|
|
| (6 intermediate revisions by the same user not shown) |
| Line 1: |
Line 1: |
| ==Setting up Mathematica for DC Theta-Phi Isotropic Cone==
| |
|
| |
|
|
| |
| We can define the constraints of the plane the DC is in
| |
|
| |
| <pre>
| |
| right = ContourPlot[
| |
| x2 == Cot[29.5 \[Degree]] y + .09156, {y, -1, 1}, {x2, 0, 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 -> Black,
| |
| PlotLegends -> Automatic];
| |
|
| |
| left = ContourPlot[
| |
| x2 == -Cot[29.5 \[Degree]] y + .09156, {y, -1, 1}, {x2, 0, 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 -> Black,
| |
| PlotLegends -> Automatic];
| |
|
| |
| </pre>
| |
|
| |
|
| |
| We can define the x coordinate of the wires as they cross the midpoint plane as shown earlier.
| |
|
| |
| <pre>
| |
| x0forWires[number_] := .23168 + .01337*(number);
| |
| </pre>
| |
|
| |
|
| |
| We can define the point midway between two parallel lines as the point where one wire is recorded versus its next highest neighbor
| |
|
| |
| <pre>
| |
| x0forWireMiddles[
| |
| number_] := ((.23168 + .01337*(number)) + (.23168 + .01337*(number \
| |
| + 1)))/2;
| |
| </pre>
| |
|
| |
| All of the conditions dependent on \[Theta] and \[Phi]
| |
|
| |
| <pre>
| |
|
| |
| \[CapitalDelta]a :=
| |
| FullSimplify[(R Sin[\[Theta] \[Degree]])/
| |
| 2 (Csc[65 \[Degree] - \[Theta] \[Degree]] -
| |
| Csc[115 \[Degree] - \[Theta] \[Degree]]), \[Theta] > 0];
| |
| e := Sin[25 \[Degree]]/Cos[\[Theta] \[Degree]];
| |
| a := FullSimplify[(R Sin[\[Theta] \[Degree]])/
| |
| 2 (Csc[65 \[Degree] - \[Theta] \[Degree]] +
| |
| Csc[115 \[Degree] - \[Theta] \[Degree]]), \[Theta] > 0];
| |
| rD1 := Simplify[(a e - \[CapitalDelta]a) Tan[
| |
| 65 \[Degree]] Cos[\[Theta] \[Degree]], \[Theta] > 0];
| |
| rD2 := Simplify[(a e + \[CapitalDelta]a) Tan[
| |
| 65 \[Degree]] Cos[\[Theta] \[Degree]], \[Theta] > 0];
| |
| xD1 := Simplify[rD1 Cos[\[Phi] \[Degree]]];
| |
| yD1 := Simplify[rD1 Sin[\[Phi] \[Degree]]];
| |
| zD1 := Simplify[rD1 Cot[\[Theta] \[Degree]], \[Theta] > 0];
| |
| xD2 := Simplify[rD2 Cos[\[Phi] \[Degree]], \[Theta] > 0];
| |
| yD2 := Simplify[rD2 Sin[\[Phi] \[Degree]], \[Theta] > 0];
| |
| zD2 := Simplify[rD2 Cot[\[Theta] \[Degree]], \[Theta] > 0];
| |
| xP := Simplify[(R Cos[\[Phi] \[Degree]])/(Cot[\[Theta] \[Degree]] +
| |
| Cos[\[Phi] \[Degree]] Cot[65 \[Degree]]), \[Theta] > 0];
| |
| yP := Simplify[(R Sin[\[Phi] \[Degree]])/(Cot[\[Theta] \[Degree]] +
| |
| Cos[\[Phi] \[Degree]] Cot[65 \[Degree]]), \[Theta] > 0];
| |
| zP := Simplify[(R Cot[\[Theta] \[Degree]])/(Cot[\[Theta] \[Degree]] +
| |
| Cos[\[Phi] \[Degree]] Cot[65 \[Degree]]), \[Theta] > 0];
| |
| x1 := Simplify[(rD2^2 - rD1^2 +
| |
| Cot[\[Theta] \[Degree]]^2 (rD2^2 - rD1^2) - 2 xP (xD2 - xD1) -
| |
| 2 yP (yD2 - yD1) - 2 zP (zD2 - zD1))/(4 a e) - a e, \[Theta] >
| |
| 0];
| |
| x := Simplify[x1 - \[CapitalDelta]a + a e, \[Theta] > 0];
| |
| xCenter := x + \[CapitalDelta]a;
| |
| n := -957.412/(Tan[\[Theta] \[Degree]] + 2.14437) + 430.626;
| |
| D2P := Simplify[((xD2 - xP)^2 + (yD2 - yP)^2 + (zD2 -
| |
| zP )^2)^.5, \[Theta] > 0] // N
| |
| D1P := Simplify[((xP - xD1)^2 + (yP - yD1)^2 + (zP -
| |
| zD1)^2)^.5, \[Theta] > 0] // N;
| |
| y := Simplify[(D1P^2 - x1^2)^.5, \[Theta] > 0] // N;
| |
| b := Simplify[a Sqrt[1 - e^2], \[Theta] > 0] // N;
| |
| R = 2.52934271645;
| |
| </pre>
| |