| 1343 |
|
\[ |
| 1344 |
|
\hat vu = v \times u |
| 1345 |
|
\] |
| 1346 |
– |
|
| 1346 |
|
Using \ref{introEqaution:RBMotionPI}, one can construct a skew |
| 1347 |
|
matrix, |
| 1348 |
|
\begin{equation} |
| 1349 |
< |
(\mathop \Pi \limits^ \bullet - \mathop \Pi \limits^ \bullet ^T |
| 1349 |
> |
(\mathop \Pi \limits^ \bullet - \mathop \Pi \limits^ {\bullet ^T} |
| 1350 |
|
){\rm{ }} = {\rm{ }}(\Pi - \Pi ^T ){\rm{ }}(J^{ - 1} \Pi + \Pi J^{ |
| 1351 |
|
- 1} ) + \sum\limits_i {[Q^T F_i (r,Q)X_i^T - X_i F_i (r,Q)^T Q]} - |
| 1352 |
|
(\Lambda - \Lambda ^T ) . \label{introEquation:skewMatrixPI} |
| 2011 |
|
\begin{array}{l} |
| 2012 |
|
\Xi _P^{tt} = \Xi _O^{tt} \\ |
| 2013 |
|
\Xi _P^{tr} = \Xi _P^{rt} = \Xi _O^{tr} - U_{OP} \Xi _O^{tt} \\ |
| 2014 |
< |
\Xi _P^{rr} = \Xi _O^{rr} - U_{OP} \Xi _O^{tt} U_{OP} + \Xi _O^{tr} U_{OP} - U_{OP} \Xi _O^{tr} ^{^T } \\ |
| 2014 |
> |
\Xi _P^{rr} = \Xi _O^{rr} - U_{OP} \Xi _O^{tt} U_{OP} + \Xi _O^{tr} U_{OP} - U_{OP} \Xi _O^{{tr} ^{^T }} \\ |
| 2015 |
|
\end{array} |
| 2016 |
|
\label{introEquation:resistanceTensorTransformation} |
| 2017 |
|
\end{equation} |
