Calculating Position and Velocity of a Soccer Ball with Magnus Force

[melquiades]

for a soccer game I'm programming, i want to calculate the position and velocity of the ball. I can get those values when I have constant acceleration, but I don't understand how to add the Magnus force. I have read some articles in the internet, and I found a formula I just can't understand:


$$F_{m}=\frac{2\pi^2 \rho\ \omega vr^4} {2r}$$

is it right? so I could say:

$$F_{m}=\pi^2 \rho\ \omega vr^3$$

But which is the velocity it refers? and, how can I relate it to v(t) and x(t)?

Could somebody explain it to me, and how to calculate position adding the magnus force?

Thank's for reading!

 

[Valerie Park]

The Magnus force is a force that acts on a spinning object moving through a fluid. It is related to the spin of the object, the velocity of the object, and the viscosity of the fluid. The formula you have written above is the general expression for the Magnus force. To calculate the position and velocity of the ball using the Magnus force, first you must determine the magnitude of the force by plugging in the appropriate values for density (ρ), angular velocity (ω), and velocity of the ball (v). Then you can use Newton's second law, F = ma, to calculate the acceleration due to the Magnus force (a = F/m). Finally, you can use the equations of motion to calculate the position and velocity of the ball over time.