What is the formula for the 3D trajectory of a curving ball?

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The trajectory of a curving ball in 3D is a complex problem rooted in fluid dynamics, lacking a closed-form solution. To analyze this trajectory, one must decompose the motion into its x, y, and z components. The discussion emphasizes the necessity of specific initial conditions, such as whether the ball starts from rest or is already in motion. Numeric solutions may be generated for simplified scenarios, but a general functional description remains elusive.

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mariokan
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Hello.
Does anybody knows the formula for trajectory of curving ball (in 3D).
 
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Sorry Physics doesn't work that way. There is no store of "equations" on the shelf waiting for each and every situation.

We can say that it is a difficult problem of fluid dynamics. You could possibly generate numeric solutions to simplified versions of the problem. But there will be no closed form solution. It is not clear to me that there can even be a "simple" functional description of the general case.
 
You'd definitely have to begin by splitting the problem into its x, y and z components and working from there. Think about projectile motion, etc. Anyway, you haven't given us enough info. Does it start from rest, is it moving, accelerating?
 

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