Plotting Different Frames - Revision history

Vanwdani at 20:34, 15 May 2018

2018-05-15T20:34:24Z

Vanwdani at 18:47, 15 May 2017

2017-05-15T18:47:39Z

Vanwdani at 18:33, 15 May 2017

2017-05-15T18:33:44Z

Vanwdani at 18:04, 15 May 2017

2017-05-15T18:04:48Z

Vanwdani at 17:59, 15 May 2017

2017-05-15T17:59:05Z

Vanwdani at 17:24, 15 May 2017

2017-05-15T17:24:23Z

Vanwdani: Replaced content with "File:part1d2.png"

2017-05-03T21:40:30Z

Replaced content with "File:part1d2.png"

Show changes

Vanwdani at 21:05, 3 May 2017

2017-05-03T21:05:50Z

Vanwdani at 21:03, 3 May 2017

2017-05-03T21:03:16Z

Vanwdani at 20:58, 3 May 2017

2017-05-03T20:58:18Z

@@ Line 1: / Line 1: @@
-<center><math>\textbf{\underline{Navigation}}</math>
+<center><math>\underline{\textbf{Navigation}}</math>
 [[The_Ellipse|<math>\vartriangleleft </math>]]
@@ Line 6: / Line 6: @@
 </center>
 [[File:part1d2.png]]
@@ Line 14: / Line 15: @@
-<center><math>\textbf{\underline{Navigation}}</math>
+<center><math>\underline{\textbf{Navigation}}</math>
 [[The_Ellipse|<math>\vartriangleleft </math>]]

← Older revision		Revision as of 18:47, 15 May 2017
Line 7:		Line 7:
	</center>		</center>
	[[File:part1d2.png]]		[[File:part1d2.png]]
		+
		+
		+
		+	----
		+

← Older revision		Revision as of 18:33, 15 May 2017
Line 7:		Line 7:
	</center>		</center>
	[[File:part1d2.png]]		[[File:part1d2.png]]
		+
		+
		+	<center><math>\textbf{\underline{Navigation}}</math>
		+
		+	[[The_Ellipse\|<math>\vartriangleleft </math>]]
		+	[[VanWasshenova_Thesis#Determining_wire-theta_correspondence\|<math>\triangle </math>]]
		+	[[Parameterizing_the_Ellipse_Equation\|<math>\vartriangleright </math>]]
		+
		+	</center>

@@ Line 1: / Line 1: @@
 <center><math>\textbf{\underline{Navigation}}</math>
-[[VanWasshenova_Thesis#Determining_wire-theta_correspondence|<math>\vartriangleleft </math>]]
+[[The_Ellipse|<math>\vartriangleleft </math>]]
 [[VanWasshenova_Thesis#Determining_wire-theta_correspondence|<math>\triangle </math>]]
 [[Parameterizing_the_Ellipse_Equation|<math>\vartriangleright </math>]]

@@ Line 3: / Line 3: @@
 [[VanWasshenova_Thesis#Determining_wire-theta_correspondence|<math>\vartriangleleft </math>]]
 [[VanWasshenova_Thesis#Determining_wire-theta_correspondence|<math>\triangle </math>]]
-[[CED_Verification_of_DC_Angle_Theta_and_Wire_Correspondance|<math>\vartriangleright </math>]]
+[[Parameterizing_the_Ellipse_Equation|<math>\vartriangleright </math>]]
 </center>
 [[File:part1d2.png]]

← Older revision		Revision as of 17:24, 15 May 2017
Line 1:		Line 1:
		+	<center><math>\textbf{\underline{Navigation}}</math>
		+
		+	[[VanWasshenova_Thesis#Determining_wire-theta_correspondence\|<math>\vartriangleleft </math>]]
		+	[[VanWasshenova_Thesis#Determining_wire-theta_correspondence\|<math>\triangle </math>]]
		+	[[CED_Verification_of_DC_Angle_Theta_and_Wire_Correspondance\|<math>\vartriangleright </math>]]
		+
		+	</center>
	[[File:part1d2.png]]		[[File:part1d2.png]]

← Older revision		Revision as of 21:05, 3 May 2017
Line 377:		Line 377:


−	~~The point that was the semi-major vertex, when rotated 6\[Degree] to the right becomes~~

