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书籍/力学书籍/OpenFast/modeling of the uae wind turbine for refinement of fast_ad/auto/modeling of the uae wind turbine for refinement of fast_ad.md

@@ -1486,10 +1486,10 @@ $$
 \begin{array}{l}{{{^E}_{\nu}{^s}=\stackrel{!}{(}\dot{q}_{7}\dot{+}\dot{q}_{9}\big)a_{I}+\stackrel{\cdot}{(}\dot{q}_{\delta}\dot{+}\dot{q}_{I0}\stackrel{\cdot}{)}\dot{\pmb{a}_{3}}+\stackrel{\cdot}{(}\dot{\theta}_{s}a_{I}+\dot{\theta}_{7}a_{s}+\dot{q}_{6}d_{2}+\dot{q}_{5}d_{3}\biggr)\times r^{o p}+}}\\ {{\ }}\\ {{\stackrel{\mathrm{(}\dot{\theta}_{s}a_{I}+\dot{\theta}_{7}a_{3}+\dot{q}_{6}d_{2}+\dot{q}_{5}d_{3}+\dot{q}_{4}d_{I}+\dot{q}_{3}g_{2}\biggr)\times r^{p Q}+}}\\ {{\ }}\\ {{\stackrel{\mathrm{(}\dot{\theta}_{s}a_{I}+\dot{\theta}_{7}a_{3}+\dot{q}_{6}d_{2}+\dot{q}_{5}d_{3}+\dot{q}_{4}d_{I}+\dot{q}_{3}g_{2}\biggr)\times r^{Q S}+{^H}_{\nu}{^s}+}}\\ {{\ }}\\ {{\stackrel{\mathrm{(}\dot{\theta}_{s}a_{I}+\dot{\theta}_{7}a_{3}+\dot{q}_{6}d_{2}+\dot{q}_{5}d_{3}+\dot{q}_{4}d_{I}+\dot{q}_{3}g_{2}\biggr)\times(r i_{3})}}\end{array}
 $$  
 
-where $\varepsilon_{\nu_{r}^{X}}$ is the $r^{\mathrm{th}}$ partial velocity21 associated with point X, which can be a function of time and the generalized coordinates but not of their time derivatives, and $\varepsilon_{\nu}^{X}{}_{t}$ is the sum of all the terms not of this form.  Similarly, the angular velocity of any reference frame $\mathrm{X}$ in the inertial reference frame, $^{E}\pmb{\omega}^{X},$ , can be expressed as:  
-
+where $^E{\nu_{r}^{X}}$ is the $r^{\mathrm{th}}$ partial velocity associated with point X, which can be a function of time and the generalized coordinates but not of their time derivatives, and $^E{\nu_{t}^{X}}$ is the sum of all the terms not of this form.  Similarly, the angular velocity of any reference frame $\mathrm{X}$ in the inertial reference frame, $^{E}\pmb{\omega}^{X},$ , can be expressed as:  
+其中，$^E{\nu_{r}^{X}}$ 是与点 X 相关的第 r 个偏速度，它可以是时间的函数和广义坐标的函数，但不是它们的时间导数，而 $^E{\nu_{t}^{X}}$ 是所有非此形式的项之和。 类似地，任何参考系 X 在惯性参考系中的角速度，$^{E}\pmb{\omega}^{X},$ 可以表示为：
 $$
-{\mathbf{\mathbf{\Sigma}}^{E}\mathbf{\omega}^{X}}=\left(\sum_{r=I}^{I5}\mathbf{\omega}_{{\mathbf{\Sigma}}^{E}}^{X}\Dot{q}_{r}\right)+{\mathbf{\mathbf{\Sigma}}^{E}\mathbf{\omega}_{t}^{X}}
+{^{E}\mathbf{\omega}^{X}}=\left(\sum_{r=1}^{15}{^{E}{\mathbf{\omega}_r}^{X}}\dot{q}_{r}\right)+{^{E}{\mathbf{\omega}_t}^{X}}
 $$  
 
 where $\varepsilon_{\pmb{\omega}^{X}\!,r}$ is the $r^{\mathrm{th}}$ partial angular velocity associated with reference frame $\mathrm{X}$ , which can be a function of time and the generalized coordinates but not of their time derivatives, and $\boldsymbol{E}_{\boldsymbol{\omega}}\boldsymbol{x}_{t}$ is the sum of all the terms not of this form.