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@ -177,7 +177,7 @@ The equations for $^E_{\nu_{r}^{S2}}\left(r\right)$ and $^E_{\nu_{t}^{S2}}\left(
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Angular Accelerations:
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Angular Accelerations:
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Recall that: $^{E}\pmb{\alpha}^{N_{i}}\left(\ddot{q},\dot{q},q,t\right)\!=\!\left(\sum_{r=l}^{22}^{E}\pmb{\omega}_{r}^{N_{i}}\left(q,t\right)\ddot{q}_{r}\right)\!+\!\left[\sum_{r=l}^{22}\frac{d}{d t}\!\left(^{E}\pmb{\omega}_{r}^{N_{i}}\left(q,t\right)\right)\!\dot{q}_{r}\right]\!+\!\frac{d}{d t}\!\left(^{E}\pmb{\omega}_{t}^{N_{i}}\left(q,t\right)\right)\!\left(^{E}\pmb{\omega}_{p}^{N_{i}}\left(q,t\right)\right),$ for each rigid body $N_{i}$ in the system. Note that the $\frac{d}{d t}\Big(^{E}\omega_{r}^{N_{i}}\Big)$ terms are all vector functions of $\left({\dot{q}},q,t\right)$ and that all of the $\frac{d}{d t}\Big(^{E}\omega_{t}^{N_{i}}\Big)$ terms are zero as will be shown.
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Recall that: $^{E}\pmb{\alpha}^{N_{i}}\left(\ddot{q},\dot{q},q,t\right)\!=\!\left(\sum_{r=l}^{22}^{E}\pmb{\omega}_{r}^{N_{i}}\left(q,t\right)\ddot{q}_{r}\right)\!+\!\left[\sum_{r=l}^{22}\frac{d}{d t}\!\left(^{E}\pmb{\omega}_{r}^{N_{i}}\left(q,t\right)\right)\!\dot{q}_{r}\right]\!+\!\frac{d}{d t}\!\left(^{E}\pmb{\omega}_{t}^{N_{i}}\left(q,t\right)\right)\!\left(^{E}\pmb{\omega}_{p}^{N_{i}}\left(q,t\right)\right)$ for each rigid body $N_{i}$ in the system. Note that the $\frac{d}{d t}\Big(^{E}\omega_{r}^{N_{i}}\Big)$ terms are all vector functions of $\left({\dot{q}},q,t\right)$ and that all of the $\frac{d}{d t}\Big(^{E}\omega_{t}^{N_{i}}\Big)$ terms are zero as will be shown.
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$$
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$$
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\begin{array}{l}{\displaystyle\frac{d}{d t}\Big(\sp\varepsilon\omega_{r}^{X}\Big)=O}\\ {\displaystyle\frac{d}{d t}\Big(\sp\varepsilon\omega_{{r}}^{X}\Big)=O}\end{array}
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\begin{array}{l}{\displaystyle\frac{d}{d t}\Big(\sp\varepsilon\omega_{r}^{X}\Big)=O}\\ {\displaystyle\frac{d}{d t}\Big(\sp\varepsilon\omega_{{r}}^{X}\Big)=O}\end{array}
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@ -200,7 +200,7 @@ The equations for ${\frac{d}{d t}}\Big[^{\,E}\pmb{\omega}_{r}^{{\scriptscriptsty
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Linear Accelerations:
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Linear Accelerations:
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Recall that: $\varepsilon_{\mathbf{}}\boldsymbol{\alpha}^{X_{i}}\left(\ddot{q},\dot{q},q,t\right)\!=\!\!\left(\sum_{r=l}^{22}\varepsilon_{\nu_{r}^{X_{i}}}\left(q,t\right)\ddot{q}_{r}\right)\!+\!\!\left[\sum_{r=l}^{22}\!\frac{d}{d t}\!\left({^{\varepsilon}\nu_{r}^{X_{i}}}\left(q,t\right)\right)\!\dot{q}_{r}\right]\!+\!\frac{d}{d t}\!\left({^{\varepsilon}\nu_{{^I}}^{X_{i}}}\left(q,t\right)\right)\!\left({^{\varepsilon}\nu_{{^I}}^{X_{i}}}\left(q,t\right)\right)\!+\!\frac{d}{d t}\!\left({^{\varepsilon}\nu_{{^I}}^{X_{i}}}\left(q,t\right)\right)\!+\!{^{\varepsilon}\nu_{{^I}}^{X_{i}}}\left(q,t\right),$ for each point $X_{i}$ in the system. Note that the ${\frac{d}{d t}}{\Big(}^{E}\nu_{r}^{X_{i}}{\Big)}$ terms are all vector functions of $\left({\dot{q}},q,t\right)$ and that all of the ${\frac{d}{d t}}{\Big(}^{E}\nu_{t}^{X_{i}}{\Big)}$ terms are zero as will be shown.
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Recall that: ${}^E{\alpha}^{X_{i}}\left(\ddot{q},\dot{q},q,t\right)\!=\!\!\left(\sum_{r=1}^{22}{}^E{V_{r}^{X_{i}}}\left(q,t\right)\ddot{q}_{r}\right)\!+\!\!\left[\sum_{r=1}^{22}\!\frac{d}{d t}\!\left({}^E{V_{r}^{X_{i}}}\left(q,t\right)\right)\!\dot{q}_{r}\right]\!+\!\frac{d}{d t}\!\left({}^EV_{r}^{X_{i}}\left(q,t\right)\right)$ for each point $X_{i}$ in the system. Note that the ${\frac{d}{d t}}{\Big(}^{E}\nu_{r}^{X_{i}}{\Big)}$ terms are all vector functions of $\left({\dot{q}},q,t\right)$ and that all of the ${\frac{d}{d t}}{\Big(}^{E}\nu_{t}^{X_{i}}{\Big)}$ terms are zero as will be shown.
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$$
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$$
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\begin{array}{l}{\displaystyle\frac{d}{d t}\Big(\sp\varepsilon\pmb{\nu}_{r}^{z}\Big)=O}\\ {\displaystyle\frac{d}{d t}\Big(\sp\varepsilon\pmb{\nu}_{{\pmb\nu}}^{z}\Big)=O}\end{array}
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\begin{array}{l}{\displaystyle\frac{d}{d t}\Big(\sp\varepsilon\pmb{\nu}_{r}^{z}\Big)=O}\\ {\displaystyle\frac{d}{d t}\Big(\sp\varepsilon\pmb{\nu}_{{\pmb\nu}}^{z}\Big)=O}\end{array}
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@ -1088,35 +1088,38 @@ $$
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# 2.5 ANGULAR ACCELERATION
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# 2.5 ANGULAR ACCELERATION
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The angular acceleration Aa of a rigid body B in a reference frame A is defined as the first time-derivative in A of the angular velocity of B in A (see Sec. 2.1):
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The angular acceleration ${}^{A}{\alpha}^{B}$ of a rigid body B in a reference frame A is defined as the first time-derivative in A of the angular velocity of B in A (see Sec. 2.1):
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刚体的角加速度 ${}^{A}{\alpha}^{B}$ 在参考系 A 中定义为 A 中对 B 在 A 中的角速度的一阶时间导数（见第 2.1 节）：
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$$
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$$
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A_{\mathfrak{A}}{}^{B}\triangleq\frac{{}^{A}d^{A}\mathfrak{A}^{B}}{d t}
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{}^{A}{\alpha}^{B}\triangleq\frac{{}^{A}d^{A}\omega^{B}}{d t}
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$$
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$$
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Since the first time-derivatives of $\mathbf{\mathit{A}}_{\mathbf{\Theta}\mathbf{\tilde{0}}}\mathbf{\mathit{B}}$ in $\pmb{A}$ andin $B$ are equal toeach other, as becomes evident when one replaces v in Eq. (2.3.1) with 4o", Eq. (1) implies that
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Since the first time-derivatives of ${}^{A}\omega^{B}$ in $\pmb{A}$ and in $B$ are equal to each other, as becomes evident when one replaces v in Eq. (2.3.1) with 4o", Eq. (1) implies that
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由于 ${}^{A}\omega^{B}$ 在 $A$ 和 $B$ 处的首次时间导数彼此相等，正如在方程 (2.3.1) 中将 v 替换为 4o" 时显而易见，则方程 (1) 意味着
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$$
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{}^{A}{\alpha}^{B}\triangleq\frac{{}^{B}d^{A}\omega^{B}}{d t}
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$$
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which furnishes a convenient way to find ${}^{A}{\alpha}^{B}$ when ${}^{A}\omega^{B}$ has been expressed in terms of components parallel to unit vectors fixed in $\boldsymbol{B}$
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这为寻找${}^{A}{\alpha}^{B}$提供了一种便捷的方法，当 ${}^{A}\omega^{B}$ 已经用平行于固定在 $\boldsymbol{B}$ 中的单位向量的组件表示时。
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If $A_{1},...,A_{n}$ are $n$ auxiliary reference frames, ${}^{A}{\alpha}^{B}$ is not, in general, equal to the sum ${}^{A}{\alpha}^{A_{i}} + {}^{A_{1}}{\alpha}^{A_{2}} + ... +{}^{A_{n}}{\alpha}^{B}$ . Thus, Eq. (2.4.1) does not, in general, have an angular acceleration counterpart.
