Changeset 4513 for trunk/doc/pslib/psLibADD.tex

Timestamp:

Jul 7, 2005, 5:58:24 PM (21 years ago)

Author:

Paul Price

Message:

Fixing up so it compiles.

File:

• trunk/doc/pslib/psLibADD.tex (modified) (5 diffs)

trunk/doc/pslib/psLibADD.tex

@@ -1 @@
-%%% $Id: psLibADD.tex,v 1.77 2005-07-08 03:55:45 price Exp $
+%%% $Id: psLibADD.tex,v 1.78 2005-07-08 03:58:24 price Exp $
 \documentclass[panstarrs]{panstarrs}
 
@@ -1523 +1523 @@
 inverse of the above equations:
 \begin{eqnarray}
-\phi & = & \atan(p_1, p_0) \\
-\theta & = & \asin(p_2) \\
-\end{eqnarray}
-Note that in this case, we neglect the scalar component of the
-quaternion --- it should be zero.
+\phi & = & \arctan(p_1, p_0) \\
+\theta & = & \arcsin(p_2) \\
+\end{eqnarray}
+where $\phi$ is the longitude and $\theta$ is the latitude.  Note that
+in this case, we neglect the scalar component of the quaternion --- it
+should be zero.
 
 \subsubsection{Quaternion for a rotation}
@@ -1541 +1542 @@
 Note that the sine and cosine are taken of the half-angle of the
 rotation.  Note also that this implies that the quaternion components
-are normalized such that $|q| \equiv q_0^2 + q_1^2 + q_2^2 + q_3^2
+are normalized such that $|r| \equiv r_0^2 + r_1^2 + r_2^2 + r_3^2
 = 1$.
 
@@ -1595 +1596 @@
 \end{eqnarray}
 \item Second, about the Y axis:
+\begin{eqnarray}
 s_0 & = & 0 \\
 s_1 & = & \sin(\delta_p/2) \\
@@ -1607 +1609 @@
 t_3 & = & \cos(\phi_p/2) \\
 \end{eqnarray}
+\end{itemize}
 
 These three quaternions may be multiplied together to yield the