diff --git a/docs/source/user/servodyn-stc/StC_Theory.rst b/docs/source/user/servodyn-stc/StC_Theory.rst index ea6608f380..f452065fb5 100644 --- a/docs/source/user/servodyn-stc/StC_Theory.rst +++ b/docs/source/user/servodyn-stc/StC_Theory.rst @@ -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`: @@ -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 @@ -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}