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The angular velocity of $\boldsymbol{B}$ in $A$ can always be expressed as ${}^{A}\mathbf{\omega}^{B}=\omega\mathbf{k}_{\omega}$ , where $\mathbf{k}_{\omega}$ is a unit vector parallel to ${}^{A}\mathbf{\omega}^{B}$ ; similarly ${}^{A}{\alpha}^{B}$ can always be expressed as ${}^{A}{\alpha}^{B}=\alpha\mathbf{k}_{\alpha}$ , where $\mathbf{k}_{\alpha}$ is a unit vector parallel to ${}^{A}{\alpha}^{B}$ In general, $\mathbf{k}_{\omega}$ differs from $\mathbf{k}_{\alpha}$ ， and $\alpha\neq d\omega/d t$ . But when $\boldsymbol{B}$ has a simple angular velocity in $A$ (see Sec. 2.2), and ${}^{A}\mathbf{\omega}^{B}$ is expressed as in Eq. (2.2.1), then
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$$
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$$
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A_{\mathfrak{A}}B=\frac{B_{d}A_{\mathfrak{A}}^{B}}{d t}
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{}^{A}{\alpha}^{B}=\alpha\mathbf{k}
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$$
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$$
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which furnishes a convenient way to find AaB when Ao3 has been expressed in terms of components parallel to unit vectors fixed in $\boldsymbol{B}$
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where $\alpha$ called a scalar angular acceleration, is given by
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If $A_{1},...,A_{n}$ are $n$ auxiliary reference frames, $A_{\alpha}B$ is not, in general, equal to the sum $\mathbf{\dot{\alpha}}^{A}\mathbf{\alpha}^{A_{1}}+\mathbf{\alpha}^{A_{1}}\mathbf{\alpha}^{A_{2}}+\mathbf{\beta}^{\dots}+\mathbf{\alpha}^{A_{n}}\mathbf{\alpha}^{B}$ . Thus, Eq. (2.4.1) does not, in general, have an angular acceleration counterpart.
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The angular velocity of $\boldsymbol{B}$ in $A$ can always be expressed as ${}^{A}\mathbf{\omega}\mathbf{\omega}^{B}=\omega\mathbf{k}_{\omega}$ , where $\mathbf{k}_{\omega}$ is a unit vector parallel to $\mathbf{\mathit{A}_{G D}}\mathbf{\mathit{B}}$ ; similarly $A_{\widetilde{\mathbf{z}}}B$ can always be expressed as $^{A}\pmb{\alpha}^{B}=\alpha\mathbf{k}_{\alpha}$ , where $\mathbf{k}_{\alpha}$ is a unit vector parall to $A_{\pmb{\alpha}}B$ In general, $\mathbf{k}_{\omega}$ differs from $\mathbf{k}_{\alpha}$ ， and $\alpha\neq d\omega/d t$ . But when $\boldsymbol{B}$ has a simple angular velocity in $A$ (see Sec. 2.2), and $\mathbf{\Pi}^{A}\mathbf{\Pi}_{\mathbf{G}\mathbf{\tilde{D}}}\mathbf{\scriptscriptstyle{B}}$ is expressed as in Eq. (2.2.1), then
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$$
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A_{\alpha}B_{\mathrm{\Phi}}={\mathfrak{X}}\mathbf{k}
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$$
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where $\pmb{\alpha}_{\ast}$ called a scalar angular acceleration, is given by
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$$
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$$
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\alpha={\frac{d\omega}{d t}}
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\alpha={\frac{d\omega}{d t}}
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$$
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$$
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Example Referring to the example in Sec. 2.4 and to Fig. 2.4.1, one can find an expression for the angular acceleration of the cone $\pmb{B}$ inreferenceframe $\pmb{A}$ asfollows:
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Example Referring to the example in Sec. 2.4 and to Fig. 2.4.1, one can find an expression for the angular acceleration of the cone $\pmb{B}$ in reference frame $\pmb{A}$ as follows:
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$$
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$$
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{\begin{array}{r l}&{{\mathbf{\nabla}}_{a{\pmb{\alpha}}^{B}}={\cfrac{a_{d}}{d t}}({\dot{q}}_{1}{\mathbf{k}}_{2}+{\dot{q}}_{2}{\mathbf{k}}_{7}+{\dot{q}}_{3}{\mathbf{k}}_{3})}\\ &{\qquad={\ddot{q}}_{1}{\mathbf{k}}_{2}+{\dot{q}}_{1}{\cfrac{a_{d}{\mathbf{k}}_{2}}{d t}}+{\ddot{q}}_{2}{\mathbf{k}}_{7}+{\dot{q}}_{2}{\cfrac{a_{d}{\mathbf{k}}_{7}}{d t}}+{\ddot{q}}_{3}{\mathbf{k}}_{3}+{\dot{q}}_{3}{\cfrac{a_{d}{\mathbf{k}}_{3}}{d t}}}\end{array}}\,,{\mathbf{\dot{\xi}}}_{{\begin{array}{r}{{\dot{\mathbf{\xi}}}_{{\mathrm{~f~i~s~}}^{A}}\end{array}}}}\,,{\mathbf{\dot{\xi}}}_{{\begin{array}{r}{{\dot{\mathbf{\xi}}}_{{\mathrm{~f~i~s~}}^{A}}\end{array}}}}\,,
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{\begin{array}{r l}&{{\mathbf{\nabla}}_{a{\pmb{\alpha}}^{B}}={\cfrac{a_{d}}{d t}}({\dot{q}}_{1}{\mathbf{k}}_{2}+{\dot{q}}_{2}{\mathbf{k}}_{7}+{\dot{q}}_{3}{\mathbf{k}}_{3})}\\ &{\qquad={\ddot{q}}_{1}{\mathbf{k}}_{2}+{\dot{q}}_{1}{\cfrac{a_{d}{\mathbf{k}}_{2}}{d t}}+{\ddot{q}}_{2}{\mathbf{k}}_{7}+{\dot{q}}_{2}{\cfrac{a_{d}{\mathbf{k}}_{7}}{d t}}+{\ddot{q}}_{3}{\mathbf{k}}_{3}+{\dot{q}}_{3}{\cfrac{a_{d}{\mathbf{k}}_{3}}{d t}}}\end{array}}\,,{\mathbf{\dot{\xi}}}_{{\begin{array}{r}{{\dot{\mathbf{\xi}}}_{{\mathrm{~f~i~s~}}^{A}}\end{array}}}}\,,{\mathbf{\dot{\xi}}}_{{\begin{array}{r}{{\dot{\mathbf{\xi}}}_{{\mathrm{~f~i~s~}}^{A}}\end{array}}}}\,,
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@ -6554,7 +6554,7 @@ $$
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F^{\,^{*\,(r)}}\;=\;F^{\,^{*}}\,\cdot\,\pmb{v}_{\!_{0}}^{(\,r\,)}\;+\;M^{\,^{*}}\,\cdot\,\pmb{\omega}^{(\,r\,)}
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F^{\,^{*\,(r)}}\;=\;F^{\,^{*}}\,\cdot\,\pmb{v}_{\!_{0}}^{(\,r\,)}\;+\;M^{\,^{*}}\,\cdot\,\pmb{\omega}^{(\,r\,)}
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$$
