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a perfect bounce with an incidence angle of <math>\theta</math> leads to<math>\Delta V = 2 v \sin\theta\,</math>
the frequency is also given by <math>\frac{\Delta
the force is <math>F_{out}=F_x+F_y+F_z=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}dF_x+\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}dF_y+\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}dF_z</math>
<math>=\sum_{axis=x}^z\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}dA \times\sigma \times\Delta v\times frequency</math>
<math>=\sum_{axis=x}^z\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}(2\pi r^2\cos\theta d\theta)(\frac{m}{4pi r^2})(2 v \sin\theta)\times frequency</math>
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