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--- mvg:lecture_03:start [2018/11/29 14:08] – [TRansformation between Lie Algebra and Lie Group] admin
+++ mvg:lecture_03:start [2018/12/23 18:45] (current) – [TRansformation between Lie Algebra and Lie Group] admin
@@ Line 85: / Line 85: @@
 Two Lie groups we will study:  $so(3), se(3)$
+=== Exponential Map ===
+ $\left\{ \dot{R}(t)=\hat{w}R(t)\right.$
+ $R(0) = I$
+How does the rotation matrix change from one time within a little time step?
+ $R(t) = e^{\hat{w}t} = \sum \ldots$  expansion. That solves the diff. eqn. above.
+ $\exp: so(3) \rightarrow SO(3)\quad \hat{w} -> e^{\hat{w}}$