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$$
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其中， $\pmb{v}_{0}^{(r)}$ 及 $\pmb{\omega}^{(r)}$ 为刚体上任意选定的参考点 $o$ 的第 $r$ 偏速度及刚体的第 $r$ 偏角速度，F和M为刚体上作用的外力主动力主矢及对O点的主矩，F\*及M\*为刚体的惯性力主矢及对 $o$ 点的主矩。设 $\pmb{\rho}_{\nu}$ 为刚体中任意点 $P_{\nu}$ 相对 $o$ 点的矢径，$\boldsymbol{P}_{\nu}$ 处作用的主动力和惯性力以小写的 $\boldsymbol{f}_{\nu}\,,\boldsymbol{f}_{\nu}^{*}$ 表示，则有
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其中， $\pmb{v}_{0}^{(r)}$ 及 $\pmb{\omega}^{(r)}$ 为刚体上任意选定的参考点 $o$ 的第 $r$ 偏速度及刚体的第 $r$ 偏角速度，$F$和$M$为刚体上作用的外力主动力主矢及对O点的主矩，$F^*$及$M^*$为刚体的惯性力主矢及对 $o$ 点的主矩。设 $\pmb{\rho}_{\nu}$ 为刚体中任意点 $P_{\nu}$ 相对 $o$ 点的矢径，$\boldsymbol{P}_{\nu}$ 处作用的主动力和惯性力以小写的 $\boldsymbol{f}_{\nu}\,,\boldsymbol{f}_{\nu}^{*}$ 表示，则有
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$$
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$$
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\begin{array}{r c l}{{\pmb F}\ =}&{{\displaystyle\sum_{\nu}{\pmb f}_{\nu}\,,}}&{{\pmb M}\ =\ \sum_{\nu}{\pmb\rho}_{\nu}\ \times{\pmb f}_{\nu}}\\ {{\pmb F}^{\star}\ =}&{{\displaystyle\sum_{\nu}{\pmb f}_{\nu}^{\star}\ =-\ \sum_{\nu}{\pmb m}_{\nu}\,\ddot{\pmb r}_{\nu}}}&{{=-\ \dot{\pmb p}\,.}}\end{array}
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\begin{array}{r c l}{{\pmb F}\ =}&{{\displaystyle\sum_{\nu}{\pmb f}_{\nu}\,,}}&{{\pmb M}\ =\ \sum_{\nu}{\pmb\rho}_{\nu}\ \times{\pmb f}_{\nu}}\\ {{\pmb F}^{\star}\ =}&{{\displaystyle\sum_{\nu}{\pmb f}_{\nu}^{\star}\ =-\ \sum_{\nu}{\pmb m}_{\nu}\,\ddot{\pmb r}_{\nu}}}&{{=-\ \dot{\pmb p}\,.}}\end{array}
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@ -6746,7 +6746,7 @@ $$
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(6.3.18)
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(6.3.18)
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可见，对于完整系统，凯恩方法中的广义主动力 ${\boldsymbol{F}}^{(r)}$ 等同于拉格朗日方程中的广义力 $Q_{r}$ D
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可见，对于完整系统，凯恩方法中的广义主动力 ${\boldsymbol{F}}^{(r)}$ 等同于拉格朗日方程中的广义力 $Q_{r}$ 。
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例6.2设例6.1所讨论系统中刚体上作用的主动力主矢及对 $o$ 点的主矩为 $F$ 及 $M$ ,其作用线均在运动平面内，弹簧变形前的长度为 $l$ ，刚度为 $K$ ，刚体 $B$ 的质量及相对 $\boldsymbol{e}_{3}$ 的惯量矩为 $m$ 及 $J$ ，质点 $P$ 的质量为 $m_{p}$ 。试用凯恩方法导出此系统的动力学方程。
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例6.2设例6.1所讨论系统中刚体上作用的主动力主矢及对 $o$ 点的主矩为 $F$ 及 $M$ ,其作用线均在运动平面内，弹簧变形前的长度为 $l$ ，刚度为 $K$ ，刚体 $B$ 的质量及相对 $\boldsymbol{e}_{3}$ 的惯量矩为 $m$ 及 $J$ ，质点 $P$ 的质量为 $m_{p}$ 。试用凯恩方法导出此系统的动力学方程。
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"cells": [
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"cells": [
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{
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{
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"cell_type": "code",
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"cell_type": "code",
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"execution_count": 120,
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"execution_count": 72,
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"metadata": {},
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"metadata": {},
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"outputs": [],
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"outputs": [],
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"source": [
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"source": [
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},
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},
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"outputs": [],
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"source": [
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},
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{
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"outputs": [
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"outputs": [
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{
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{
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"0"
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"0"
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]
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]
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"cos(q_yaw) a_x + -sin(q_yaw) a_z"
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"cos(q_yaw) a_x + -sin(q_yaw) a_z"
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]
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]
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"↪ _overhang⋅sin(q_yaw)⋅cos(θₜᵢₗₜ) a_z"
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"↪ _overhang⋅sin(q_yaw)⋅cos(θₜᵢₗₜ) a_z"
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{
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"↪ w⋅cos(θₜᵢₗₜ) c_z, u_yaw a_y, u_yaw a_y, (u_drtr + u_geaz) c_x + u_yaw a_y)"
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"↪ w⋅cos(θₜᵢₗₜ) c_z, u_yaw a_y, u_yaw a_y, (u_drtr + u_geaz) c_x + u_yaw a_y)"
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]
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]
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},
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},
|
||||||
"execution_count": 127,
|
"execution_count": 79,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"output_type": "execute_result"
|
"output_type": "execute_result"
|
||||||
}
|
}
|
||||||
@ -217,7 +217,7 @@
|
|||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 128,
|
"execution_count": 80,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
@ -242,7 +242,7 @@
|
|||||||
"↪ _yaw⋅cos(θₜᵢₗₜ) c_z + u_ẏaw a_y⎠"
|
"↪ _yaw⋅cos(θₜᵢₗₜ) c_z + u_ẏaw a_y⎠"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"execution_count": 128,
|
