vault backup: 2025-06-03 08:16:24

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

@@ -1507,41 +1507,47 @@ $$
 {^{E}\mathbf{\omega}^{X}}=\left(\sum_{r=1}^{15}{^{E}{\mathbf{\omega}_r}^{X}}\dot{q}_{r}\right)+{^{E}{\mathbf{\omega}_t}^{X}}
 $$  
 
-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.  
+where $^{E}{\pmb{\omega}_r}^{X},$ 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 $^{E}{\pmb{\omega}_t}^{X},$ is the sum of all the terms not of this form.  
+
+其中，$^{E}{\pmb{\omega}_r}^{X},$ 是与参考系 $\mathrm{X}$ 相关的第 $r^{\mathrm{th}}$ 偏角速度，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 $^{E}{\pmb{\omega}_t}^{X},$ 是所有非此形式项的总和。
 
 As an example, the partial velocities associated with a point $\mathrm{T}$ in the tower are:  
-
+例如，塔内一点 $\mathrm{T}$ 相关的偏速度如下：
 $$
-\begin{array}{r}{\varepsilon_{\nu_{r}^{T}}=\left\{\phi_{l T}(h)a_{I}\quad f o r\,r=7\right.}\\ {\quad\left.\phi_{2T}(h)a_{I}\quad f o r\,r=9\right.}\\ {\quad\varepsilon_{\nu_{r}^{T}}=\left\{\phi_{l T}(h)a_{3}\quad f o r\,r=8\quad\left(r=I,2,...,I\,5\right)\right.}\\ {\quad\left.\phi_{2T}(h)a_{3}\quad f o r\,r=I\,0\right.}\\ {\quad\left.\theta\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}\end{array}
+\begin{array}{r}{\varepsilon_{\nu_{r}^{T}}=\left\{\phi_{l T}(h)a_{I}\quad f o r\,r=7\right.}\\ {\quad\left.\phi_{2T}(h)a_{I}\quad f o r\,r=9\right.}\\ {\quad\varepsilon_{\nu_{r}^{T}}=\left\{\phi_{l T}(h)a_{3}\quad f o r\,r=8\quad\left(r=I,2,...,I\,5\right)\right.}\\ {\quad\left.\phi_{2T}(h)a_{3}\quad f o r\,r=I\,0\right.}\end{array}
 $$  
 
 It is also evident that:  
 
 $$
-{\boldsymbol{\varepsilon}}_{\boldsymbol{\nu}_{t}^{T}}={\boldsymbol{0}}
+^E{\boldsymbol{\nu}_{t}^{T}}={\boldsymbol{0}}
 $$  
 
-Accelerations can be found by taking time derivatives of the velocities.  When differentiating Eq. (3.93) with respect to time, one arrives at the acceleration of any point $\mathrm{X}$ in the inertial frame, $\dot{\pmb{{\cal E}}}_{\pmb{q}}\pmb{{\cal X}}$ :  
+Accelerations can be found by taking time derivatives of the velocities.  When differentiating Eq. (3.93) with respect to time, one arrives at the acceleration of any point $\mathrm{X}$ in the inertial frame, $^E{a_{}^{X}}$ :  
 
+加速度可以通过对速度进行时间导数来获得。对公式(3.93)关于时间求导，可以得到惯性系中任意点X的加速度，表示为$^E{a_{}^{X}}$：
 $$
-{^{E}\!\!u}^{X}=\!\left(\sum_{r=l}^{l5}{^{E}\!\nu}{_{\nu}}^{X}{\ddot{q}}_{r}\right)\!\!+\!\left[\sum_{r=l}^{l5}\!\frac{d}{d t}\!\left({^{E}\nu}_{r}^{X}\right)\!\!{\dot{q}}_{r}\right]\!\!+\!\frac{d}{d t}\!\left({^{E}\nu}_{_{t}}^{X}\right)
+^E{a_{}^{X}}=\!\left(\sum_{r=1}^{15}{^{E}\nu}{_{r}}^{X}{\ddot{q}}_{r}\right)+\left[\sum_{r=1}^{15}\frac{d}{d t}\left({^{E}\nu}_{r}^{X}\right){\dot{q}}_{r}\right]+\frac{d}{d t}\left({^{E}\nu}_{_{t}}^{X}\right)
 $$  
 
 or alternatively:  
 
 $$
-{\}^{E}{\pmb u}^{X}=\left(\sum_{r=l}^{l5}{\pmb v}_{r}^{X}\ddot{q}_{r}\right)\!+^{E}{\pmb u}_{t}^{X}
+^{E}{a}^{X}=\left(\sum_{r=1}^{15}{}^E{\nu}_{r}^{X}\ddot{q}_{r}\right)+^{E}{a}_{t}^{X}
 $$  
 
 where,  
 
 $$
-{}^{E}{\pmb{a}}_{t}^{X}=\[\sum_{r=I}^{I5}\!\frac{d}{d t}\!\left({\pmb{\varepsilon}}_{{\pmb{\nu}}_{r}^{X}}\right)\!\dot{q}_{r}\]\!+\!\frac{d}{d t}\!\left({\pmb{\varepsilon}}_{{\pmb{\nu}}_{t}^{X}}\right)
+{}^{E}{\pmb{a}}_{t}^{X}=\left[\sum_{r=1}^{15}\frac{d}{d t}\left({^{E}\nu}_{r}^{X}\right){\dot{q}}_{r}\right]+\frac{d}{d t}\left({^{E}\nu}_{_{t}}^{X}\right)
+
+
 $$  
 
 # 3.4 Kinetics  
 
-The kinematics expressions for the entire wind turbine structure found in section 3.3 can be used to form kinetics expressions.  Kane’s equations of motion (see section 3.5) use two sets of scalar quantities called generalized inertia forces, $F_{r}{}^{*}\mathbf{\cdot}\mathbf{s}.$ , and generalized active forces, $F_{r}$ ’s:  
+The kinematics expressions for the entire wind turbine structure found in section 3.3 can be used to form kinetics expressions.  Kane’s equations of motion (see section 3.5) use two sets of scalar quantities called generalized inertia forces, $F_{r}{}^{*}$'s , and generalized active forces, $F_{r}$ ’s:  
+3.3节中可用于构建动力学表达式的风轮整体结构运动学表达式，可用于构建动力学表达式。Kane运动方程（见3.5节）使用两组标量量，分别称为广义惯性力，$F_{r}{}^{*}$'s，和广义主动力，$F_{r}$ ’s：
 
 $$
 F_{\,r}^{\;\,*}\!=\!\sum_{i=I}^{\nu}{^{E}{\nu}_{\!r}^{X_{i}}\cdot\left(-{m_{\,x_{i}}}\,^{E}{\bf{a}}^{X_{i}}\right)}\quad\left(r=I,\!2,\!...,\!I\,\bar{\bf{\var S}}\right)