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An element for an arbitry coordinate transformation. This element can be used to express an off-axis element.
Usage: COORD name=(DX=dx DY=dy CHI1=chi1 CHI2=chi2 CHI3=chi3 DIR=dir);
If dir is zero (default), the transformation of the coordinate by COORD is
\begin{pmatrix}
x1 \\ y1 \\ z1
\end{pmatrix}
=
\begin{pmatrix}
c3 & -s3 & 0 \\ s3 & c3 & 0 \\ 0 & 0 & 1
\end{pmatrix} \begin{pmatrix}
1 & 0 & 0 \\ 0 & c2 & s2 \\ 0 & -s2 & c2
\end{pmatrix} \begin{pmatrix}
c1 & 0 & s1 \\ 0 & 1 & 0 \\ -s1 & 0 & c1
\end{pmatrix} \begin{pmatrix}
x-dx \\ y-dy \\ z
\end{pmatrix} }} and if dir is nonzero,
\begin{pmatrix}
x1 \\ y1 \\ z1
\end{pmatrix}
=
\begin{pmatrix}
dx \\ -dy \\ 0
\end{pmatrix}
+
\begin{pmatrix}
c3 & -s3 & 0 \\ s3 & c3 & 0 \\ 0 & 0 & 1
\end{pmatrix} \begin{pmatrix}
1 & 0 & 0 \\ 0 & c2 & -s2 \\ 0 & s2 & c2
\end{pmatrix} \begin{pmatrix}
c1 & 0 & s1 \\ 0 & 1 & 0 \\ -s1 & 0 & c1
\end{pmatrix} \begin{pmatrix}
x \\ y \\ z
\end{pmatrix} }} where {x1, y1, z1} is the new coordinate and c1=cos(chi1), s1=sin(chi1), etc.
Note that these are NOT the inverese to each other.
To use this element, you have to calculate the values of those parameters carefully. DISP G may help you but there is no automatic way to get them. You may also have to be careful when you use a line with this element in the reverse direction. A better way to do an equivalent thing in most cases is to use SOL. Unlike COORD, SOL automatically determines the parameters for the coordinate transformation.