"execution_count": 80,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"output_type": "execute_result"
|
"output_type": "execute_result"
|
||||||
}
|
}
|
||||||
@ -260,7 +260,7 @@
|
|||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 129,
|
"execution_count": 81,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
@ -272,7 +272,7 @@
|
|||||||
"(d_y, 0, 0)"
|
"(d_y, 0, 0)"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"execution_count": 129,
|
"execution_count": 81,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"output_type": "execute_result"
|
"output_type": "execute_result"
|
||||||
}
|
}
|
||||||
@ -287,7 +287,7 @@
|
|||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 130,
|
"execution_count": 82,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
@ -299,7 +299,7 @@
|
|||||||
"((u_drtr + u_geaz) c_x + u_yaw a_y, sin(θₜᵢₗₜ) c_x + cos(θₜᵢₗₜ) c_y, c_x, c_x)"
|
"((u_drtr + u_geaz) c_x + u_yaw a_y, sin(θₜᵢₗₜ) c_x + cos(θₜᵢₗₜ) c_y, c_x, c_x)"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"execution_count": 130,
|
"execution_count": 82,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"output_type": "execute_result"
|
"output_type": "execute_result"
|
||||||
}
|
}
|
||||||
@ -314,7 +314,7 @@
|
|||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 131,
|
"execution_count": 83,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
@ -326,22 +326,22 @@
|
|||||||
"(Nx d_x + Ny d_y + Nz d_z, Nz d_x + -Nx d_z, Nz d_x + -Nx d_z, 0, 0)"
|
"(Nx d_x + Ny d_y + Nz d_z, Nz d_x + -Nx d_z, Nz d_x + -Nx d_z, 0, 0)"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"execution_count": 131,
|
"execution_count": 83,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"output_type": "execute_result"
|
"output_type": "execute_result"
|
||||||
}
|
}
|
||||||
],
|
],
|
||||||
"source": [
|
"source": [
|
||||||
"# U点\n",
|
"# U点\n",
|
||||||
"v_U_1 = U.vel(A).diff(u_yaw, A).express(D)\n",
|
"v_U_1 = U.vel(A).diff(u_yaw, A)\n",
|
||||||
"v_U_2 = U.vel(A).diff(u_drtr, A).express(D)\n",
|
"v_U_2 = U.vel(A).diff(u_drtr, A)\n",
|
||||||
"v_U_3 = U.vel(A).diff(u_geaz, A).express(D)\n",
|
"v_U_3 = U.vel(A).diff(u_geaz, A)\n",
|
||||||
"U.pos_from(O).express(D), w_D_1.cross(U.pos_from(O).express(D)), v_U_1, v_U_2, v_U_3"
|
"U.pos_from(O).express(D), w_D_1.cross(U.pos_from(O).express(D)), v_U_1, v_U_2, v_U_3"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 132,
|
"execution_count": 84,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
@ -353,7 +353,7 @@
|
|||||||
"(Iₓ d_x + I_y d_y + I_z d_z, I_z d_x + -Iₓ d_z, I_z d_x + -Iₓ d_z, 0, 0)"
|
"(Iₓ d_x + I_y d_y + I_z d_z, I_z d_x + -Iₓ d_z, I_z d_x + -Iₓ d_z, 0, 0)"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"execution_count": 132,
|
"execution_count": 84,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"output_type": "execute_result"
|
"output_type": "execute_result"
|
||||||
}
|
}
|
||||||
@ -368,32 +368,231 @@
|
|||||||
},
|
},
|
||||||
{
|
{
|
||||||
"cell_type": "code",
|
"cell_type": "code",
|
||||||
"execution_count": 133,
|
"execution_count": 85,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"outputs": [
|
"outputs": [
|
||||||
{
|
{
|
||||||
"data": {
|
"data": {
|
||||||
"text/latex": [
|
"text/latex": [
|
||||||
"$\\displaystyle \\left( L_{overhang} \\cos{\\left(\\theta_{tilt} \\right)}\\mathbf{\\hat{d}_x} + (L_{overhang} \\sin{\\left(\\theta_{tilt} \\right)} + L_{t2s})\\mathbf{\\hat{d}_y}, \\ - L_{overhang} \\cos{\\left(\\theta_{tilt} \\right)}\\mathbf{\\hat{d}_z}, \\ - L_{overhang} \\cos{\\left(\\theta_{tilt} \\right)}\\mathbf{\\hat{d}_z}, \\ 0, \\ 0\\right)$"
|
"$\\displaystyle \\left( L_{overhang} \\cos{\\left(\\theta_{tilt} \\right)}\\mathbf{\\hat{d}_x} + (L_{overhang} \\sin{\\left(\\theta_{tilt} \\right)} + L_{t2s})\\mathbf{\\hat{d}_y}, \\ - L_{overhang} \\cos{\\left(\\theta_{tilt} \\right)}\\mathbf{\\hat{d}_z}, \\ - L_{overhang} \\cos{\\left(\\theta_{tilt} \\right)}\\mathbf{\\hat{c}_z}, \\ 0, \\ 0\\right)$"
|
||||||
],
|
],
|
||||||
"text/plain": [
|
"text/plain": [
|
||||||
"(L_overhang⋅cos(θₜᵢₗₜ) d_x + (L_overhang⋅sin(θₜᵢₗₜ) + Lₜ₂ₛ) d_y, -L_overhang⋅c ↪\n",
|
"(L_overhang⋅cos(θₜᵢₗₜ) d_x + (L_overhang⋅sin(θₜᵢₗₜ) + Lₜ₂ₛ) d_y, -L_overhang⋅c ↪\n",
|
||||||
"\n",
|
"\n",
|
||||||
"↪ os(θₜᵢₗₜ) d_z, -L_overhang⋅cos(θₜᵢₗₜ) d_z, 0, 0)"
|
"↪ os(θₜᵢₗₜ) d_z, -L_overhang⋅cos(θₜᵢₗₜ) c_z, 0, 0)"
|
||||||
]
|
]
|
||||||
},
|
},
|
||||||
"execution_count": 133,
|
"execution_count": 85,
|
||||||
"metadata": {},
|
"metadata": {},
|
||||||
"output_type": "execute_result"
|
"output_type": "execute_result"
|
||||||
}
|
}
|
||||||
],
|
],
|
||||||
"source": [
|
"source": [
|
||||||
"# P点\n",
|
"# P点\n",
|
||||||
"v_P_1 = P.vel(A).diff(u_yaw, A).express(D)\n",
|
"v_P_1 = P.vel(A).diff(u_yaw, A)\n",
|
||||||
"v_P_2 = P.vel(A).diff(u_drtr, A).express(D)\n",
|
"v_P_2 = P.vel(A).diff(u_drtr, A)\n",
|
||||||
"v_P_3 = P.vel(A).diff(u_geaz, A).express(D)\n",
|
"v_P_3 = P.vel(A).diff(u_geaz, A)\n",
|
||||||
"P.pos_from(O).express(D), w_D_1.cross(P.pos_from(O).express(D)), v_P_1, v_P_2, v_P_3"
|
"P.pos_from(O).express(D), w_D_1.cross(P.pos_from(O).express(D)), v_P_1, v_P_2, v_P_3"
|
||||||
]
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 86,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/latex": [
|
||||||
|
"$\\displaystyle \\left[\\begin{matrix}L_{overhang} g m_{hub} \\cos{\\left(\\theta_{tilt} \\right)} \\cos{\\left(q_{drtr} + q_{geaz} \\right)} + Nx g m_{nac}\\\\0\\\\0\\end{matrix}\\right]$"
|
||||||
|
],
|
||||||
|
"text/plain": [
|
||||||
|
"⎡L_overhang⋅g⋅m_hub⋅cos(θₜᵢₗₜ)⋅cos(q_drtr + q_geaz) + Nx⋅g⋅m_nac⎤\n",
|
||||||
|
"⎢ ⎥\n",
|
||||||
|
"⎢ 0 ⎥\n",
|
||||||
|
"⎢ ⎥\n",
|
||||||
|
"⎣ 0 ⎦"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 86,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"# 主动力\n",
|
||||||
|
"# yaw\n",
|
||||||
|
