[cig-commits] r7003 - cs/cigma/trunk/doc/manual

[sue at geodynamics.org]

Author: sue
Date: 2007-05-30 13:01:52 -0700 (Wed, 30 May 2007)
New Revision: 7003

Modified:
   cs/cigma/trunk/doc/manual/cigma.lyx
Log:
more equations added

Modified: cs/cigma/trunk/doc/manual/cigma.lyx
===================================================================
--- cs/cigma/trunk/doc/manual/cigma.lyx	2007-05-30 19:12:45 UTC (rev 7002)
+++ cs/cigma/trunk/doc/manual/cigma.lyx	2007-05-30 20:01:52 UTC (rev 7003)
@@ -451,6 +451,27 @@
 
 \end_layout
 
+\begin_layout Standard
+Below, substitute 
+\begin_inset Formula $\alpha_{i}$
+\end_inset
+
+'s and collect the 
+\begin_inset Formula $x_{R}$
+\end_inset
+
+'s:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\]
+
+\end_inset
+
+
+\end_layout
+
 \begin_layout LyX-Code
 \begin_inset Formula \[
 x\left(\xi\eta\zeta\right)=\alpha_{0}+\alpha_{1}\xi+\alpha_{2}\eta+\alpha_{3}\zeta+\alpha_{4}\xi\eta+\alpha_{5}\xi\zeta+\alpha_{6}\eta\zeta+\alpha_{7}\xi\eta\zeta\]
@@ -663,10 +684,111 @@
 
 \end_layout
 
-\begin_layout Standard
+\begin_layout LyX-Code
 
 \end_layout
 
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+\begin_inset Formula $\vec{x}=x\hat{x}+y\hat{y}+z\hat{z}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout LyX-Code
+\begin_inset Formula $=\sum_{i=0}^{7}N_{i}\left(\vec{\xi}\right)\left(x_{i}\hat{x}+y_{i}\hat{y}+z_{i}\hat{z}\right)$
+\end_inset
+
+
+\end_layout
+
+\begin_layout LyX-Code
+\begin_inset Formula $=\sum_{i=0}^{7}N_{i}\left(\vec{\xi}\right)\vec{x}_{i}\,\,\,\,\,\mathrm{tabulate\, the}\, N_{i}\left(\vec{\xi}\right)\mathrm{'s\, for\, each\, required}\,\vec{\xi}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+\begin_inset Formula \[
+x\left(\vec{\xi}_{R}\right)=\sum_{i=0}^{7}N_{i}\left(\vec{\xi}\right)x_{i}=\left[N_{0}\left(\vec{\xi}_{R}\right)N_{1}\left(\vec{\xi}_{R}\right)N_{2}\left(\vec{\xi}_{R}\right)\ldots\ldots N_{7}\left(\vec{\xi}_{R}\right)\right]\left[\begin{array}{c}
+x_{0}\\
+x_{1}\\
+x_{2}\\
+\vdots\\
+x_{7}\end{array}\right]\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout LyX-Code
+\begin_inset Formula \[
+\left[\begin{array}{c}
+x\left(\vec{\xi}_{0}\right)\\
+x\left(\vec{\xi}_{1}\right)\\
+x\left(\vec{\xi}_{2}\right)\\
+\vdots\\
+x\left(\vec{\xi}_{q-1}\right)\end{array}\right]\left[\begin{array}{ccccc}
+N_{0}\left(\vec{\xi}_{0}\right) & N_{1}\left(\vec{\xi}_{0}\right) & N_{2}\left(\vec{\xi}_{0}\right) & \ldots & N_{7}\left(\vec{\xi}_{0}\right)\\
+N_{0}\left(\vec{\xi}_{1}\right) & N_{1}\left(\vec{\xi}_{1}\right) & N_{2}\left(\vec{\xi}_{1}\right) & \ldots & N_{7}\left(\vec{\xi}_{1}\right)\\
+N_{0}\left(\vec{\xi}_{2}\right) & N_{1}\left(\vec{\xi}_{2}\right) & N_{2}\left(\vec{\xi}_{2}\right) & \ldots & N_{7}\left(\vec{\xi}_{2}\right)\\
+\vdots & \vdots & \vdots &  & \vdots\\
+N_{0}\left(\vec{\xi}_{q-1}\right) & N_{1}\left(\vec{\xi}_{q-1}\right) & N_{2}\left(\vec{\xi}_{q-1}\right) & \ldots & N_{7}\left(\vec{\xi}_{q-1}\right)\end{array}\right]\left[\begin{array}{c}
+x_{0}\\
+x_{1}\\
+x_{2}\\
+\vdots\\
+x_{7}\end{array}\right]\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout LyX-Code
+\begin_inset Formula \[
+\left[\begin{array}{ccc}
+x\left(\vec{\xi}_{0}\right) & y\left(\vec{\xi}_{0}\right) & z\left(\vec{\xi}_{0}\right)\\
+x\left(\vec{\xi}_{1}\right) & y\left(\vec{\xi}_{1}\right) & z\left(\vec{\xi}_{1}\right)\\
+\vdots & \vdots & \vdots\\
+x\left(\vec{\xi}_{q-1}\right) & y\left(\vec{\xi}_{q-1}\right) & z\left(\vec{\xi}_{q-1}\right)\end{array}\right]=\left[\begin{array}{ccccc}
+N_{0}\left(\vec{\xi}_{0}\right) & N_{1}\left(\vec{\xi}_{0}\right) & N_{2}\left(\vec{\xi}_{0}\right) & \ldots & N_{7}\left(\vec{\xi}_{0}\right)\\
+N_{0}\left(\vec{\xi}_{1}\right) & N_{1}\left(\vec{\xi}_{1}\right) & N_{2}\left(\vec{\xi}_{1}\right) & \ldots & N_{7}\left(\vec{\xi}_{1}\right)\\
+\vdots & \vdots & \vdots &  & \vdots\\
+N_{0}\left(\vec{\xi}_{q-1}\right) & N_{1}\left(\vec{\xi}_{q-1}\right) & N_{2}\left(\vec{\xi}_{q-1}\right) & \ldots & N_{7}\left(\vec{\xi}_{q-1}\right)\end{array}\right]\left[\begin{array}{ccc}
+x{}_{0} & y_{0} & z_{0}\\
+x_{1} & y_{1} & z_{1}\\
+\vdots & \vdots & \vdots\\
+x_{7} & y_{7} & z_{7}\end{array}\right]\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout LyX-Code
+\begin_inset Formula \[
+\left[q\times3\right]\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[q\times8\right]\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[8\times3\right]\]
+
+\end_inset
+
+
+\end_layout
+
 \begin_layout Chapter
 \begin_inset Formula $ $
 \end_inset