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hyperboloid geodesics.nb
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hyperboloid geodesics.nb
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Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu",
Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ =
"\"untitled\"", Typeset`specs$$ = {{{
Hold[$CellContext`vsep$$], 0.1}, 0, 2}, {{
Hold[$CellContext`\[Theta]0$$], 0.1}, 0, 1}, {{
Hold[$CellContext`\[Tau]max$$], 100}, 0, 100}}, Typeset`size$$ = {
360., {181., 185.8179089521267}}, Typeset`update$$ = 0,
Typeset`initDone$$, Typeset`skipInitDone$$ = True},
DynamicBox[Manipulate`ManipulateBoxes[
1, StandardForm,
"Variables" :> {$CellContext`vsep$$ = 0.1, $CellContext`\[Theta]0$$ =
0.1, $CellContext`\[Tau]max$$ = 100}, "ControllerVariables" :> {},
"OtherVariables" :> {
Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$,
Typeset`animator$$, Typeset`animvar$$, Typeset`name$$,
Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
Typeset`skipInitDone$$},
"Body" :> ({$CellContext`\[CapitalTheta]1, $CellContext`V1} =
ReplaceAll[{$CellContext`\[Theta], $CellContext`v},
Part[
NDSolve[{$CellContext`\[Theta]Eq == 0, $CellContext`vEq == 0,
Derivative[1][$CellContext`v][0] == 0,
Derivative[1][$CellContext`\[Theta]][
0] == $CellContext`\[Theta]0$$, $CellContext`\[Theta][0] ==
0, $CellContext`v[
0] == $CellContext`vsep$$}, {$CellContext`\[Theta], \
$CellContext`v}, {$CellContext`\[Tau], 0, $CellContext`\[Tau]max$$}],
1]]; {$CellContext`\[CapitalTheta]2, $CellContext`V2} =
ReplaceAll[{$CellContext`\[Theta], $CellContext`v},
Part[
NDSolve[{$CellContext`\[Theta]Eq == 0, $CellContext`vEq == 0,
Derivative[1][$CellContext`v][0] == 0,
Derivative[1][$CellContext`\[Theta]][
0] == $CellContext`\[Theta]0$$, $CellContext`\[Theta][0] ==
0, $CellContext`v[
0] == -$CellContext`vsep$$}, {$CellContext`\[Theta], \
$CellContext`v}, {$CellContext`\[Tau], 0, $CellContext`\[Tau]max$$}], 1]];
Show[{
ParametricPlot3D[{$CellContext`a Cosh[$CellContext`v]
Cos[$CellContext`\[Theta]], $CellContext`c
Sinh[$CellContext`v], $CellContext`b Cosh[$CellContext`v]
Sin[$CellContext`\[Theta]]}, {$CellContext`v, -2,
2}, {$CellContext`\[Theta], 0, 2 Pi},
AxesLabel -> {"x", "y", "z"},
PlotRange -> {{-4, 4}, {-8, 8}, {-4, 4}}],
ParametricPlot3D[{$CellContext`a Cosh[
$CellContext`V1[$CellContext`\[Tau]]] Cos[
$CellContext`\[CapitalTheta]1[$CellContext`\[Tau]]], \
$CellContext`c Sinh[
$CellContext`V1[$CellContext`\[Tau]]], $CellContext`b Cosh[
$CellContext`V1[$CellContext`\[Tau]]] Sin[
$CellContext`\[CapitalTheta]1[$CellContext`\[Tau]]]}, \
{$CellContext`\[Tau], 0, $CellContext`\[Tau]max$$},
PlotStyle -> {Thick, Red}],
ParametricPlot3D[{$CellContext`a Cosh[
$CellContext`V2[$CellContext`\[Tau]]] Cos[
$CellContext`\[CapitalTheta]2[$CellContext`\[Tau]]], \
$CellContext`c Sinh[
$CellContext`V2[$CellContext`\[Tau]]], $CellContext`b Cosh[
$CellContext`V2[$CellContext`\[Tau]]] Sin[
$CellContext`\[CapitalTheta]2[$CellContext`\[Tau]]]}, \
{$CellContext`\[Tau], 0, $CellContext`\[Tau]max$$},
PlotStyle -> {Thick, Blue}]}]),
"Specifications" :> {{{$CellContext`vsep$$, 0.1}, 0,
2}, {{$CellContext`\[Theta]0$$, 0.1}, 0,
1}, {{$CellContext`\[Tau]max$$, 100}, 0, 100}}, "Options" :> {},
"DefaultOptions" :> {}],
ImageSizeCache->{842., {210., 216.}},
SingleEvaluation->True],
Deinitialization:>None,
DynamicModuleValues:>{},
SynchronousInitialization->True,
UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
UnsavedVariables:>{Typeset`initDone$$},
UntrackedVariables:>{Typeset`size$$}], "Manipulate",
Deployed->True,
StripOnInput->False],
Manipulate`InterpretManipulate[1]]], "Output",
CellChangeTimes->{
3.842414339311787*^9, 3.8424144219841704`*^9, {3.8424144845536427`*^9,
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3.8424146860630445`*^9, 3.8424147008696227`*^9}, 3.8424148164486804`*^9, {
3.8424148615047398`*^9, 3.842414883041161*^9}, {3.842414989560676*^9,
3.8424150272178*^9}, 3.842415057998166*^9, 3.842415098402952*^9,
3.8424152573300943`*^9, {3.8424152960969076`*^9, 3.842415324726474*^9}},
CellLabel->
"Out[154]=",ExpressionUUID->"4419603b-60ee-4165-aaa8-5908aac869e6"]
}, Open ]]
},
WindowSize->{960, 484},
WindowMargins->{{-5.5, Automatic}, {Automatic, -5.5}},
FrontEndVersion->"12.1 for Microsoft Windows (64-bit) (March 18, 2020)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"1e1201e9-558e-4f96-871c-3d219a22e86f"
]
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