"F_yaw = sm.Function('q_yaw, u_yaw')\n",
|
||||||
|
"# 考虑 机舱重力，轮毂重力\n",
|
||||||
|
"m_nac, g, m_hub = sm.symbols(\"m_nac, g, m_hub\")\n",
|
||||||
|
"R_nac = -m_nac * g * D.z\n",
|
||||||
|
"R_hub = -m_hub * g * G.z\n",
|
||||||
|
"\n",
|
||||||
|
"F1 = v_U_1.dot(R_nac) + v_P_1.dot(R_hub)\n",
|
||||||
|
"F2 = v_U_2.dot(R_nac) + v_P_2.dot(R_hub)\n",
|
||||||
|
"F3 = v_U_3.dot(R_nac) + v_P_3.dot(R_hub)\n",
|
||||||
|
"\n",
|
||||||
|
"Fr = sm.Matrix([F1, F2, F3])\n",
|
||||||
|
"Fr"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 93,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/latex": [
|
||||||
|
"$\\displaystyle \\left[\\begin{matrix}- L_{overhang}^{2} m_{hub} \\cos^{2}{\\left(\\theta_{tilt} \\right)} \\dot{u}_{yaw} + Nx m_{nac} \\left(- Nx \\dot{u}_{yaw} - Nz u_{yaw}^{2}\\right) - Nz m_{nac} \\left(- Nx u_{yaw}^{2} + Nz \\dot{u}_{yaw}\\right) - \\left(Nac_{YIner} - m_{nac} \\left(Nx^{2} + Ny^{2}\\right)\\right) \\dot{u}_{yaw} + \\left(- \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) \\left(- \\left(u_{drtr} + u_{geaz}\\right) u_{yaw} \\sin{\\left(q_{drtr} + q_{geaz} \\right)} \\cos{\\left(\\theta_{tilt} \\right)} + \\cos{\\left(\\theta_{tilt} \\right)} \\cos{\\left(q_{drtr} + q_{geaz} \\right)} \\dot{u}_{yaw}\\right) + \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) \\left(u_{drtr} + u_{geaz} + u_{yaw} \\sin{\\left(\\theta_{tilt} \\right)}\\right) u_{yaw} \\sin{\\left(q_{drtr} + q_{geaz} \\right)} \\cos{\\left(\\theta_{tilt} \\right)}\\right) \\cos{\\left(\\theta_{tilt} \\right)} \\cos{\\left(q_{drtr} + q_{geaz} \\right)} + \\left(- \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) \\left(\\sin{\\left(\\theta_{tilt} \\right)} \\dot{u}_{yaw} + \\dot{u}_{drtr} + \\dot{u}_{geaz}\\right) - \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) u_{yaw}^{2} \\sin{\\left(q_{drtr} + q_{geaz} \\right)} \\cos^{2}{\\left(\\theta_{tilt} \\right)} \\cos{\\left(q_{drtr} + q_{geaz} \\right)}\\right) \\sin{\\left(\\theta_{tilt} \\right)}\\\\- \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) \\left(\\sin{\\left(\\theta_{tilt} \\right)} \\dot{u}_{yaw} + \\dot{u}_{drtr} + \\dot{u}_{geaz}\\right) - \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) u_{yaw}^{2} \\sin{\\left(q_{drtr} + q_{geaz} \\right)} \\cos^{2}{\\left(\\theta_{tilt} \\right)} \\cos{\\left(q_{drtr} + q_{geaz} \\right)}\\\\- \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) \\left(\\sin{\\left(\\theta_{tilt} \\right)} \\dot{u}_{yaw} + \\dot{u}_{drtr} + \\dot{u}_{geaz}\\right) - \\left(Hub_{Iner} - hub_{cm}^{2} m_{hub}\\right) u_{yaw}^{2} \\sin{\\left(q_{drtr} + q_{geaz} \\right)} \\cos^{2}{\\left(\\theta_{tilt} \\right)} \\cos{\\left(q_{drtr} + q_{geaz} \\right)}\\end{matrix}\\right]$"
|
||||||
|
],
|
||||||
|
"text/plain": [
|
||||||
|
"⎡ 2 2 ⎛ 2⎞ ↪\n",
|
||||||
|
"⎢- L_overhang ⋅m_hub⋅cos (θₜᵢₗₜ)⋅u_ẏaw + Nx⋅m_nac⋅⎝-Nx⋅u_ẏaw - Nz⋅u_yaw ⎠ - Nz ↪\n",
|
||||||
|
"⎢ ↪\n",
|
||||||
|
"⎢ ↪\n",
|
||||||
|
"⎢ ↪\n",
|
||||||
|
"⎢ ↪\n",
|
||||||
|
"⎢ ↪\n",
|
||||||
|
"⎣ ↪\n",
|
||||||
|
"\n",
|
||||||
|
"↪ ⎛ 2 ⎞ ⎛ ⎛ 2 2⎞⎞ ⎛ ↪\n",
|
||||||
|
"↪ ⋅m_nac⋅⎝- Nx⋅u_yaw + Nz⋅u_ẏaw⎠ - ⎝Nac_YIner - m_nac⋅⎝Nx + Ny ⎠⎠⋅u_ẏaw + ⎝- ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"\n",
|
||||||
|
"↪ ⎛ 2 ⎞ ↪\n",
|
||||||
|
"↪ ⎝Hub_Iner - hub_cm ⋅m_hub⎠⋅(-(u_drtr + u_geaz)⋅u_yaw⋅sin(q_drtr + q_geaz)⋅c ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ⎛ ↪\n",
|
||||||
|
"↪ - ⎝Hub_Iner - ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ⎛ ↪\n",
|
||||||
|
"↪ - ⎝Hub_Iner - ↪\n",
|
||||||
|
"\n",
|
||||||
|
"↪ ⎛ 2 ↪\n",
|
||||||
|
"↪ os(θₜᵢₗₜ) + cos(θₜᵢₗₜ)⋅cos(q_drtr + q_geaz)⋅u_ẏaw) + ⎝Hub_Iner - hub_cm ⋅m_h ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ 2 ⎞ ⎛ 2 ↪\n",
|
||||||
|
"↪ hub_cm ⋅m_hub⎠⋅(sin(θₜᵢₗₜ)⋅u_ẏaw + u_dṙtr + u_gėaz) - ⎝Hub_Iner - hub_cm ⋅m ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ 2 ⎞ ⎛ 2 ↪\n",
|
||||||
|
"↪ hub_cm ⋅m_hub⎠⋅(sin(θₜᵢₗₜ)⋅u_ẏaw + u_dṙtr + u_gėaz) - ⎝Hub_Iner - hub_cm ⋅m ↪\n",
|
||||||
|
"\n",
|
||||||
|
"↪ ⎞ ↪\n",
|
||||||
|
"↪ ub⎠⋅(u_drtr + u_geaz + u_yaw⋅sin(θₜᵢₗₜ))⋅u_yaw⋅sin(q_drtr + q_geaz)⋅cos(θₜᵢₗ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ⎞ 2 2 ↪\n",
|
||||||
|
"↪ _hub⎠⋅u_yaw ⋅sin(q_drtr + q_geaz)⋅cos (θₜᵢₗₜ)⋅cos(q_drtr + q_geaz) ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ⎞ 2 2 ↪\n",
|
||||||
|
"↪ _hub⎠⋅u_yaw ⋅sin(q_drtr + q_geaz)⋅cos (θₜᵢₗₜ)⋅cos(q_drtr + q_geaz) ↪\n",
|
||||||
|
"\n",
|
||||||
|
"↪ ⎞ ⎛ ⎛ 2 ⎞ ↪\n",
|
||||||
|
"↪ ₜ)⎠⋅cos(θₜᵢₗₜ)⋅cos(q_drtr + q_geaz) + ⎝- ⎝Hub_Iner - hub_cm ⋅m_hub⎠⋅(sin(θₜᵢ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"\n",
|
||||||
|
"↪ ⎛ 2 ⎞ 2 ↪\n",
|
||||||
|
"↪ ₗₜ)⋅u_ẏaw + u_dṙtr + u_gėaz) - ⎝Hub_Iner - hub_cm ⋅m_hub⎠⋅u_yaw ⋅sin(q_drtr ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"↪ ↪\n",
|
||||||
|
"\n",
|
||||||
|
"↪ 2 ⎞ ⎤\n",
|
||||||
|
"↪ + q_geaz)⋅cos (θₜᵢₗₜ)⋅cos(q_drtr + q_geaz)⎠⋅sin(θₜᵢₗₜ)⎥\n",
|
||||||
|
"↪ ⎥\n",
|
||||||
|
"↪ ⎥\n",
|
||||||
|
"↪ ⎥\n",
|
||||||
|
"↪ ⎥\n",
|
||||||
|
"↪ ⎥\n",
|
||||||
|
"↪ ⎦"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 93,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"# 惯性力\n",
|
||||||
|
"\n",
|
||||||
|
"# 机舱惯性\n",
|
||||||
|
"Nac_YIner = sm.symbols(\"Nac_YIner\")\n",
|
||||||
|
"Inertia_nac = (Nac_YIner - m_nac * (N_x**2 + N_y**2)) * me.outer(D.y, D.y)\n",
|
||||||
|
"Inertia_nac\n",
|
||||||
|
"\n",
|
||||||
|
"# hub惯性\n",
|
||||||
|
"Hub_Iner, hub_cm = sm.symbols(\"Hub_Iner, hub_cm\")\n",
|
||||||
|
"Inertia_hub = (Hub_Iner - m_hub * hub_cm**2) * me.outer(G.x, G.x) + (Hub_Iner - m_hub * hub_cm**2) * me.outer(G.y, G.y)\n",
|
||||||
|
"Inertia_hub\n",
|
||||||
|
"\n",
|
||||||
|
"T_nac = -(D.ang_acc_in(A).dot(Inertia_nac) + me.cross(D.ang_vel_in(A), Inertia_nac).dot(D.ang_vel_in(A)))\n",
|
||||||
|
"T_hub = -(G.ang_acc_in(A).dot(Inertia_hub) + me.cross(G.ang_vel_in(A), Inertia_hub).dot(G.ang_vel_in(A)))\n",
