From 539f32ad66cd6e0036ccdfeb869562f0c7b962c8 Mon Sep 17 00:00:00 2001
From: Frank Dellaert <dellaert@gmail.com>
Date: Thu, 15 Nov 2012 20:07:11 +0000
Subject: [PATCH] Small typos

---
 doc/LieGroups.lyx | 18 ++++++++++++++----
 1 file changed, 14 insertions(+), 4 deletions(-)

diff --git a/doc/LieGroups.lyx b/doc/LieGroups.lyx
index 03116dbc9..0ceb6da09 100644
--- a/doc/LieGroups.lyx
+++ b/doc/LieGroups.lyx
@@ -1744,7 +1744,7 @@ For small angles
  we have 
 \begin_inset Formula 
 \[
-e^{\skew{\omega}}\approx\skew{\omega}=\omega\skew 1
+e^{\skew{\omega}}\approx I+\skew{\omega}=I+\omega\skew 1
 \]
 
 \end_inset
@@ -2122,7 +2122,7 @@ Analoguous to
 \begin_inset Formula $\SEthree$
 \end_inset
 
-, we can compute a velocity 
+ (see below), we can compute a velocity 
 \begin_inset Formula $\xihat\hat{p}$
 \end_inset
 
@@ -3143,8 +3143,7 @@ p\\
 
 \end_inset
 
-We would now like to know what an incremental rotation parameterized by
- 
+We would now like to know what an incremental pose parameterized by 
 \begin_inset Formula $\xi$
 \end_inset
 
@@ -3227,6 +3226,17 @@ v
 
 \end_inset
 
+yielding the derivative
+\begin_inset Formula 
+\[
+\deriv{\hat{q}(\xi)}{\xi}=T\deriv{}{\xi}\left(\xihat\hat{p}\right)=T\left[\begin{array}{cc}
+-\Skew p & I_{3}\\
+0 & 0
+\end{array}\right]
+\]
+
+\end_inset
+
 The inverse action 
 \begin_inset Formula $T^{-1}p$
 \end_inset