Conic Sections - Revision history

Vanwdani at 20:22, 15 May 2018

2018-05-15T20:22:20Z

← Older revision		Revision as of 20:22, 15 May 2018
Line 1:		Line 1:
	<center><math>\~~textbf~~{\~~underline~~{Navigation}}</math>		<center><math>\underline{\textbf{Navigation}}</math>

	[[Detector_Geometry_Simulation\|<math>\vartriangleleft </math>]]		[[Detector_Geometry_Simulation\|<math>\vartriangleleft </math>]]
Line 6:		Line 6:

	</center>		</center>



	=Conic Sections=		=Conic Sections=
Line 52:		Line 54:


	<center><math>\~~textbf~~{\~~underline~~{Navigation}}</math>		<center><math>\underline{\textbf{Navigation}}</math>

	[[Detector_Geometry_Simulation\|<math>\vartriangleleft </math>]]		[[Detector_Geometry_Simulation\|<math>\vartriangleleft </math>]]

Vanwdani at 18:43, 15 May 2017

2017-05-15T18:43:00Z

← Older revision		Revision as of 18:43, 15 May 2017
Line 47:		Line 47:

	Examining the different conic sections possible we know that:		Examining the different conic sections possible we know that:


			----


			<center><math>\textbf{\underline{Navigation}}</math>

			[[Detector_Geometry_Simulation\|<math>\vartriangleleft </math>]]
			[[VanWasshenova_Thesis#Determining_wire-theta_correspondence\|<math>\triangle </math>]]
			[[Circular_Cross_Sections\|<math>\vartriangleright </math>]]

			</center>

Vanwdani at 18:27, 15 May 2017

2017-05-15T18:27:37Z

← Older revision		Revision as of 18:27, 15 May 2017
Line 47:		Line 47:

	Examining the different conic sections possible we know that:		Examining the different conic sections possible we know that:

	~~=[[VanWasshenova_Thesis#Conic_Sections\|^Up]]=~~
	~~=[[Detector_Geometry_Simulation\|<-Back]]=~~
	~~=[[Circular_Cross_Sections\|Forward->]]=~~

Vanwdani at 18:15, 15 May 2017

2017-05-15T18:15:20Z

← Older revision		Revision as of 18:15, 15 May 2017
Line 1:		Line 1:
	<center><math>\textbf{\underline{Navigation}}</math>		<center><math>\textbf{\underline{Navigation}}</math>

	[[~~VanWasshenova_Thesis#Determining_wire-theta_correspondence~~\|<math>\vartriangleleft </math>]]		[[Detector_Geometry_Simulation\|<math>\vartriangleleft </math>]]
	[[VanWasshenova_Thesis#Determining_wire-theta_correspondence\|<math>\triangle </math>]]		[[VanWasshenova_Thesis#Determining_wire-theta_correspondence\|<math>\triangle </math>]]
	[[Circular_Cross_Sections\|<math>\vartriangleright </math>]]		[[Circular_Cross_Sections\|<math>\vartriangleright </math>]]

Vanwdani at 17:36, 15 May 2017

2017-05-15T17:36:34Z

← Older revision		Revision as of 17:36, 15 May 2017
Line 3:		Line 3:
	[[VanWasshenova_Thesis#Determining_wire-theta_correspondence\|<math>\vartriangleleft </math>]]		[[VanWasshenova_Thesis#Determining_wire-theta_correspondence\|<math>\vartriangleleft </math>]]
	[[VanWasshenova_Thesis#Determining_wire-theta_correspondence\|<math>\triangle </math>]]		[[VanWasshenova_Thesis#Determining_wire-theta_correspondence\|<math>\triangle </math>]]
	[[~~CED_Verification_of_DC_Angle_Theta_and_Wire_Correspondance~~\|<math>\vartriangleright </math>]]		[[Circular_Cross_Sections\|<math>\vartriangleright </math>]]

	</center>		</center>

Vanwdani at 17:29, 15 May 2017

2017-05-15T17:29:37Z

← Older revision		Revision as of 17:29, 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>

	=Conic Sections=		=Conic Sections=
	Looking just at sector 1, we can see that the intersection of level 1 and the cone of constant angle theta forms a conic section.		Looking just at sector 1, we can see that the intersection of level 1 and the cone of constant angle theta forms a conic section.

Vanwdani at 05:52, 4 March 2017

2017-03-04T05:52:58Z

← Older revision		Revision as of 05:52, 4 March 2017
Line 39:		Line 39:

	Examining the different conic sections possible we know that:		Examining the different conic sections possible we know that:

			=[[VanWasshenova_Thesis#Conic_Sections\|^Up]]=
			=[[Detector_Geometry_Simulation\|<-Back]]=
			=[[Circular_Cross_Sections\|Forward->]]=

Vanwdani: Created page with "=Conic Sections= Looking just at sector 1, we can see that the intersection of level 1 and the cone of constant angle theta forms a conic section.

 Show[sector1,PhiCone,Beam…"

2017-03-04T05:51:00Z

Created page with "=Conic Sections= Looking just at sector 1, we can see that the intersection of level 1 and the cone of constant angle theta forms a conic section. <pre> Show[sector1,PhiCone,Beam…"

New page

=Conic Sections=
Looking just at sector 1, we can see that the intersection of level 1 and the cone of constant angle theta forms a conic section.
<pre>
Show[sector1,PhiCone,BeamLine,Bisector0Sector1,Bisector0perpSector1,Bisector0Cone,Bisector0perpCone,RightAngleVertical,RightAngleHorizontal,RightAngleVertical2,RightAngleHorizontal2]
</pre>

[[File:Projection_side_view.png|thumb|center|600px|alt=Cone of constant Theta for varying Phi|'''Figure 5:''' A cone of constant Theta with varying Phi.]]
Without loss of generalization, we can extend the triangle to an infinite plane to aid in viewing the conic section. Again, this falls outside of the experimental design range, but simulations would not occur in this forbidden zone.

<pre>
sector1plane =
Graphics3D[{Red, Opacity[.8],
InfinitePlane[{{0, 0, 2.53}, {3.13 \[Sqrt]3, .617,
0}, {3.13 \[Sqrt]3, -3.13, 0}}]},
BoxStyle -> Dashing[{0.02, 0.02}], Axes -> True,
AxesLabel -> {"x", "y", "z"}, Ticks -> None,
AxesStyle -> Thickness[0.01]];

Show[sector1plane, PhiCone, BeamLine, Bisector0Sector1, \
Bisector0perpSector1, Bisector0Cone, Bisector0perpCone, \
RightAngleVertical, RightAngleHorizontal, RightAngleVertical2, \
RightAngleHorizontal2]
</pre>

[[File:Projection_Rear_view.png|thumb|center|600px|alt=Cone of constant Theta for varying Phi|'''Figure 5:''' A cone of constant Theta with varying Phi.]]

Following the rules of conic sections we know that the eccentricity of the conic is given by:

<center><math>e=\frac{\sin \beta}{\sin\alpha}</math></center>

where β is the angle between the plane and the horizontal and α is the angle between the cone's base and the horizontal.

Examining the different conic sections possible we know that: