diff --git a/README.md b/README.md index 81f9b1e8..b5675c0d 100644 --- a/README.md +++ b/README.md @@ -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 $$ -ẋ_C = \dot{v_x} - \dot{\omega_y} R, +ẋ_C = \dot{v_x} - \dot{\omega_y} R \qquad ẏ_C = \dot{v_y} + \dot{\omega_x} R $$ $$ -\phi' = \arctan\left(\frac{ẏ'_I}{ẋ_I}\right), +\phi' = \arctan\left(\frac{ẏ'_I}{ẋ_I}\right) \qquad s' = \sqrt{(ẋ_C)^2 + (ẏ_C)^2} $$