}, {0, 2}}, ShowCellBracket -> False, CellMargins -> {{48, 48}, {10, 30}}, CellGroupingRules -> {"SectionGrouping", 30}, CellFrameMargins -> {{8, 8}, {8, 2}}, CellFrameColor -> RGBColor[0.870588, 0.521569, 0.121569], StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 12], Cell[ StyleData["ManipulateCaptionSection"], CellFrame -> {{0, 0}, {0, 2}}, ShowCellBracket -> False, CellMargins -> {{48, 48}, {10, 30}}, CellGroupingRules -> {"SectionGrouping", 30}, CellFrameMargins -> {{8, 8}, {8, 2}}, CellFrameColor -> RGBColor[0.870588, 0.521569, 0.121569], DefaultNewCellStyle -> "ManipulateCaption", StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 12, FontColor -> GrayLevel[0.45098]], Cell[ StyleData["ManipulateCaption"], ShowCellBracket -> False, CellMargins -> {{48, 48}, {10, 16}}, ReturnCreatesNewCell -> True, StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 11, FontColor -> GrayLevel[0]], Cell[ StyleData[ "SeeAlsoSection", StyleDefinitions -> StyleData["DemoSection"]], ShowCellBracket -> False, DefaultNewCellStyle -> "SeeAlso"], Cell[ StyleData["SeeAlso", StyleDefinitions -> StyleData["DemoNotes"]], CellDingbat -> Cell[ "\[FilledSmallSquare]", FontColor -> RGBColor[0.928786, 0.43122, 0.104662]], ShowCellBracket -> False, FontColor -> GrayLevel[0.45098]], Cell[ StyleData[ "RelatedLinksSection", StyleDefinitions -> StyleData["DemoSection"]], ShowCellBracket -> False, DefaultNewCellStyle -> "RelatedLinks"], Cell[ StyleData[ "RelatedLinks", StyleDefinitions -> StyleData["DemoNotes"]], CellDingbat -> Cell["\[FilledSmallSquare]", FontColor -> RGBColor[0.928786, 0.43122, 0.104662]], ShowCellBracket -> False, FontColor -> GrayLevel[0.45098]], Cell[ StyleData[ "CategoriesSection", StyleDefinitions -> StyleData["DemoSection"]], ShowCellBracket -> False, DefaultNewCellStyle -> "Categories"], Cell[ StyleData["Categories", StyleDefinitions -> StyleData["DemoNotes"]], ShowCellBracket -> False], Cell[ StyleData[ "AuthorSection", StyleDefinitions -> StyleData["DemoSection"]], ShowCellBracket -> False, CellMargins -> {{48, 48}, {4, 18}}, CellElementSpacings -> {"CellMinHeight" -> 3}, CellFrameMargins -> {{48, 48}, {6, 3}}, DefaultNewCellStyle -> "Author", FontSize -> 1, FontColor -> GrayLevel[1]], Cell[ StyleData["Author", StyleDefinitions -> StyleData["DemoNotes"]], CellDingbat -> Cell["\[FilledSmallSquare]", FontColor -> GrayLevel[0.64]], ShowCellBracket -> False], Cell[ StyleData[ "DetailNotes", StyleDefinitions -> StyleData["DemoNotes"]], ShowCellBracket -> False, FontColor -> GrayLevel[0]], Cell[ StyleData[ "CitationSection", StyleDefinitions -> StyleData["DemoSection"]], ShowCellBracket -> False, CellMargins -> {{48, 48}, {8, 14}}, DefaultNewCellStyle -> "Categories"], Cell[ StyleData["Citations", StyleDefinitions -> StyleData["DemoNotes"]], ShowCellBracket -> False, ParagraphSpacing -> {0, 6}], Cell[ StyleData[ "RevisionSection", StyleDefinitions -> StyleData["DemoSection"]], DefaultNewCellStyle -> "RevisionNotes"], Cell[ StyleData[ "RevisionNotes", StyleDefinitions -> StyleData["DemoNotes"]], ShowCellBracket -> False]}, Closed]], Cell[ CellGroupData[{ Cell[ "Specific Styles", "Section", CellChangeTimes -> {{3.34971724802035*^9, 3.34971724966638*^9}, { 3.35091840608065*^9, 3.35091840781999*^9}, {3.35091845122987*^9, 3.35091845356607*^9}, {3.36230868322317*^9, 3.36230868335672*^9}, { 3.36928857618576*^9, 3.36928857640452*^9}, {3.3737586217185173`*^9, 3.373758622077897*^9}}], Cell[ StyleData["InitializationSection"], CellFrame -> {{0, 0}, {0, 2}}, ShowCellBracket -> False, CellMargins -> {{48, 48}, {10, 