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Update theory_set_reduction.md
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SteveDoyle2 authored Apr 13, 2024
1 parent ce47a43 commit cfbfda5
Showing 1 changed file with 2 additions and 6 deletions.
8 changes: 2 additions & 6 deletions dev_docs/theory_set_reduction.md
Original file line number Diff line number Diff line change
Expand Up @@ -99,15 +99,15 @@ $$ \begin{bmatrix} M_{SN} & M_{SM} \\
\begin{bmatrix} R_{SN}^T & 0_{MN}^T \\
0_{SM}^T & R_{MM}^T \end{bmatrix}
\begin{Bmatrix} q_S \\
q_M \end{Bmatrix}
q_M \end{Bmatrix} $$

$$ \textsf{\color{red} start} $$

$$ R_{MN} U_N + R_{MM} U_M $$

$$ R_{MM} U_M = -R_{MN} U_N $$

$$ U_M = \underbrace{ -R_{MM}^{-1} R_{MN} }_\text{G_{MN}} U_N $$
$$ U_M = \underbrace{ -R_{MM}^{-1} R_{MN} }_\text{GMN} U_N $$

$$ U_M = -R_{MM}^{-1} R_{MN} U_N $$

Expand All @@ -119,10 +119,6 @@ where:

$$ G_{MN} = -R_{MM}^{-1} R_{MN} $$

use underbrace for GMN...

$$ \underbrace{(x + 2)^3}_\text{text 1} $$

$$ \textsf{\color{red} end} $$

The bars over the N-set mass, stiffness and loads matrices are used for convenience to distinguish
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