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| − | [[File:part1d1.pdf]]
| + | <center><math>\underline{\textbf{Navigation}}</math> |
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| | + | [[Plotting_Different_Frames|<math>\vartriangleleft </math>]] |
| | + | [[VanWasshenova_Thesis#Determining_wire-theta_correspondence|<math>\triangle </math>]] |
| | + | [[Change_in_Wire_Bin_Number|<math>\vartriangleright </math>]] |
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| − | The point that was the semi-major vertex, when rotated 6\[Degree] to the right becomes
| + | </center> |
| | + | [[File:part1d3.png]] |
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| − | <pre>
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| − | In[1603]:= rFromYtoX.{1.6831832367824053`, 0, 0} // MatrixForm
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| − | Out[1603]//MatrixForm= \!\(
| + | ---- |
| − | TagBox[
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| − | RowBox[{"(", "",
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| − | TagBox[GridBox[{
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| − | {"1.6739625828969429`"},
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| − | {"0.17594055713873974`"},
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| − | {"0.`"}
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| − | },
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| − | GridBoxAlignment->{
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| − | "Columns" -> {{Center}}, "ColumnsIndexed" -> {},
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| − | "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
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| − | GridBoxSpacings->{"Columns" -> {
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| − | Offset[0.27999999999999997`], {
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| − | Offset[0.5599999999999999]},
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| − | Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
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| − | Offset[0.2], {
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| − | Offset[0.4]},
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| − | Offset[0.2]}, "RowsIndexed" -> {}}],
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| − | Column], "", ")"}],
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| − | Function[BoxForm`e$,
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| − | MatrixForm[BoxForm`e$]]]\)
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| − | </pre>
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| − | Solving for the ellipse parameter given the angle and the corresponding X'' and Y'' components
| + | <center><math>\underline{\textbf{Navigation}}</math> |
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| | + | [[Plotting_Different_Frames|<math>\vartriangleleft </math>]] |
| | + | [[VanWasshenova_Thesis#Determining_wire-theta_correspondence|<math>\triangle </math>]] |
| | + | [[Change_in_Wire_Bin_Number|<math>\vartriangleright </math>]] |
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| − | <pre>
| + | </center> |
| − | X = 1.6739625828969429`;
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| − | Y = 0.17594055713873974`;
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| − | \[Theta] = 40;
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| − | t = t /. Solve[
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| − | X^2 (Cos[6 \[Degree]])^2 +
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| − | Y^2 (Sin[6 \[Degree]])^2 + \[CapitalDelta]a^2 +
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| − | 2 X Y Cos[6 \[Degree]] Sin[6 \[Degree]] +
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| − | 2 X \[CapitalDelta]a Cos[6 \[Degree]] +
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| − | 2 Y \[CapitalDelta]a Sin[6 \[Degree]] +
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| − | X^2 (Sin[6 \[Degree]])^2 + Y^2 (Cos[6 \[Degree]])^2 -
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| − | 2 X Y Sin[6 \[Degree]] Cos[6 \[Degree]] ==
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| − | a^2 (Cos[t])^2 (Cos[6 \[Degree]])^2 +
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| − | b^2 (Sin[t])^2 (Sin[6 \[Degree]])^2 + \[CapitalDelta]a^2 +
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| − | 2 a b Cos[t] Cos[6 \[Degree]] Sin[t] Sin[6 \[Degree]] +
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| − | 2 a \[CapitalDelta]a Cos[t] Cos[6 \[Degree]] +
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| − | 2 b \[CapitalDelta]a Sin[t] Sin[6 \[Degree]] +
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| − | a^2 (Cos[t])^2 (Sin[6 \[Degree]])^2 +
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| − | b^2 (Sin[t])^2 (Cos[6 \[Degree]])^2 -
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| − | 2 a b Cos[t] Sin[6 \[Degree]] Cos[6 \[Degree]] Sin[t], t]
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| − | ClearAll[X, Y, \[Theta]];
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| − | </pre>
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| − | | |
| − | | |
| − | <pre>{-1.31406, 1.4676, 3.06482 - 1.66742 I, 3.06482 + 1.66742 I}</pre>
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| − | | |
| − | We can see that at the vertex position, the parameter reaches it's minimum at 1.4676. This point reflects the right and left sides of the ellipse and the corresponding decreases in wire number as the parameter is increased.
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