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andrew-platt merged 2 commits into from
Dec 22, 2025
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Docs: updates to StC docs #3109

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Docs: updates to StC docs
andrew-platt Dec 19, 2025
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Docs: correction to previous commits
andrew-platt Dec 21, 2025
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14 changes: 7 additions & 7 deletions docs/source/user/servodyn-stc/StC_Theory.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -473,7 +473,7 @@ Therefore :math:`\ddot{z}_{_{TMD_Z/P_N}}` is governed by the equations



The forces :math:`F_{X_{_{TMD_Z/O_N}}}` and :math:`F_{Z_{_{TMD_Z/O_N}}}`
The forces :math:`F_{X_{_{TMD_Z/O_N}}}` and :math:`F_{Y_{_{TMD_Z/O_N}}}`
are solved noting
:math:`\ddot{x}_{_{TMD_Z/P_N}} = \ddot{y}_{_{TMD_Z/P_N}} = 0`:

Expand Down Expand Up @@ -565,11 +565,11 @@ first-order equations of the form
A(\vec{u}) = \left[
\begin{array}{cccccc}
0& 1 &0&0&0&0 \\
(\dot{\phi}_{_{P/O_N}}^2 + \dot{\psi}_{_{P/O_N}}^2-\frac{k_x}{m_x}) & - (\frac{c_x}{m_x}) &0&0&0&0 \\
(\dot{\phi}_{_{N/O_N}}^2 + \dot{\psi}_{_{N/O_N}}^2-\frac{k_x}{m_x}) & - (\frac{c_x}{m_x}) &0&0&0&0 \\
0&0&0& 1 &0&0 \\
0&0& (\dot{\theta}_{_{P/O_N}}^2 + \dot{\psi}_{_{P/O_N}}^2-\frac{k_y}{m_y}) & - (\frac{c_y}{m_y}) &0&0 \\
0&0& (\dot{\theta}_{_{N/O_N}}^2 + \dot{\psi}_{_{N/O_N}}^2-\frac{k_y}{m_y}) & - (\frac{c_y}{m_y}) &0&0 \\
0&0&0&0&0& 1 \\
0&0&0&0& (\dot{\theta}_{_{P/O_N}}^2 + \dot{\phi}_{_{P/O_N}}^2-\frac{k_z}{m_z}) & - (\frac{c_z}{m_z}) \\
0&0&0&0& (\dot{\theta}_{_{N/O_N}}^2 + \dot{\phi}_{_{N/O_N}}^2-\frac{k_z}{m_z}) & - (\frac{c_z}{m_z}) \\
\end{array} \right]

and
Expand Down Expand Up @@ -615,9 +615,9 @@ The output includes reaction forces corresponding to
\begin{aligned}
\vec{F}_{_{P_G}} = R^T_{_{N/G}} & \left[
\begin{array}{l}
k_x {x}_{_{TMD/P_N}} + c_x \dot{x}_{_{TMD/P_N}} - F_{StopFrc_{X}} - F_{ext_x} - F_{X_{_{TMD_Y/O_N}}} - F_{X_{_{TMD_Z/O_N}}} \\
k_y {y}_{_{TMD/P_N}} + c_y \dot{y}_{_{TMD/P_N}} - F_{StopFrc_{Y}} - F_{ext_y} - F_{Y_{_{TMD_X/O_N}}} - F_{Y_{_{TMD_Z/O_N}}} \\
k_z {z}_{_{TMD/P_N}} + c_z \dot{z}_{_{TMD/P_N}} - F_{StopFrc_{Z}} - F_{ext_z} - F_{Z_{_{TMD_X/O_N}}} - F_{Z_{_{TMD_Y/O_N}}} - F_{Z_{PreLoad}}
k_x {x}_{_{TMD_X/P_N}} + c_x \dot{x}_{_{TMD_X/P_N}} - F_{StopFrc_{X}} - F_{ext_x} - F_{X_{_{TMD_Y/O_N}}} - F_{X_{_{TMD_Z/O_N}}} \\
k_y {y}_{_{TMD_Y/P_N}} + c_y \dot{y}_{_{TMD_Y/P_N}} - F_{StopFrc_{Y}} - F_{ext_y} - F_{Y_{_{TMD_X/O_N}}} - F_{Y_{_{TMD_Z/O_N}}} \\
k_z {z}_{_{TMD_Z/P_N}} + c_z \dot{z}_{_{TMD_Z/P_N}} - F_{StopFrc_{Z}} - F_{ext_z} - F_{Z_{_{TMD_X/O_N}}} - F_{Z_{_{TMD_Y/O_N}}} - F_{Z_{PreLoad}}
\end{array}
\right]
\end{aligned}
Expand Down
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