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tailuge committed Nov 25, 2024
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Expand Up @@ -80,24 +80,24 @@ This is based on a paper by [Mathaven](https://billiards.colostate.edu/physics_a
Slip velocity at cushion contact point I

$$
ẋ_I = \dot{v_x} + \dot{\omega_y} R \sin \theta - \dot{\omega_z} R \cos \theta,
ẋ_I = \dot{v_x} + \dot{\omega_y} R \sin \theta - \dot{\omega_z} R \cos \theta \qquad
ẏ'_I = -\dot{v_y} \sin \theta + \dot{\omega_x} R
$$

$$
\phi = \arctan\left(\frac{ẏ'_I}{ẋ_I}\right),
\phi = \arctan\left(\frac{ẏ'_I}{ẋ_I}\right) \qquad
s = \sqrt{(ẋ_I)^2 + (ẏ'_I)^2}
$$

Slip velocity at table contact point C

$$
ẋ_C = \dot{v_x} - \dot{\omega_y} R,
ẋ_C = \dot{v_x} - \dot{\omega_y} R \qquad
ẏ_C = \dot{v_y} + \dot{\omega_x} R
$$

$$
\phi' = \arctan\left(\frac{ẏ'_I}{ẋ_I}\right),
\phi' = \arctan\left(\frac{ẏ'_I}{ẋ_I}\right) \qquad
s' = \sqrt{(ẋ_C)^2 + (ẏ_C)^2}
$$

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