−	~~<pre>~~
−	~~In[1603]:= rFromYtoX.{1.6831832367824053`, 0, 0} // MatrixForm~~
−
−	~~Out[1603]//MatrixForm= \!\(~~
−	~~TagBox[~~
−	~~RowBox[{"(", "",~~
−	~~TagBox[GridBox[{~~
−	~~{"1.6739625828969429`"},~~
−	~~{"0.17594055713873974`"},~~
−	~~{"0.`"}~~
−	},
−	~~GridBoxAlignment->{~~
−	~~"Columns" -> {{Center}}, "ColumnsIndexed" -> {},~~
−	~~"Rows" -> {{Baseline}}, "RowsIndexed" -> {}},~~
−	~~GridBoxSpacings->{"Columns" -> {~~
−	~~Offset[0.27999999999999997`], {~~
−	~~Offset[0.5599999999999999]},~~
−	~~Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {~~
−	~~Offset[0.2], {~~
−	~~Offset[0.4]},~~
−	~~Offset[0.2]}, "RowsIndexed" -> {}}],~~
−	~~Column], "", ")"}],~~
−	~~Function[BoxForm`e$,~~
−	~~MatrixForm[BoxForm`e$]]]\)~~
−	~~</pre>~~
−
−
−	~~Solving for the ellipse parameter given the angle and the corresponding X'' and Y'' components~~
−
−
−	~~<pre>~~
−	~~X = 1.6739625828969429`;~~
−	~~Y = 0.17594055713873974`;~~
−	~~\[Theta] = 40;~~
−	~~t = t /. Solve[~~
−	~~X^2 (Cos[6 \[Degree]])^2 +~~
−	~~Y^2 (Sin[6 \[Degree]])^2 + \[CapitalDelta]a^2 +~~
−	~~2 X Y Cos[6 \[Degree]] Sin[6 \[Degree]] +~~
−	~~2 X \[CapitalDelta]a Cos[6 \[Degree]] +~~
−	~~2 Y \[CapitalDelta]a Sin[6 \[Degree]] +~~
−	~~X^2 (Sin[6 \[Degree]])^2 + Y^2 (Cos[6 \[Degree]])^2 -~~
−	~~2 X Y Sin[6 \[Degree]] Cos[6 \[Degree]] ==~~
−	~~a^2 (Cos[t])^2 (Cos[6 \[Degree]])^2 +~~
−	~~b^2 (Sin[t])^2 (Sin[6 \[Degree]])^2 + \[CapitalDelta]a^2 +~~
−	~~2 a b Cos[t] Cos[6 \[Degree]] Sin[t] Sin[6 \[Degree]] +~~
−	~~2 a \[CapitalDelta]a Cos[t] Cos[6 \[Degree]] +~~
−	~~2 b \[CapitalDelta]a Sin[t] Sin[6 \[Degree]] +~~
−	~~a^2 (Cos[t])^2 (Sin[6 \[Degree]])^2 +~~
−	~~b^2 (Sin[t])^2 (Cos[6 \[Degree]])^2 -~~
−	~~2 a b Cos[t] Sin[6 \[Degree]] Cos[6 \[Degree]] Sin[t], t]~~
−	~~ClearAll[X, Y, \[Theta]];~~
−	~~</pre>~~
−
−
−	~~<pre>{-1.31406, 1.4676, 3.06482 - 1.66742 I, 3.06482 + 1.66742 I}</pre>~~
−
−	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.

	<pre>		<pre>

← Older revision		Revision as of 21:03, 3 May 2017
Line 436:		Line 436:

	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.		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.
		+
		+	<pre>
		+	\[Theta] = 40;
		+	ellipse40full =
		+	ContourPlot[(x + \[CapitalDelta]a)^2/a^2 + y^2/b^2 == 1, {y, -3,
		+	3}, {x, -4, 1.8}, Frame -> {True, True, False, False},
		+	PlotLabel ->
		+	"X'/X'' & Y'Y'' position on DC sector plane as a function of \
		+	\[Phi] for \[Theta]=40\[Degree]",
		+	FrameLabel -> {"y'/y'' (meters)", "x'/x'' (meters)"},
		+	ContourStyle -> Red, PlotLegends -> Automatic];
		+	ellipse40Rotatedfull =
		+	ContourPlot[(X Cos[6 \[Degree]] +
		+	Y Sin[6 \[Degree]] + \[CapitalDelta]a)^2/
		+	a^2 + (-X Sin[6 \[Degree]] + Y Cos[6 \[Degree]])^2/b^2 ==
		+	1, {Y, -3, 3}, {X, -4, 1.8}, Frame -> {True, True, False, False},
		+	PlotLabel ->
		+	"X'' & Y'' position on DC sector wires a function of \[Phi] for \
		+	\[Theta]=40\[Degree]", FrameLabel -> {"y'' (meters)", "x'' (meters)"},
		+	ContourStyle -> Blue, PlotLegends -> Automatic];
		+	SemiMajorAxisfull =
		+	ContourPlot[Y == 0, {Y, -3, 3}, {X, -4, 1.8},
		+	Frame -> {True, True, False, False},
		+	PlotLabel ->
		+	"Right side limit of DC as a function of X and Y",
		+	FrameLabel -> {"y (meters)", "x (meters)"}, ContourStyle -> Red,
		+	PlotLegends -> Automatic];
		+	SemiMajorAxisRotatedfull =
		+	ContourPlot[X == 9.614 Y, {Y, -3, 3}, {X, 0 - 4, 1.8},
		+	Frame -> {True, True, False, False},
		+	PlotLabel ->
		+	"Right side limit of DC as a function of X/X'' and Y",
		+	FrameLabel -> {"y (meters)", "x (meters)"}, ContourStyle -> Blue,
		+	PlotLegends -> Automatic];
		+
		+
		+	Show[ellipse40full, ellipse40Rotatedfull, SemiMajorAxisRotatedfull, \
		+	SemiMajorAxisfull]
		+	</pre>
		+
		+
		+	[[File:X1x2&y1y2ellipse.png]]

