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
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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?
answered Jan 10, 2013 at 14:14
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$\begingroup$ Thanks it's exactly this, I was blind with the complexity of higher dimensions logarithms . Didn't figured out that was just a simply term inverse. $\endgroup$– massudawCommented Jan 10, 2013 at 16:07