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书籍/力学书籍/CASEstab_theory_manual/auto/CASEstab_theory_manual.md
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@ -187,11 +187,11 @@ where $\mathsf{r}_{k}$ is the local position vector in the frame of substructure
In the subsequent derivations, we will need the time derivatives:
$$
\mathbf{r}_{0,b} = \sum_{k=0}^{b-1} \mathbf{R}_{0,k} \mathbf{r}_k\tag{1.14a}
\dot{\mathbf{r}}_{0,b} = \sum_{k=0}^{b-1} \dot{\mathbf{R}}_{0,k} \mathbf{r}_k\tag{1.14a}
$$
$$
\dot{\mathbf{R}}_{0,b} = \sum_{k=0}^{b-1} \left( \prod_{l=0}^{k-1} \mathbf{O}_l \right) s_k \dot{\mathbf{B}}_k \mathbf{R}_k \mathbf{S}_k^T \left( \prod_{l=k+1}^{b-1} \mathbf{O}_l \right) s_b \mathbf{B}_b + \left( \prod_{l=0}^{b-1} \mathbf{O}_l \right) s_b \dot{\mathbf{B}}_b\tag{1.14b}
\dot{\mathbf{R}}_{0,b} = \sum_{k=0}^{b-1} \left( \prod_{l=0}^{k-1} \mathbf{O}_l \right) S_k \dot{\mathbf{B}}_k \mathbf{R}_k \mathbf{S}_k^T \left( \prod_{l=k+1}^{b-1} \mathbf{O}_l \right) S_b \mathbf{B}_b + \left( \prod_{l=0}^{b-1} \mathbf{O}_l \right) S_b \dot{\mathbf{B}}_b\tag{1.14b}
$$
$$