[cig-commits] commit: Fixed typos in dynamic equations.

[Mercurial]

changeset:   31:9776c68413c2
tag:         tip
user:        Brad Aagaard <baagaard at usgs.gov>
date:        Tue Jan 26 21:22:38 2010 -0800
files:       friction.tex
description:
Fixed typos in dynamic equations.


diff -r 55c31563b0f2 -r 9776c68413c2 friction.tex
--- a/friction.tex	Thu Jan 14 13:49:23 2010 -0800
+++ b/friction.tex	Tue Jan 26 21:22:38 2010 -0800
@@ -167,7 +167,7 @@ In the dynamic case we write the system 
       A(t) & C^T \\
       C & 0 \end{array} \right)
   \left( \begin{array}{c} u(t+\Delta t) \\ l(t+\Delta t) \end{array} \right) =
-  \left( \begin{array}{c} b(t) \\ d(t) \end{array} \right).
+  \left( \begin{array}{c} b(t) \\ d(t+\Delta t) \end{array} \right).
 \end{equation}
 We know the solution at time $t$, so we write $u(t+\Delta t)$ as $u(t) +
 du(t)$ and $l(t+\Delta t)$ as $l(t) + dl(t)$, where $du(t)$ is the increment
@@ -180,7 +180,7 @@ Lagrange multipliers as the unknowns,
       A(t) & C^T \\
       C & 0 \end{array} \right)
   \left( \begin{array}{c} du(t) \\ dl(t) \end{array} \right) =
-  \left( \begin{array}{c} b(t) \\ d(t) \end{array} \right) -
+  \left( \begin{array}{c} b(t) \\ d(t+\Delta t) \end{array} \right) -
   \left( \begin{array}{cc}
       A(t) & C^T \\
       C & 0 \end{array} \right)
@@ -197,7 +197,7 @@ and the residual,
 and the residual,
 \begin{align}
   r &= 
-  \left( \begin{array}{c} b(t) \\ d(t) \end{array} \right) -
+  \left( \begin{array}{c} b(t) \\ d(t+\Delta t) \end{array} \right) -
   \left( \begin{array}{cc}
       A(t) & C^T \\
       C & 0 \end{array} \right)
@@ -207,7 +207,7 @@ and the residual,
       C & 0 \end{array} \right)
   \left( \begin{array}{c} du(t) \\ dl(t) \end{array} \right) \\
   &=
-    \left( \begin{array}{c} b(t) \\ d(t) \end{array} \right) -
+    \left( \begin{array}{c} b(t) \\ d(t+\Delta t) \end{array} \right) -
     \left( \begin{array}{cc}
       A(t) & C^T \\
       C & 0 \end{array} \right)