← Older revision		Revision as of 20:58, 3 May 2017
Line 375:		Line 375:

	<center>[[File:x2y2plane.png]]</center>		<center>[[File:x2y2plane.png]]</center>
		+
		+
		+	The point that was the semi-major vertex, when rotated 6\[Degree] to the right becomes
		+
		+	<pre>
		+	In[1603]:= rFromYtoX.{1.6831832367824053`, 0, 0} // MatrixForm
		+
		+	Out[1603]//MatrixForm= \!\(
		+	TagBox[
		+	RowBox[{"(", "",
		+	TagBox[GridBox[{
		+	{"1.6739625828969429`"},
		+	{"0.17594055713873974`"},
		+	{"0.`"}
		+	},
		+	GridBoxAlignment->{
		+	"Columns" -> {{Center}}, "ColumnsIndexed" -> {},
		+	"Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
		+	GridBoxSpacings->{"Columns" -> {
		+	Offset[0.27999999999999997`], {
		+	Offset[0.5599999999999999]},
		+	Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
		+	Offset[0.2], {
		+	Offset[0.4]},
		+	Offset[0.2]}, "RowsIndexed" -> {}}],
		+	Column], "", ")"}],
		+	Function[BoxForm`e$,
		+	MatrixForm[BoxForm`e$]]]\)
		+	</pre>
		+
		+
		+	Solving for the ellipse parameter given the angle and the corresponding X'' and Y'' components
		+
		+
		+	<pre>
		+	X = 1.6739625828969429`;
		+	Y = 0.17594055713873974`;
		+	\[Theta] = 40;
		+	t = t /. Solve[
		+	X^2 (Cos[6 \[Degree]])^2 +
		+	Y^2 (Sin[6 \[Degree]])^2 + \[CapitalDelta]a^2 +
		+	2 X Y Cos[6 \[Degree]] Sin[6 \[Degree]] +
		+	2 X \[CapitalDelta]a Cos[6 \[Degree]] +
		+	2 Y \[CapitalDelta]a Sin[6 \[Degree]] +
		+	X^2 (Sin[6 \[Degree]])^2 + Y^2 (Cos[6 \[Degree]])^2 -
		+	2 X Y Sin[6 \[Degree]] Cos[6 \[Degree]] ==
		+	a^2 (Cos[t])^2 (Cos[6 \[Degree]])^2 +
		+	b^2 (Sin[t])^2 (Sin[6 \[Degree]])^2 + \[CapitalDelta]a^2 +
		+	2 a b Cos[t] Cos[6 \[Degree]] Sin[t] Sin[6 \[Degree]] +
		+	2 a \[CapitalDelta]a Cos[t] Cos[6 \[Degree]] +
		+	2 b \[CapitalDelta]a Sin[t] Sin[6 \[Degree]] +
		+	a^2 (Cos[t])^2 (Sin[6 \[Degree]])^2 +
		+	b^2 (Sin[t])^2 (Cos[6 \[Degree]])^2 -
		+	2 a b Cos[t] Sin[6 \[Degree]] Cos[6 \[Degree]] Sin[t], t]
		+	ClearAll[X, Y, \[Theta]];
		+	</pre>
		+
		+
		+	<pre>{-1.31406, 1.4676, 3.06482 - 1.66742 I, 3.06482 + 1.66742 I}</pre>
		+
		+	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.