|
||||||
|
"\n",
|
||||||
|
"F1s = v_U_1.dot(-m_nac * U.acc(A)) + v_P_1.dot(-m_hub * P.acc(A)) + w_D_1.dot(T_nac) + w_C_1.dot(T_hub)\n",
|
||||||
|
"F2s = v_U_2.dot(-m_nac * U.acc(A)) + v_P_2.dot(-m_hub * P.acc(A)) + w_D_2.dot(T_nac) + w_C_2.dot(T_hub)\n",
|
||||||
|
"F3s = v_U_3.dot(-m_nac * U.acc(A)) + v_P_3.dot(-m_hub * P.acc(A)) + w_D_3.dot(T_nac) + w_C_3.dot(T_hub)\n",
|
||||||
|
"\n",
|
||||||
|
"Frs = sm.Matrix([F1s, F2s, F3s])\n",
|
||||||
|
"Frs"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 94,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/latex": [
|
||||||
|
"$\\displaystyle \\left\\{q_{drtr}, q_{geaz}\\right\\}$"
|
||||||
|
],
|
||||||
|
"text/plain": [
|
||||||
|
"{q_drtr, q_geaz}"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 94,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"me.find_dynamicsymbols(Fr)"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 95,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"data": {
|
||||||
|
"text/latex": [
|
||||||
|
"$\\displaystyle \\left\\{q_{drtr}, q_{geaz}, u_{drtr}, u_{geaz}, u_{yaw}, \\dot{u}_{drtr}, \\dot{u}_{geaz}, \\dot{u}_{yaw}\\right\\}$"
|
||||||
|
],
|
||||||
|
"text/plain": [
|
||||||
|
"{q_drtr, q_geaz, u_drtr, u_geaz, u_yaw, u_dṙtr, u_gėaz, u_ẏaw}"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"execution_count": 95,
|
||||||
|
"metadata": {},
|
||||||
|
"output_type": "execute_result"
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"me.find_dynamicsymbols(Frs)"
|
||||||
|
]
|
||||||
}
|
}
|
||||||
],
|
],
|
||||||
"metadata": {
|
"metadata": {
|
||||||
|
|||||||
16
多体+耦合求解器/sympy_test.ipynb
Normal file
16
多体+耦合求解器/sympy_test.ipynb
Normal file
@ -0,0 +1,16 @@
|
|||||||
|
{
|
||||||
|
"cells": [],
|
||||||
|
"metadata": {
|
||||||
|
"kernelspec": {
|
||||||
|
"display_name": "MinerU",
|
||||||
|
"language": "python",
|
||||||
|
"name": "python3"
|
||||||
|
},
|
||||||
|
"language_info": {
|
||||||
|
"name": "python",
|
||||||
|
"version": "3.10.16"
|
||||||
|
}
|
||||||
|
},
|
||||||
|
"nbformat": 4,
|
||||||
|
"nbformat_minor": 2
|
||||||
|
}
|
||||||
1
多体+耦合求解器/资料收集/FAST 中耦合叶片模态.md
Normal file
1
多体+耦合求解器/资料收集/FAST 中耦合叶片模态.md
Normal file
@ -0,0 +1 @@
|
|||||||
|
https://forums.nrel.gov/t/coupled-blade-modes-in-fast/314/9
|
||||||
@ -10,6 +10,9 @@ tags: [excalidraw]
|
|||||||
# Excalidraw Data
|
# Excalidraw Data
|
||||||
|
|
||||||
## Text Elements
|
## Text Elements
|
||||||
|
Q1： yaw 主动力为何如此计算？
|
||||||
|
由控制计算，作为一个外力直接施加 ^enHSE5Ed
|
||||||
|
|
||||||
## Embedded Files
|
## Embedded Files
|
||||||
c0166535889251fc00499757c5d32377c8fd6767: [[Pasted Image 20250120103502_252.png]]
|
c0166535889251fc00499757c5d32377c8fd6767: [[Pasted Image 20250120103502_252.png]]
|
||||||
|
|
||||||
@ -1562,560 +1565,496 @@ lqlKnKa84GMCXbT+alNIP8vm8vGppA7SwMm9iK3cTB0l8I66tWWqkFldRPZbawWOkBHQxq1NaoCa48DR
|
|||||||
|
|
||||||
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|
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||||||
|
|
||||||
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||||||
|
|
||||||
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||||||
|
|
||||||
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||||||
|
|
||||||
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|
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|
||||||
|
|
||||||
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|
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|
||||||
|
|
||||||
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|
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||||||
|
|
||||||
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|
||||||
|
|
||||||
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|
||||||
|
|
||||||
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|
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|
||||||
|
|
||||||
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|
Z5wzU84YuM5GdH0z0yD3S4+kYlIv6ViU8ip5pS//GyZOWmGxufseFitx4quBkYqbKM604OLEm4aRx3ZnnEPVt6mwwaxnvBK1iXmI1CQgkYmGHYADjcNCqXoAsVQEACi1DyOpaMN9J4WSlsYHDM56RqpBeo53SzhnlDJ12sB02TePoc7unETPF6fs49EJ5EyyKk7SJxKTZIk/Ri9wO9Sze1zIlsbDTMvQyAyBFhlxEYeMsVpZNcOYwVlKYBuW4hbB
|
||||||
|
|
||||||
OLEm4aRx3ZnnEPVt6mwxTxnvBK1iSZpPtY9oRLTpSTOjSIJGJhh2AA43DQql6ALFUBAAotQ8jqWjDfSeFkpbGMIyBekaqQXqOd0pEZMwyddrAdNk3j6HO7pJky5en7OPRCRZMsipO0icSk2SJP0YvcDvUs3tcyJbGw0zEcM3IZJwyAyBFhlxERcM4Apu4zrBHmXQrKUwDctxC2DAQ4gWIG+nwfFH+w/M9AnXVPeGdNQ4ZSaH8GRBhTP6wHxkYVA9
|
gIcQLEDfT4Pij/YfmegTrqkLDLx9HxkYVA96EgxpcRilUt0yMmGz/UyO51ADeAXJMvYi6/SQxmDjPCLCpMmgZ+/TBem6VP+Mmxo7SZRdkSJksDLImVF0p4ZMNSggmLpPVcPJYUUhQW4nbK3lDtWgEMliZtkyiyCw119sdfw6W+TOjQFE+pwBIa9fDHS269H1I7e2/UgTUyOOBh9+JGplypWn1M5ayiSDN8YH10retH3fyZnbjkWkYZCWoJ4oSdAp
|
||||||
|
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YBdQDdNUPqgQAXtYIez4DlaiCy7WSAAwACDAogAuFD4KClUO+AqU7NSN8FDCKA5o+wAJAAnACzgCXAOmAM9ANJhSpTfvHSegZWcUjoQBhXBWkZPAL6sSbQ4UwNDLMgAPegjxUqU7dZiXCHiyPQIZsJgA1pHnSNy0FdIxrof0ja6tBJIHvWCKKGR7tA8KpizASEEKSJkANtACbrWAB7rBIQPHgKCAfuBpgDxOF0CGJEFHAmpRFR3F6yjIVeAc1Vgw
|
|
||||||
|
|
||||||
BjjmMw16nNHIqPOegDzTljEEsrCTVFWg3WhNX5DaC32FpARhQ0FIPcGZPvv9fv+xSD+ybkgMMUumXIoGR5wj6Jv44U9oZ4YqeRBdPqJEAj9OtO1ejCTtqrvDeCO67udzQay3ZhJM7JP2JDtCcRra+HDSXb/IMUnqzQ00EGC2p9J7NEmzX9ZZZfCPg1vFAQDbOCB+Q4h2ToJGlpMziJAUftYwGkOGaZn9maRg/fcPdX81G4R4f3woaoI9Qhmgjojb
|
|
||||||
|
|
||||||
JkNxVhFtPcyW91oBQ5K1ddq9QMvyAmCU5HufUzkZypBJBArDIzr8yROVCzBWpnQT69NMltoRtiFphuYrCjRoQiC16Ic2w1jNaVg52U7Q1T9vqSeyifIurB1q2g9FC+UlFwBBAN4VqyOhIqSjBn2OdyBZAB914lsAvM+RuI+uGgJVZx/3+YGPcE3DvZ78IMpYfiseGAZF9iklx4LS7DuxRCQWSFxwYcFY4Mmgo3OGvats5H4KM/4coBk7krXFqZTH
|
|
||||||
|
|
||||||
kMB3seRVoUnt59IHIZmhnzsg8au/71IH6zD3YXqepY+mlwF7HNShmvbOsPVYBpi1QjTyHVcPSsZqA9NVIblH3KO+nAOpp9q4tg4xxf4miloDgGPcNRDOray3C+UeMA8FR+2goVHn9Kdc0QFaAMSKjXkbiTHm6UCo5uW/UtiVHfMq4LoxeCzwOKjOaihm7JwCSo6A+6XVqpcCL37OzZpYGOpowI+QGNnT4qrKTLKvYd5YH6HjsoBsPG2sK3i9nT+Z
