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copilot-conversations/20250822_090314__[[CASEstab_theory_manual]]整篇文稿的逻辑是什么.md
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@ -173,6 +173,7 @@ $$
\mathbf{r}_{1,b,n} = \sum_{p=0}^{P+3}\left(\mathbf{r}_{o,b,n,p} + x\,\mathbf{r}_{x,b,n,p} + y\,\mathbf{r}_{y,b,n,p}\right)\zeta^{p} \mathbf{r}_{1,b,n} = \sum_{p=0}^{P+3}\left(\mathbf{r}_{o,b,n,p} + x\,\mathbf{r}_{x,b,n,p} + y\,\mathbf{r}_{y,b,n,p}\right)\zeta^{p}
$$ $$
This brilliant step separates the position vector into parts that depend only on the nodal DOFs and the lengthwise coordinate $\zeta$ (the $\mathbf{r}_{o,x,y}$ vectors), and parts that depend on the cross-section coordinates ($x, y$). This is the key that unlocks the integration in the next stage. This brilliant step separates the position vector into parts that depend only on the nodal DOFs and the lengthwise coordinate $\zeta$ (the $\mathbf{r}_{o,x,y}$ vectors), and parts that depend on the cross-section coordinates ($x, y$). This is the key that unlocks the integration in the next stage.
最终目标是找到叶片中任何质点的位置矢量 $\mathbf{r}$，因为所有惯性力都由此导出（参见式 1.8）。 最终目标是找到叶片中任何质点的位置矢量 $\mathbf{r}$，因为所有惯性力都由此导出（参见式 1.8）。
**1.1. 宏观视角：子结构位置（式 1.12）** **1.1. 宏观视角：子结构位置（式 1.12）**