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tailuge committed Nov 10, 2024
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Expand Up @@ -17,7 +17,7 @@ The common normal line Z at the contact point with the cushion makes an angle θ

## Given inputs to the numerical approximation

```math
```text
V₀: Initial velocity magnitude
α: Incident angle with 0 being perpendicular
ω₀T: Initial topspin angular velocity along line of travel of ball
Expand All @@ -28,29 +28,29 @@ V₀: Initial velocity magnitude

Centroid Velocities (Linear Velocities):

```math
```text
(ẋG)₁ = V₀ cos(α) // Initial x velocity perpendicular to cushion
(ẏG)₁ = V₀ sin(α)
(żG)₁ = 0
```

Angular Velocities:

```math
```text
(θ̇x)₁ = -ω₀T sin(α) // Initial angular velocity around x-axis
(θ̇y)₁ = ω₀T cos(α) // Initial angular velocity around y-axis
(θ̇z)₁ = ω₀S // Initial angular velocity around z-axis (sidespin)
```

Slip Speed at Point I (cushion contact):

```math
```text
s(0) = √[(V₀ cos(α) + R(ω₀T cos(α)sin(θ) - ω₀S cos(θ)))² + (-V₀ sin(α)sin(θ) - Rω₀T sin(α))²]
```

Slip Speed at Point C (table contact):

```math
```text
s'(0) = |V₀ - Rω₀T|
```

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