|
|
||||||
|
|
||||||
7EXAzEpm5U7lubkahB1kc4+A2RogwZRbciPv6C46Ll8AO6JsrPCRm00JqPyyVEjiKGjYN+oaqIw+h1wNPPL9FSRknyrtrMSaOqmE79AKUZz7S6DZSjWhF+dmRKpKQ1ParEIrNsFD5HErk8Lhew0Vo9ToqPfQdeg9G+mkeZQHN3YHEaF9RHhwGZT0GdlHWIppFhoh25t6d8Of2M63QdfXozIIeVGzKNgwABo2lRwTZqMNf2CA0dneaDQurak7UBB3
|
|
||||||
|
|
||||||
BiHcowjR9V4RM6hEN9RHULHS+z8xqNGX4IUXulYAxkSLAaNHQIMWaHTALb4EtovdQ91irqDeqVmzYlkh70cKX1npyVm8YFijjoMyi0L1GDioJ1FdwRy1kD17LmeXd+QFAEMbAHY0/kemozJh5FDjhGRsMtvr9BS8s1uqJIa8FbDDv0ShtRyOI05GlKNwUd2o03ex5dkoyuiGWmmWKXI7H2YFNjAJWoWLfUisAtN4sRRuaMsyEy3VEs14+4HdYE5m
|
|
||||||
|
|
||||||
qP76RxUoT07FijaM2DUI2hnMGAexh7baPMOXto606fmBUCwXaMZ80CCrUMSAelujy2BzFJEQ17RnmjvUGQb30vpDKWkq4OjxtHQ6OT7pItV+UyXmT98xz4AKKuSHPU3hpeWC06PpVIbnSWB8CAL2605jQ4r28SaYT1KTQAKAiHACm6Ca9YQA5EgSWSdUZx4VpOKhg95GmyMRAuanW2R7ijd16DTyUEZ7I2Fmtwtb6ptDUJ/HUUnrMHqi+5dazjza
|
|
||||||
|
|
||||||
E9UptRgndIEMdqOIQrug4VhxQq7erCWG/4uuQ8I4uwp8D7IZnmXuKQ2102D9UnsxRn2ENkBeyMsxd8OkzE36ltzVZIG6buzNiev1ptsNQ0ymzUFHz6Mrw9WhMANPgX+WCQheUYF4AoAG5Y3GIxrDOqNjSAr/OmqZIm/VGtsyqYVh+GHGPi91D6VtX9YZP3REm4/9p96pkOcfpTtlM2OFmu5TwnarxCcgBVsUejmmHx6OK0cno+CanK9rj6YkOiDr
|
|
||||||
|
|
||||||
6IQGpfips56iTXAYapQ1RHEk1GQ71G2ADs7/eBEoxtxoGr10WuLIYaPuzoD9xGGI29Aqn3TKfVfu/Ck16bWkRASCEAUWWuCBFuiESA/o9PQL+j3ewf6N4lpUGMHFIajcRwRqN1cBPVfrB+QDuAGDJ2b3IK8YrsztWktcy33NRvDJAemAYGk5G5aMwUYVozW+DBjzj7HYN+fMYg63i0lDbS73pX7Hshw94I0Rm3RHuX4piPBaK0B33D6xGvkUkvvH
|
|
||||||
|
|
||||||
Q8Ta4CDDGaQYMZXkIyEy0cQwalYsJCcoEi8AlJTAA271qYnOtqlRUJwOgEJb7RGMF8SsLUH0SRjgEduswIj2ypm1kdujijGQt35eo/5p4oYbdiiBEOkQqK41ay4KAoUFG9GOKUe2o+gx+cjf4G1T3uKpDlVz+3/eE/SsxHE2KAsUAOjhpD1K3IO/pCy2Za0lOu+KMxRnzMrAw8yi34Dgt7tyNmnvh2RCBs4kyStQ3DdThegrytRXAxmpZsBRUxvC
|
|
||||||
|
|
||||||
p1R1wcLnwsDj90cWnRUIQajyTGADVSIrXwqn+yhD/NGfUMzUbvQzfhkbD+37GEJOUmXcKVdRI+Nalf8m6MdsSPLRipjhjGqmOaobm3f2yjetnwHMHSibKwPqVawB5F46XmrvfonwzERw1DbDVAWOOvPJtYfVEdUdIiuURWkWLYv7DOIgl4UqBQf0eagCIxyVEzMYEmN0BH/ow0gOlxAlahUN7Lm7LWURopd9g79oMn/sAo+j+zZyBgJfEyxlpfsH
|
|
||||||
|
|
||||||
bStJ0HFYO+iy0YeY/oxp5jc5GEKMrpqf/TARm8tNz7AlmdQazPaRM8+ZF47rw00mqsFcNQ+YjOKiIMNtAecwzpQ+xjW2GoCMsXzZgxAq7WFcca+vUbhop6AWCr6ovf7BGa8wLIehtur01vk6zGkXAeAqeEaiAN+ijHANFXp0tTamgXN+8Hx26dTgY6Jeg6oABphe8JiGF7Jt+YYIDUTGNUC3kbro42RmFdL7Be8CXbFcsMt49POglb3dYCUffg3g
|
|
||||||
|
|
||||||
B17DA7CmijTWsX5K+JDNd5T6J0C9EsZY2zel7FE9GXmOaHuOrQ3NNrVgrGMlUMTrZsK14mcd62HNX0EUdLMl6Kyk9uMhcABh3P4IoRkAZcEpHBbQMwwesra9PlWZMKUWOxMbRY9o+0YVTdHRSxvkd6wxUA+SDNG6soOKLqSA13R2P44CRhr043D+of6+/bRNrEcUoj0bKY1tRtBjzzG2WNbroE3XevAyJv5RDqVH0fsdYbOwpJlzUd2NiwYlwxfR
|
|
||||||
|
|
||||||
iO9e2hvl27/hEMp52BlC5vgodDn4CQ0pFbPiIzVBOqP/rE9Y71Rh8j9xBu8RYsYDY37QtRWCK7WNHsBERo2qkX04obHB2MevuUg/2Rs/9qE7CUrlXDKfaP2ZoCq3wnR3t+BQY5wRhdjrLGzjZkGVRLH+xp6gGb4RSKs0who6DRqugP9s+KO4cYaMEFtCiE6HGMOO6jCcqGbnSGjB7wKOMEcduI9vB4HtYMAcbDgHNyo8ehVQ11taQTh3MKj4G2HP
|
|
||||||
|
|
||||||
l0YR7G+rTYGWYy2x00kbbGYV12Ek7Y6+RiheI+AjaUZMekw/YRoWjAFHpUMDDpRsnlnPfhx36aX5VyRWGkmxsL612zU2NLsa1Q9eK84DX/6e25iuu9zVIhkNFu/5V56YSGV+JaYEiWBgBOIy8zUyAJFE1zdhCrFwjMUb2GozR/ltHpgxOPtkZhQw3uzKjt2xQGNH3uKXSSxyBjgFHfh30SuFkkNoJMD+2iaITKXtKY0yx8pjSHGVKNzgfb1TXQM2
|
|
||||||
|
|
||||||
Rbf6/OP3TWMWcVINLjfkHEcNlgYioyrmPcjSDlYqhSujsHNjEMgIjohqnl4BmTnnaQRC5jL1VmNm5TYo/dm/0wSTHdfw7MblAyh41FYr/lxd1N7tsI4qB7o1kqH5OMPodSA6/OTNwSh4O30zyRCiCz5ZBjc7Gx6MwYx046pRh9dl1GGq5IxqqTctx0FQXXHMONq4riCFBgfGjsQ7pdKrDsGTc9RmXDeTyKL3r8vqQ+l27Nytdc0ZivAGDcL+vUYA
|
|
||||||
|
|
||||||
rQBvAAFsUPeUtBna6DXHWKMCjSsLXsRP1joAZAGM+LQJlVZlKajRzHBaOzUdJY9KhjYDjqlnixSCsKYwmvAMYv+7OrYIcd8I4lxpWjHRGm5HN52Oo9Qe1Y5iRs8f7/Me77Q8Sz9dPI9NQ32YeuCdgulWAi39KtkkTszOb3+1nNada7j0WVsbWbeIT5Rzq6F55dy2+rBMAGQAa/MTLXUiIGnEiAOs9UqLhIAxMaE43tVGesFMAWyMvke8425sYVts
|
|
||||||
|
|
||||||
O6AaN9sakw1Th2edht66COooYrHZHMuMKyhhAzkH3P+3ACC+Sjs3HUGPzccqY7pxt5jSJqy10svsoWapfGx1YJDTMnfwIOPWCQnu9X0Qjj2U3OnMWFR+X1MrGtnVrbvMw/lu6xpy16Qe0AyopVi3SyOBSr6vePL4so9ZOOkc2E/dcHrTm1YZnm0nKjAMqS77T4wSqeiIKjm9P9PxUHnO76cTYxCJjzSSqPkQyWAdHyqNpJdKSbBFeCyoxDtDngaH
|
|
||||||
|
|
||||||
H0OOeUdWXaIczu6pHHy+PnLrAKTLxoKjdizcE1iaCL4/DC3pS2XHTOIeArisE3x2KjrHHQEDgAAMgNvgO9h6oAb4B6kegADCADIAORAAOCrAAYAJVYNBAOxN3SMekcjI9PxrLtxKB7EDzQfSAOqAUVD9ylS1giAFTQOvx/QArwx6u078dX41kAffjzyDThrH8b34/OAKSgTjZL+Nr8ev45vxvsBd/HT+PX8aYeTqKZ/j4Ohr+PekczhB/xs/jnAA
|
|
||||||
|
|
||||||
90ZJgGVAEopZfju/H7+PpABwhFkAQvEyMgE4UlABX41fx9IAP1YjAk9kzhALgQJ8Ae+rUaC/8Yf44KfJTY8mwl+CYCfSALzNHUgxRRPXBiqHwE/y8DUg8Wt4dCno1lANPDPUAs6x6QAZ4B0MYBhesj0jUuCx0CYpAMkqRR+Hexkrgc3syEQNgEoubWg0ABJ4AlI74AS/QBpAyBNv8dNFHqAfFI9wYuQAhOBIAFAJ6Qo0/GBQAKCfnAPOsbiA8gnU
|
|
||||||
|
|
||||||
ZjTYBYOgNpVMjrChNBOzECTwOggbOmilAZYMAAApoPjpEinAFYJ6gAztQAACUuoAMeRBdhqwODgMkoPIALBMuIj3FCSALwTtgmAkAOCfEE3AJ+xAj/HqQDt1mwQZwAPYUGWoMeTZgBegsM4JPAiZG9BPvHC6AEA26h4A2kJ+PUPGEAN3vE9YRohxBN2AEkqZtgSQiA2k6YbaCd5mj8Rofw23BsEGMAHxmPUOoQTJnKVSNKfVgmA1YUNZZrhUZAVC
|
|
||||||
|
|
||||||
aFRiUXQhAk6hwACu8ATI9GAYAAfuAQEBAAA=
|
|
||||||
```
|
```
|
||||||
%%
|
%%
|
||||||
@ -1,10 +1,10 @@
|
|||||||
{
|
{
|
||||||
"nodes":[
|
"nodes":[
|
||||||
{"id":"b698e88ca5fb9c51","type":"text","text":"状态指标：\n推进OKR的时候也要关注这些事情，它们是完成OKR的保障。\n\n\n效率状态 green","x":-96,"y":80,"width":456,"height":347},
|
{"id":"b698e88ca5fb9c51","type":"text","text":"状态指标：\n推进OKR的时候也要关注这些事情，它们是完成OKR的保障。\n\n\n效率状态 green","x":-96,"y":80,"width":456,"height":347},
|
||||||
{"id":"58be7961ae7275a7","type":"text","text":"# 计划\n这周要做的3~5件重要的事情，这些事情能有效推进实现OKR。\n\nP1 必须做。P2 应该做\n\nP1 多体原理学习 YouTube课程 018\nP1 气动模块联合调试，跑通 no\nP1 稳态工况多体动力学求解方法\nP1 使用python搭建风电机组多体模型\nP1 叶片模态叠加法算法\n\n","x":-620,"y":-307,"width":450,"height":347},
|
{"id":"58be7961ae7275a7","type":"text","text":"# 计划\n这周要做的3~5件重要的事情，这些事情能有效推进实现OKR。\n\nP1 必须做。P2 应该做\n\nP1 多体原理学习 YouTube课程 018\nP1 气动模块联合调试，跑通 no\nP1 稳态工况多体动力学求解方法\nP1 使用python搭建风电机组多体模型 刚性部件主动力、惯性力计算\nP1 柔性部件 叶片、塔架主动力惯性力算法\n\n","x":-620,"y":-307,"width":450,"height":347},
