mvg:lecture_03:start
Differences
This shows you the differences between two versions of the page.
| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| 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: $so(3), se(3)$ | 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. | ||
| + | |||
| + | $\exp: so(3) \rightarrow SO(3)\quad \hat{w} -> e^{\hat{w}}$ | ||
| + | | ||
| + | |||
mvg/lecture_03/start.1543500492.txt.gz · Last modified: 2018/11/29 14:08 by admin