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书籍/力学书籍/力学/Flexible Multibody Dynamics (O. A. Bauchau) (Z-Library)/auto/Flexible Multibody Dynamics (O. A. Bauchau) (Z-Library).md

@@ -2872,13 +2872,13 @@ Figure 3.2 depicts a particle of mass $m$ whose position is described by positio
 ### Definition  
 
 By definition, force $\underline{{F}}$ is conservative if and only if the work it performs along any path joining the same initial and final points is identical. This is expressed by the following equation  
-根据定义，力 $\underline{{F}}$ 仅当它在连接相同起始点和终点的任意路径上所做的功相同，才被认为是保守力。这由以下方程表达：
+根据定义，**力 $\underline{{F}}$ 仅当它在连接相同起始点和终点的任意路径上所做的功相同，才被认为是保守力**。这由以下方程表达：
 $$
 W_{A\rightarrow B}=\int_{\mathrm{Path~ACB}}\underline{{F}}^{T}\mathrm{d}\underline{{r}}=\int_{\mathrm{Path~ADB}}\underline{{F}}^{T}\mathrm{d}\underline{{r}}.
 $$  
 
 Since reversing the limits of integration simply changes the sign of the integral, the work done by the force along path ADB is equal in magnitude and opposite in sign to that along path BDA. Equation (3.13) then implies the vanishing of the work done by the force over the closed path ACBDA. Because path ACB and ADB are arbitrary paths joining points $\mathbf{A}$ and $\mathbf{B}$ , it follows that a force is conservative if and only if the work it performs vanishes over any arbitrary closed path,  
-由于反转积分上下限仅仅改变积分的符号，因此力沿路径ADB所做的功，其大小等于沿路径BDA所做的功，但符号相反。由此，方程(3.13)推导出，力在闭合路径ACBDA上所做的功为零。因为路径ACB和ADB是连接点$\mathbf{A}$和$\mathbf{B}$的任意路径，因此可以得出，如果力所做的功在任意闭合路径上消失，则该力是保守力。
+由于反转积分上下限仅仅改变积分的符号，因此力沿路径ADB所做的功，其大小等于沿路径BDA所做的功，但符号相反。由此，方程(3.13)推导出，力在闭合路径ACBDA上所做的功为零。因为路径ACB和ADB是连接点$\mathbf{A}$和$\mathbf{B}$的任意路径，**因此可以得出，如果力所做的功在任意闭合路径上消失，则该力是保守力**。
 
 $$
 W=\oint_{\mathrm{Any~path}}\underline{{F}}^{T}\mathrm{d}\underline{{r}}=\oint_{\mathbb{C}}\underline{{F}}^{T}\mathrm{d}\underline{{r}}=0,
@@ -2914,7 +2914,7 @@ If a vector field, $\underline{{F}}$ , can be derived from a scalar function, $V
 It has now been established that if a force is conservative, it can be “derived from a potential.” In more mathematical terms, a conservative force must be the gradient a scalar function, called the potential of the force. If $\mathcal{T}=(\bar{\iota}_{1},\bar{\iota}_{2},\bar{\iota}_{3})$ is an orthonormal basis, conservative forces can be expressed as  
 如果一个向量场 $\underline{{F}}$ 可以由一个标量函数 $V$ 推导出来，则称该函数为势函数，并且称该向量函数“是由势函数推导出来的”。由于势函数是一个任意标量函数，因此负号是冗余的，但后续会对其进行合理的解释。
 
