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Correct typos caught by Divya Sanghi #283

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merged 2 commits into from
Mar 1, 2024
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Correct typos caught by Divya Sanghi #283

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6937337
Correct typos caught by Divya Sanghi
bbahiam Feb 29, 2024
ddff06b
Update lingebm.py
rafapalacios Mar 1, 2024
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20 changes: 10 additions & 10 deletions sharpy/linear/src/lingebm.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1464,23 +1464,23 @@ def newmark_ss(M, C, K, dt, num_damp=1e-4, M_is_SPD=False):
\mathbf{q}_{n} \\
\mathbf{\dot q}_{n}
\end{Bmatrix}
- \mathbf{A_{ss1}}^{-1}\mathbf{B_{ss1}} \mathbf{f}_n
- \mathbf{A}_{\mathbf{ss1}}^{-1}\mathbf{B_{ss1}} \mathbf{f}_n

Then

.. math::
\mathbf{x}_{n+1} &= \mathbf{A_{ss1}}^{-1}[
\mathbf{x}_{n+1} &= \mathbf{A}_{\mathbf{ss1}}^{-1}[
\mathbf{A_{ss0}} \mathbf{x}_n + (
\mathbf{A_{ss0}}\mathbf{A_{ss1}}^{-1}\mathbf{B_{ss1}}
\mathbf{A_{ss0}}\mathbf{A}_{\mathbf{ss1}}^{-1}\mathbf{B_{ss1}}
+ \mathbf{B_{ss0}}
)
\mathbf{f}_n
] \\
\begin{Bmatrix}
\mathbf{\dot q}_{n} \\
\mathbf{\ddot q}_{n}
\mathbf{q}_{n} \\
\mathbf{\dot q}_{n}
\end{Bmatrix}
&= \mathbf{x}_n + \mathbf{B_{ss1}} \mathbf{f}_n
&= \mathbf{x}_n + \mathbf{A}_{\mathbf{ss1}}^{-1}\mathbf{B_{ss1}} \mathbf{f}_n

See also :func:`sharpy.linear.src.libss.SSconv` for more details on the elimination of the term
multiplying :math:`\mathbf{f}_{n+1}` in the state equation.
Expand All @@ -1494,11 +1494,11 @@ def newmark_ss(M, C, K, dt, num_damp=1e-4, M_is_SPD=False):
where

.. math::
\mathbf{A_{ss}} &= \mathbf{A_{ss1}}^{-1}\mathbf{A_{ss0}} \\
\mathbf{B_{ss}} &= \mathbf{A_{ss1}}^{-1}(\mathbf{B_{ss0}}
+ \mathbf{A_{ss0}}\mathbf{A_{ss1}}^{-1}\mathbf{B_{ss1}}) \\
\mathbf{A_{ss}} &= \mathbf{A}_{\mathbf{ss1}}^{-1}\mathbf{A_{ss0}} \\
\mathbf{B_{ss}} &= \mathbf{A_{\mathbf{ss1}}^{-1}(\mathbf{B_{ss0}}
+ \mathbf{A_{ss0}}\mathbf{A_{\mathbf{ss1}}^{-1}\mathbf{B_{ss1}}) \\
\mathbf{C_{ss}} &= \mathbf{I} \\
\mathbf{D_{ss}} &= \mathbf{B_{ss1}}
\mathbf{D_{ss}} &= \mathbf{A_{\mathbf{ss1}}^{-1}\mathbf{B_{ss1}}


.. admonition:: Notation is used in the code
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