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Update README.md
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tailuge authored Dec 7, 2024
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#### collisions

Based on [paper](https://billiards.colostate.edu/technical_proofs/new/TP_A-14.pdf) by Alciatore and incorporates throw effect due to small amount of friction between the balls. Figures to prove consistency with paper [here](https://tailuge.github.io/billiards/dist/diagrams/mathaven.html).
Based on paper by [Alciatore](https://billiards.colostate.edu/technical_proofs/new/TP_A-14.pdf) incorporating throw effect due to the small amount of friction between balls. Figures to prove consistency with paper [here](https://tailuge.github.io/billiards/dist/diagrams/mathaven.html).


For ball $a$:

$$
\vec{v}_a \leftarrow \vec{v}_a + \frac{J_{\text{normal}}}{m}\hat{n} + \frac{J_{\text{tangential}}}{m}\hat{t}
$$
![Equation 1](https://latex.codecogs.com/gif.latex?%5Cvec%7Bv%7D_a%20%5Cleftarrow%20%5Cvec%7Bv%7D_a%20%2B%20%5Cfrac%7BJ_%7B%5Ctext%7Bnormal%7D%7D%7D%7Bm%7D%5Chat%7Bn%7D%20%2B%20%5Cfrac%7BJ_%7B%5Ctext%7Btangential%7D%7D%7D%7Bm%7D%5Chat%7Bt%7D)

For ball $b$:

$\vec{v}_b \leftarrow \vec{v}_b - \frac{J_{\text{normal}}}{m}\hat{n} - \frac{J_{\text{tangential}}}{m}\hat{t}$
![Equation 2](https://latex.codecogs.com/gif.latex?%5Cvec%7Bv%7D_b%20%5Cleftarrow%20%5Cvec%7Bv%7D_b%20-%20%5Cfrac%7BJ_%7B%5Ctext%7Bnormal%7D%7D%7D%7Bm%7D%5Chat%7Bn%7D%20-%20%5Cfrac%7BJ_%7B%5Ctext%7Btangential%7D%7D%7D%7Bm%7D%5Chat%7Bt%7D)

Where:

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