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$$
  \frac{\mathrm{d}^2 \mathbf{r}_i}{\mathrm{d} t^2} = \frac{\mathrm{d} \mathbf{v}_i}{\mathrm{d} t}=\mathbf{F}_{i}=\sum_{i\neq j}(\mathbf{F}_{ij}^{C}+\mathbf{F}_{ij}^{D}+\mathbf{F}_{ij}^{R}),
$$

$$
  \frac{\mathrm{d} C_{i}}{\mathrm{d} t}= Q_{i} = \sum_{i\neq j}(Q_{ij}^{D}+Q_{ij}^{R}) + Q_{i}^{S}, 
$$

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