30}}, CellGroupingRules -> {"SectionGrouping", 30}, CellFrameMargins -> {{8, 8}, {8, 2}}, CellFrameColor -> RGBColor[0.870588, 0.521569, 0.121569], StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 12, FontColor -> GrayLevel[0.45098]], Cell[ CellGroupData[{ Cell[ StyleData["AnchorBar"], ShowCellBracket -> False, CellMargins -> {{48, 44}, {3, 6}}, StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 9, FontColor -> GrayLevel[0.5]], Cell[ StyleData["AnchorBar", "Presentation"], FontSize -> 18], Cell[ StyleData["AnchorBar", "SlideShow"], StyleMenuListing -> None], Cell[ StyleData["AnchorBar", "Printout"], FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["AnchorLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontColor -> RGBColor[0.5, 0.5, 0.5], ButtonBoxOptions -> { Active -> True, ButtonFunction :> (FrontEndExecute[{ FrontEnd`NotebookLocate[#2]}]& ), ButtonNote -> ButtonData}], Cell[ StyleData["AnchorLink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["GamePadStatus"], ShowCellBracket -> False, CellMargins -> {{48, 48}, {5, 5}}, StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 10], Cell[ StyleData["GamePadStatus", "Printout"], CellMargins -> {{24, 0}, {0, 10}}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DemoInstruction"], CellMargins -> {{48, 48}, {5, 5}}, ReturnCreatesNewCell -> True, CellFrameLabelMargins -> 2, MenuPosition -> 800, MenuCommandKey -> "8", StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 11, Background -> RGBColor[1, 0.85, 0.5]], Cell[ StyleData["DemoInstruction", "Printout"], CellMargins -> {{24, 0}, {0, 10}}, Hyphenation -> True, HyphenationOptions -> {"HyphenationCharacter" -> "-"}, LineSpacing -> {1., 2, 2.}, FontSize -> 9]}, Closed]], Cell[ StyleData[ "ImplementationSection", StyleDefinitions -> StyleData["DemoSection"]], Deletable -> True, DefaultNewCellStyle -> "ImplementationNotes"], Cell[ StyleData[ "ImplementationNotes", StyleDefinitions -> StyleData["DemoNotes"]]], Cell[ StyleData[ "StatusSection", StyleDefinitions -> StyleData["DemoSection"]], DefaultNewCellStyle -> "StatusNotes"], Cell[ StyleData[ "StatusNotes", StyleDefinitions -> StyleData["DemoNotes"]]], Cell[ CellGroupData[{ Cell[ StyleData["SectionGloss"], StyleMenuListing -> None, FontSize -> 0.85 Inherited, FontWeight -> "Plain", FontColor -> GrayLevel[0.6]], Cell[ StyleData["SectionGloss", "Printout"]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InlineFormula"], "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LanguageCategory -> "Formula", AutoSpacing -> True, ScriptLevel -> 1, AutoMultiplicationSymbol -> False, SingleLetterItalics -> False, SpanMaxSize -> 1, StyleMenuListing -> None, FontFamily -> "Courier", FontSize -> 1.05 Inherited, ButtonBoxOptions -> {ButtonFrame -> "None"}, FractionBoxOptions -> {BaseStyle -> {SpanMaxSize -> Automatic}}, GridBoxOptions -> { GridBoxItemSize -> { "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}}], Cell[ StyleData["InlineFormula", "Printout"], CellMargins -> {{2, 0}, {0, 8}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InlineOutput"], CellHorizontalScrolling -> True, "TwoByteSyntaxCharacterAutoReplacement" -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LanguageCategory -> None, AutoMultiplicationSymbol -> False, StyleMenuListing -> None, FontFamily -> "Courier", FontSize -> 1.05 Inherited], Cell[ StyleData["InlineOutput", "Printout"], CellMargins -> {{2, 0}, {0, 8}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InlineMath"], DefaultFormatType -> "DefaultTextFormatType", DefaultInlineFormatType -> "TraditionalForm", LanguageCategory -> "Formula", AutoSpacing -> True, ScriptLevel -> 1, AutoMultiplicationSymbol -> False, SingleLetterItalics -> True, SpanMaxSize -> DirectedInfinity[1], StyleMenuListing -> None, FontFamily -> "Times", FontSize -> 1.05 Inherited, ButtonBoxOptions -> {ButtonFrame -> "None"}, GridBoxOptions -> { GridBoxItemSize -> { "Columns" -> {{Automatic}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}}], Cell[ StyleData["InlineMath", "Printout"], CellMargins -> {{2, 0}, {0, 8}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["TableBase"], CellMargins -> {{48, 48}, {4, 4}}, SpanMaxSize -> 1, StyleMenuListing -> None, FontFamily -> "Courier", FontSize -> 11, ButtonBoxOptions -> {ButtonFrame -> "None"}, GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}}], Cell[ StyleData["TableBase", "Printout"], CellMargins -> {{2, 0}, {0, 8}}, FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "1ColumnTableMod", StyleDefinitions -> StyleData["TableBase"]], GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> { Scaled[0.04], { Scaled[0.966]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.28], Offset[0.126], { Offset[0.77]}, Offset[0.28]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData[ "1ColumnTableMod", "Printout", StyleDefinitions -> StyleData["TableBase", "Printout"]], GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> { Scaled[0.078], { Scaled[0.922]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.28], { Offset[0.56]}, Offset[0.28]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.56]}, Offset[0.2]}, "RowsIndexed" -> {}}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "2ColumnTableMod", StyleDefinitions -> StyleData["TableBase"]], GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> { Scaled[0.05], Scaled[0.41], { Scaled[0.565]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.28], Offset[0.14], { Offset[0.77]}, Offset[0.28]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData[ "2ColumnTableMod", "Printout", StyleDefinitions -> StyleData["TableBase", "Printout"]], GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> { Scaled[0.079], Scaled[0.363], { Scaled[0.558]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.28], { Offset[0.56]}, Offset[0.28]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.56]}, Offset[0.2]}, "RowsIndexed" -> {}}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "3ColumnTableMod", StyleDefinitions -> StyleData["TableBase"]], GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> { Scaled[0.04], Scaled[0.266], Scaled[0.26], { Scaled[0.44]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.28], Offset[0.14], { Offset[0.77]}, Offset[0.28]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData[ "3ColumnTableMod", "Printout", StyleDefinitions -> StyleData["TableBase", "Printout"]], GridBoxOptions -> {GridBoxItemSize -> {"Columns" -> { Scaled[0.08], Scaled[0.25], Scaled[0.25], { Scaled[0.42]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.28], { Offset[0.56]}, Offset[0.28]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.56]}, Offset[0.2]}, "RowsIndexed" -> {}}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["TableText"], Deletable -> False, StyleMenuListing -> None, FontFamily -> "Verdana", FontSize -> 0.952 Inherited], Cell[ StyleData["TableText", "Printout"], CellMargins -> {{24, 0}, {0, 8}}, Hyphenation -> True, HyphenationOptions -> {"HyphenationCharacter" -> "-"}, LineSpacing -> {1., 2, 2.}]}, Closed]], Cell[ StyleData["Continuation"], FontColor 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