Hi there, so for my Differential equations class we are trying to model the vertical displacement of a curveball that is only in 2 dimensions, the X-Y plane, with Y being the vertical displacement, and X being the horizontal displacement.(adsbygoogle = window.adsbygoogle || []).push({});

To do this we were told that the 2 forces acting on the ball would be the force of gravity, and the magnus force due to the rotation of the ball. the problem is, the ball is thrown at an upward angle with a forward spin, and because the magnus force always acts perpendicular to the velocity of the ball it will always have 2 components, also x and y.

So far I have gotten my equations for the acceleration in both directions, and I think the equations for velocity in both directions, but im having trouble solving the differential equations themselves. He hinted that using Runge-Kutta4 would be our best bet, but the equations are confusing me.

These are the 2nd derivative of displacement in each direction:

If A_{y}= -g - kV_{x}ω Where kV_{x}ω is the Y component of the magnus force.

Then A_{x}= +KV_{y}ω which is the X compenent of the magnus force,

Then our velocity equaions, which are the firs derivative of displacement, of should be:

V_{y}=A_{y}*t + V_{y0}and

V_{x}=A_{x}*t + V_{x0}

But I'm totally stuck on how to apply Runge-Kutta4 to this.

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# Curveball Modeling

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