|
||||||
{"id":"2b068bfe5df15a72","type":"text","text":"# 目标：多体动力学模块完善\n### 每周盘点一下它们\n\n\n关键结果：建模原理、建模方法掌握 （6.8/10）\n\n关键结果：对标Bladed模块完成 （7.2/10）\n\n关键结果：风机多体动力学文献调研情况完成 （5/10）","x":-96,"y":-307,"width":456,"height":347},
|
{"id":"2b068bfe5df15a72","type":"text","text":"# 目标：多体动力学模块完善\n### 每周盘点一下它们\n\n\n关键结果：建模原理、建模方法掌握 （6.8/10）\n\n关键结果：对标Bladed模块完成 （7.2/10）\n\n关键结果：风机多体动力学文献调研情况完成 （5/10）","x":-96,"y":-307,"width":456,"height":347},
|
||||||
{"id":"01ee5c157d0deeae","type":"text","text":"# 推进计划\n未来四周计划推进的重要事情\n\n文献调研启动\n\n建模重新推导\n\n\n","x":-620,"y":80,"width":456,"height":347},
|
{"id":"01ee5c157d0deeae","type":"text","text":"# 推进计划\n未来四周计划推进的重要事情\n\n文献调研启动\n\n建模重新推导\n\n\n","x":-620,"y":80,"width":456,"height":347},
|
||||||
{"id":"1ebeabaf5c73ddbb","x":-440,"y":520,"width":440,"height":340,"type":"text","text":"# 本月已完成\n\n多体原理学习 YouTube课程 018"}
|
{"id":"1ebeabaf5c73ddbb","type":"text","text":"# 本月已完成\n\n多体原理学习 YouTube课程 018","x":-440,"y":520,"width":440,"height":340}
|
||||||
],
|
],
|
||||||
"edges":[]
|
"edges":[]
|
||||||
}
|
}
|
||||||
BIN
工作总结/周报/~$71-郭翼泽.docx
Normal file
BIN
工作总结/周报/~$71-郭翼泽.docx
Normal file
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BIN
工作总结/周报/周报72-郭翼泽.docx
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BIN
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@ -1,9 +1,10 @@
|
|||||||
{
|
{
|
||||||
"nodes":[
|
"nodes":[
|
||||||
{"id":"b698e88ca5fb9c51","type":"text","text":"状态指标：\n推进OKR的时候也要关注这些事情，它们是完成OKR的保障。\n\n\n","x":-96,"y":80,"width":456,"height":347},
|
{"id":"b698e88ca5fb9c51","type":"text","text":"状态指标：\n推进OKR的时候也要关注这些事情，它们是完成OKR的保障。\n\n\n","x":-96,"y":80,"width":456,"height":347},
|
||||||
{"id":"58be7961ae7275a7","type":"text","text":"# 计划\n这周要做的3~5件重要的事情，这些事情能有效推进实现OKR。\n\nP1 必须做。P2 应该做\n\nP1 短剧自动化系统维护 差不多吧\nP1 海龟方法回顾与代码编写 \n- 基础class写完了\n一点点🤏进步，主要是数据库不懂\n\n","x":-620,"y":-307,"width":450,"height":347},
|
{"id":"58be7961ae7275a7","type":"text","text":"# 计划\n这周要做的3~5件重要的事情，这些事情能有效推进实现OKR。\n\nP1 必须做。P2 应该做\n\n\nP1 海龟方法回顾与代码编写 \n- 邮件交互方法\n- 开始测试\n- 网页\n一点点🤏进步，主要是数据库不懂\n\n","x":-620,"y":-307,"width":450,"height":347},
|
||||||
{"id":"2b068bfe5df15a72","type":"text","text":"# 目标：海龟 短剧 AI项目推进\n### 每周盘点一下它们\n\n\n关键结果：形成海龟系统可行方案 （5.5/10）\n\n关键结果：短剧粉丝达到5000 （5/10）\n\n关键结果：文献调研智能体搭建 （5/10）","x":-96,"y":-307,"width":456,"height":347},
|
{"id":"2b068bfe5df15a72","type":"text","text":"# 目标：海龟 短剧 AI项目推进\n### 每周盘点一下它们\n\n\n关键结果：形成海龟系统可行方案 （5.5/10）\n\n关键结果：短剧粉丝达到5000 （5/10）\n\n关键结果：文献调研智能体搭建 （5/10）","x":-96,"y":-307,"width":456,"height":347},
|
||||||
{"id":"01ee5c157d0deeae","type":"text","text":"# 推进计划\nRag系统、agent系统调研\n\n\n","x":-620,"y":80,"width":456,"height":347}
|
{"id":"01ee5c157d0deeae","type":"text","text":"# 推进计划\nRag系统、agent系统调研\n新闻 公众号\n货物管理系统\n","x":-620,"y":80,"width":456,"height":347},
|
||||||
|
{"id":"bb79a506966d8746","type":"text","text":"# 本月已完成\n\n短剧自动化系统维护","x":-340,"y":500,"width":440,"height":340}
|
||||||
],
|
],
|
||||||
"edges":[]
|
"edges":[]
|
||||||
}
|
}
|
||||||
@ -11,8 +11,14 @@
|
|||||||
{"id":"67a07cb33040e073","type":"text","text":"线加速度 求法","x":510,"y":700,"width":250,"height":60},
|
{"id":"67a07cb33040e073","type":"text","text":"线加速度 求法","x":510,"y":700,"width":250,"height":60},
|
||||||
{"id":"eeb7df4b945bff86","type":"text","text":"各个部件inertia dyadic求法","x":155,"y":820,"width":250,"height":60},
|
{"id":"eeb7df4b945bff86","type":"text","text":"各个部件inertia dyadic求法","x":155,"y":820,"width":250,"height":60},
|
||||||
{"id":"931f7a20403882f5","type":"text","text":"塔架、叶片的GAF GIF求法","x":155,"y":940,"width":250,"height":60},
|
{"id":"931f7a20403882f5","type":"text","text":"塔架、叶片的GAF GIF求法","x":155,"y":940,"width":250,"height":60},
|
||||||
{"id":"9ba9cf03738bfda2","type":"text","text":"Sympy优势：\n- linear acc、angular acc内置方法\n- GIF求解，按照公式，清晰明了\n\n劣势：\n- 不支持柔性体","x":155,"y":1060,"width":355,"height":220},
|
{"id":"9ba9cf03738bfda2","type":"text","text":"Sympy优势：\n- linear acc、angular acc内置方法\n- GIF求解，按照公式，清晰明了\n\n劣势：\n- 不支持柔性体\n- 主动力没有好办法","x":155,"y":1060,"width":355,"height":240},
|
||||||
{"id":"869b7f96937e4202","type":"text","text":"低速轴、高速轴、发电机、摩擦力等求法","x":510,"y":820,"width":250,"height":60}
|
{"id":"869b7f96937e4202","type":"text","text":"低速轴、高速轴、发电机、摩擦力等求法","x":510,"y":820,"width":250,"height":60},
|
||||||
|
{"id":"690b6cebbb1e52ad","x":840,"y":700,"width":250,"height":60,"type":"text","text":"是否正确？"},
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{"id":"50d5c2753f1f2ec3","x":840,"y":790,"width":250,"height":90,"type":"text","text":"广义主动力还可以怎么求？yaw、低速轴、高速轴"},
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{"id":"9fc02c3e78a69a7a","x":510,"y":940,"width":250,"height":60,"type":"text","text":"坐标系定义好之后，原点无所谓，有方向即可"},
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{"id":"f13fc730aad4e78c","x":840,"y":940,"width":250,"height":180,"type":"text","text":" 偏速度$\\pmb{v}_{\\nu}^{(\\,r\\,)}$ 或 $\\pmb{\\omega}_{i}^{(\\prime)}$ 是将**标量形式的广义速率**赋予**方向性的矢量系数**。从具体算例可以看出， $\\pmb{v}_{\\nu}^{(r)}$ 或 $\\pmb{\\omega}_{i}^{(r)}$ 实际上就是某些基矢量或基矢量的线性组合。"},
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{"id":"01e5d049c040e822","x":840,"y":1180,"width":250,"height":220,"type":"text","text":"所谓偏速度 $\\pmb{v}_{\\nu}^{(\\textrm{r})}\\left(\\,r=1\\,,2\\,,\\cdots,f\\right)$ 实际上是某些特定的基矢量或基矢量的线性组合，因此，广义主动力或广义惯性力就是系统内全部主动力或惯性力沿这些特定基矢量方向的投影。"},
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{"id":"8867bfcfd58ae90b","x":1180,"y":940,"width":250,"height":120,"type":"text","text":"对于完整系统，凯恩方法中的广义主动力 ${\\boldsymbol{F}}^{(r)}$ 等同于拉格朗日方程中的广义力 $Q_{r}$ 。 "}
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],
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],
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"edges":[
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Reference in New Issue
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