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Commit 98560297 authored by Amira Abdel-Rahman's avatar Amira Abdel-Rahman
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small change documentation

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......@@ -124,6 +124,22 @@ Then the forces on each node is calculated as follows:
F_t= \sum_{b=1}^{b=n} \vec{F_b} \\
M_t= \sum_{b=1}^{b=n} \vec{M_b}
```
---
### Integration
Double euler integration is used from timestep $t_n$ to $t_{n+1}=t+dt$:
$$
\vec{P}_{t_{n+1}}=\vec{P}_{t_{n}}+F_tdt \\
\vec{D}_{t_{n+1}}=\vec{D}_{t_{n}}+\frac{\vec{P}_{t_{n+1}}}{m}dt \\
\vec{\phi}_{t_{n+1}}=\vec{\phi}_{t_{n}}+M_tdt \\
\vec{\theta}_{t_{n+1}}=\vec{\theta}_{t_{n}}+\frac{\vec{\phi}_{t_{n+1}}}{I}dt \\
$$
where $\vec{D}$ is the three dimensional position vector, $\vec{\theta}$ is the three dimensional rotational, $\vec{P}$ is the three dimensional linear momentum, $\vec{\phi}$ is the rotational momentum. Finally, $m$ is the mass and $I$ is the rotational inertia.
---
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......@@ -39,6 +39,7 @@ I am now using this gitlab project for documentation only, the code lives [here]
---
## Search
- [Inverse Design of Discrete Mechanical Metamaterial](https://gitlab.cba.mit.edu/amiraa/inverse-design-of-discrete-mechanical-metamaterial/-/blob/main/documentation.md)
- [Topology Optimization](02_Presentation/top_opt/search.md)
- [Hybrid Cellular Automata](https://amiraa.pages.cba.mit.edu/cpp_frep/hca.html)
- [Voxel Design Tool](02_Presentation/top_opt/voxel_designer/voxelDesignTool.md)
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