I want the rodrigues like formula using sin and cos , not a matrix series expansion.


I've found some references for se(n) , n > 3 in : 
 <ftp://ftp.cis.upenn.edu/pub/papers/gallier/rodrig.pdf>



How to compute SE(2) group exponential and logarithm?
Just computing the exponential gives
$$
\exp\left(
\begin{matrix}
0 & 0 & 0 \cr
x & 0 & -t\cr
y & t & 0
\end{matrix}
\right)
= \left(
\begin{matrix}
1 & 0 & 0 \cr
x\frac{\sin t}{t}-y\frac{1{-}\cos t}{t} & \cos t & -\sin t\cr
x\frac{1{-}\cos t}{t}+y\frac{\sin t}{t} & \sin t & \cos t
\end{matrix}
\right),
$$
and inverting this gives you the (multi-valued) logarithm. Is this what you wanted?