-目前已经确定，如果一个力是保守力，那么它可以“由势函数推导出来”。用更数学化的语言来说，保守力必须是标量函数（称为该力的势函数）的梯度。如果 $\mathcal{T}=(\bar{\iota}_{1},\bar{\iota}_{2},\bar{\iota}_{3})$ 是一个正交基，那么保守力可以表示为：
+目前已经确定，**如果一个力是保守力，那么它可以“由势函数推导出来”**。**用更数学化的语言来说，保守力必须是标量函数（称为该力的势函数）的梯度**。如果 $\mathcal{T}=(\bar{\iota}_{1},\bar{\iota}_{2},\bar{\iota}_{3})$ 是一个正交基，那么保守力可以表示为：
 
 
 $$
@@ -2922,7 +2922,7 @@ $$
 $$  
 
 The work done by a conservative force over an arbitrary path joining point 1 to point 2, with position vectors $\underline{{r}}_{1}$ and $\underline{{r}}_{2}$ , respectively, is then  
-
+由保守力对连接点 1 到点 2 的任意路径所做的功，其中位置向量分别为 $\underline{{r}}_{1}$ 和 $\underline{{r}}_{2}$，则为
 $$
 \begin{array}{l}{{W_{1\to2}=\displaystyle\int_{\frac{T_{1}}{\underline{{r}}_{1}}}^{\frac{T_{2}}{\underline{{r}}}} 
 $$  
@@ -2967,23 +2967,23 @@ At first glance, the potential of a gravity force and the strain energy of an el
 
 乍一看，重力势能和弹性弹簧的应变能似乎是截然不同、无关的概念。然而，这两个量都共享一个共同的属性：力可以从这些标量势能中推导出来。考虑一个质量为 $m$ 的粒子，该粒子连接到刚度常数为 $k$ 的弹性弹簧，并且受到一个在弹簧方向上的重力作用。粒子的向下位移 $u$ 测量了弹簧的伸长量和粒子的高度。施加的外部重力可以从势能 $V\,=\,m g u$ 中推导出来，得到 $F_{g}\,=\,-\partial V/\partial u\,=\,-m g$；弹簧中的回复力可以从应变能 $V=1/2\,k u^{2}$ 中推导出来，后者也可以被视为内部力的势能，得到 $F_{s}=-\partial V/\partial u=-k u.$ 。因此，作用在粒子上的两个力可以从势能中推导出来。
 
-Blade翻译为叶片，flapwise翻译为挥舞，edgewise翻译为摆振，pitch angle翻译成变桨角度，twist angle翻译为扭角，rotor翻译为风轮，span翻译为展向。
+
 # 3.2.1 Principle of conservation of energy  
 
 The forces applied to a particle can be divided into two categories: the conservative forces, which can be derived from a potential, and the non-conservative forces, for which no potential function exists. The principle of work and energy, eq. (3.11), now becomes  
-
+作用于颗粒的力可以分为两类：保守力，它可以从势函数导出；以及非保守力，对于非保守力不存在势函数。做功与能量原理，公式 (3.11)，现在变为
 $$
-\mathrm{d}W=\mathrm{d}W_{c}+\mathrm{d}W_{n c}=-\mathrm{d}(V)+\mathrm{d}\underline{{r}}^{T}\underline{{E}}_{n c}=\mathrm{d}(K),
+\mathrm{d}W=\mathrm{d}W_{c}+\mathrm{d}W_{n c}=-\mathrm{d}(V)+\mathrm{d}\underline{{r}}^{T}\underline{{F}}_{n c}=\mathrm{d}(K),
 $$  
 
 where $\mathrm{d}W_{c}$ and $\mathrm{d}W_{n c}$ indicate the differential work done by the conservative and non-conservatives forces, respectively, and $\underline{{F}}_{n c}$ denotes the non-conservative forces. The work done by these forces over the period from time $t_{i}$ to $t_{f}$ now becomes  
-
+其中，$\mathrm{d}W_{c}$ 和 $\mathrm{d}W_{n c}$ 分别表示保守力和非保守力所做的微分功，$\underline{{F}}_{n c}$ 表示非保守力。现在，这些力在时间 $t_{i}$ 到 $t_{f}$ 期间所做的功变为
 $$
 \int_{t_{i}}^{t_{f}}-\mathrm{d}(V)+\int_{t_{i}}^{t_{f}}\underline{{F}}_{n c}^{T}\mathrm{d}\underline{{r}}=K_{f}-K_{i}.
 $$  
 
 The first term of this expression readily integrates to yield  
-
+该表达式的第一项可以很容易地积分得到
 $$
 \int_{t_{i}}^{t_{f}}\underline{{F}}_{n c}^{T}\mathrm{d}\underline{{r}}=(K_{f}+V_{f})-(K_{i}+V_{i}),
 $$  
@@ -2991,12 +2991,15 @@ $$
 where $V_{i}\,=\,V(t_{i})$ and $V_{f}\,=\,V(t_{f})$ are the values of the potential function at the initial and final times, respectively.  
 
