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<H2><A NAME="SECTION000488000000000000000">SLA_EULER - Rotation Matrix from Euler Angles</A>
<A NAME="xref_SLA_EULER"> </A><A NAME="SLA_EULER"> </A>
</H2>
<DL>
<DT><STRONG>ACTION:</STRONG>
<DD>Form a rotation matrix from the Euler angles - three
successive rotations about specified Cartesian axes
(single precision).
<P> <DT><STRONG>CALL:</STRONG>
<DD><TT>CALL sla_EULER (ORDER, PHI, THETA, PSI, RMAT)</TT>
<P> </DL>
<P> <DL>
<DT><STRONG>GIVEN:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>ORDER</EM></TD>
<TH ALIGN="LEFT"><B>C*(*)</B></TH>
<TD ALIGN="LEFT" NOWRAP>specifies about which axes the rotations occur</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>PHI</EM></TD>
<TD ALIGN="LEFT"><B>R</B></TD>
<TD ALIGN="LEFT" NOWRAP>1st rotation (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>THETA</EM></TD>
<TD ALIGN="LEFT"><B>R</B></TD>
<TD ALIGN="LEFT" NOWRAP>2nd rotation (radians)</TD>
</TR>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>PSI</EM></TD>
<TD ALIGN="LEFT"><B>R</B></TD>
<TD ALIGN="LEFT" NOWRAP>3rd rotation (radians)</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>RETURNED:</STRONG>
<DD>
<BR>
<TABLE CELLPADDING=3>
<TR VALIGN="TOP"><TD ALIGN="LEFT"><EM>RMAT</EM></TD>
<TH ALIGN="LEFT"><B>R(3,3)</B></TH>
<TD ALIGN="LEFT" NOWRAP>rotation matrix</TD>
</TR>
</TABLE></DL>
<P> <DL>
<DT><STRONG>NOTES:</STRONG>
<DD><DL COMPACT>
<DT>1.
<DD>A rotation is positive when the reference frame rotates
anticlockwise as seen looking towards the origin from the
positive region of the specified axis.
<DT>2.
<DD>The characters of ORDER define which axes the three successive
rotations are about. A typical value is `ZXZ', indicating that
RMAT is to become the direction cosine matrix corresponding to
rotations of the reference frame through PHI radians about the
old <I>z</I>-axis, followed by THETA radians about the resulting
<I>x</I>-axis,
then PSI radians about the resulting <I>z</I>-axis. In detail:
<UL>
<LI> The axis names can be any of the following, in any order or
combination: X, Y, Z, uppercase or lowercase, 1, 2, 3. Normal
axis labelling/numbering conventions apply;
the <I>xyz</I> (<IMG WIDTH="44" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
SRC="img67.gif"
ALT="$\equiv123$">) triad is right-handed. Thus, the `ZXZ' example given above
could be written `zxz' or `313' (or even `ZxZ' or `3xZ').
<LI> ORDER is terminated by length or by the first unrecognized
character.
<LI> Fewer than three rotations are acceptable, in which case
the later angle arguments are ignored.
</UL>
<DT>3.
<DD>Zero rotations produces a unit RMAT.
</DL></DL>
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<ADDRESS>
<I>SLALIB --- Positional Astronomy Library<BR>Starlink User Note 67<BR>P. T. Wallace<BR>12 October 1999<BR>E-mail:ptw@star.rl.ac.uk</I>
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