Difference between revisions of "Right Hand Wall"
| Line 7: | Line 7: | ||
Parameterizing this | Parameterizing this | ||
| − | <center><math>r \mapsto {cot 29.5^{\circ} | + | <center><math>r \mapsto {y\ cot 29.5^{\circ} + 0.09156, y, 0}</math></center> |
| − | <center><math>t \mapsto {cos 29.5^{\circ} | + | <center><math>t \mapsto {t\ cos 29.5^{\circ} + 0.09156, t\ sin\ 29.5^{\circ} , 0}</math></center> |
| − | + | <center><math>\begin{bmatrix} | |
| − | + | x'' \\ | |
| − | y'' | + | y'' \\ |
| − | z'' | + | z'' |
| − | + | \end{bmatrix}= | |
| − | + | \begin{bmatrix} | |
| − | sin 6\ | + | cos\ 6^{\circ} & -sin\ 6^{\circ} & 0 \\ |
| − | 0 0 1 | + | sin\ 6^{\circ} & cos\ 6^{\circ}& 0 \\ |
| − | + | 0 & 0 & 1 | |
| − | + | \end{bmatrix}\cdot | |
| − | y' | + | \begin{bmatrix} |
| + | x' \\ | ||
| + | y' \\ | ||
z' | z' | ||
| + | \end{bmatrix}</math></center> | ||
| − | |||
(x'' | (x'' | ||
Revision as of 03:20, 28 April 2017
This same process can be applied to the side walls for the detector. For the sidewalls, we have approximated them as lines following the equation
Parameterizing this
(x
y
z
)=(cos 6\[Degree] -sin 6\[Degree] 0 sin 6\[Degree] cos 6\[Degree] 0 0 0 1
) . (t cos 29.5\[Degree]+0.09156 t sin 29.5\[Degree] 0
)
(x y z
)= (0.09156cos 6 \[Degree]+t cos 6 \[Degree]cos 29.5\[Degree]-t sin 6 \[Degree]sin 29.5\[Degree] t cos 6 \[Degree]sin 29.5\[Degree]+0.09156 sin 6 \[Degree]+t cos 29.5\[Degree]sin 6 \[Degree] 0
)
(x y z
)= (0.09156cos 6 \[Degree]+t (cos 6 \[Degree]cos 29.5\[Degree]- sin 6 \[Degree]sin 29.5\[Degree]) 0.09156 sin 6 \[Degree]+t (sin 6 \[Degree] cos 29.5\[Degree]+cos 6 \[Degree]sin 29.5\[Degree]) 0
)
Using the equation for y we can solve for t
Substituting this into the expression for x
rightRotated =
ContourPlot[x2 == 1.401949 y + 0.077641, {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];