 The total mechanical energy, $E$ , is defined as the sum of the kinetic energy and potential function,  
+其中，$V_{i}\,=\,V(t_{i})$ 和 $V_{f}\,=\,V(t_{f})$ 分别是势函数在初始时间和最终时间的取值。
 
+总机械能，记为 $E$ ，定义为动能和势函数之和。
 $$
 E=K+V.
 $$  
 
-The principle of work an energy principle now becomes  
+The principle of work and energy principle now becomes  
+工作原理现在成为一个能量原理。
 
 $$
 \int_{t_{i}}^{t_{f}}\underline{{F}}_{n c}^{T}\mathrm{d}\underline{{r}}=E_{f}-E_{i}.
@@ -3010,14 +3013,20 @@ $$
 
 This statement is known as the principle of conservation of energy.  
 
-Principle 2 (Principle of conservation of energy for a particle) If a particle is subjected to conservative forces only, the total mechanical energy is preserved.  
+**Principle 2 (Principle of conservation of energy for a particle)** If a particle is subjected to conservative forces only, the total mechanical energy is preserved.  
 
 Clearly, the term “conservative forces” stems from the fact that in the sole presence of such forces, the total mechanical energy of the particle is conserved.  
 
 In view of the principle of work and energy, work, kinetic energy, potential energy, and total mechanical energy all share the same units, force times distance, $\mathbf{N}{\cdot}\mathbf{m}$ . A Joule is defined as $1\;\mathrm{J}=1\;\mathrm{N}{\cdot}\mathrm{m}$ . Although the moment of a force has the same units, $\mathbf{N}{\cdot}\mathbf{m}$ , Joules are used only when dealing with energy; in other words, a $10\,\mathrm{{N\cdotm}}$ moment should not be referred to as a $10\,\mathrm{J}$ moment.  
 
 The work done by force over a period of time from $t_{i}$ to $t_{f}$ , see eq. (3.12), can be written as  
+**原理 2 (单个粒子的能量守恒原理)** 如果一个粒子仅受到保守力作用，则其总机械能守恒。
 
+显然，“保守力”一词源于这样一个事实：仅在这些力单独存在的情况下，粒子的总机械能才得以守恒。
+
+鉴于功与能量的原理，功、动能、势能和总机械能都具有相同的单位，即力乘以距离，$\mathbf{N}{\cdot}\mathbf{m}$。 一焦耳被定义为 $1\;\mathrm{J}=1\;\mathrm{N}{\cdot}\mathrm{m}$。 尽管力矩也具有相同的单位，$\mathbf{N}{\cdot}\mathbf{m}$，但焦耳仅用于处理能量；换句话说，一个 $10\,\mathrm{{N\cdotm}}$ 的力矩不应被称为 $10\,\mathrm{J}$ 的力矩。
+
+在时间 $t_{i}$ 到 $t_{f}$ 期间，力所做的功，见公式 (3.12)，可以写为</text>
 $$
 W_{t_{i}\rightarrow t_{f}}=\int_{t_{i}}^{t_{f}}\underline{{F}}^{T}\mathrm{d}\underline{{r}}=\int_{t_{i}}^{t_{f}}\underline{{F}}^{T}\frac{\mathrm{d}\underline{{r}}}{\mathrm{d}t}\,\mathrm{d}t=\int_{t_{i}}^{t_{f}}\underline{{F}}^{T}\underline{{v}}\,\mathrm{d}t.
 $$  

软件组工作讨论/2025.2.20 25年度计划-孙博士提意见.md

@@ -4,6 +4,8 @@
 
 前后处理都写好
 
+
+
 有验证