Baseball trajectory with drag and wind

I am working on modelling the trajectory of a baseball considering the drag from the velocity of the baseball, as well as a headwind. I have the following to setup my ode function:

function dudt = wind(~,u)

vx = u(3);

vy = u(4);

vmag = sqrt((vwind - vx)^2+vy^2);

dudt = [vx;vy;-dr*vmag*(vwind-vx);-g - dr*vmag*vy];

end

(dr, vwind, g are constants)

and to solve

[times,solnw] = ode45(@wind,[tstart,tstop],u0);

I get the following error:

Warning: Failure at t=1.959253e+00. Unable to meet integration tolerances without reducing the step size below the smallest value

allowed (3.552714e-15) at time t.

My equations seem to be correct wrt my model but I'm sure I am doing something wrong with vy for it to be breaking.

Thanks for the help.

[Image Analyst]

I don't see a specific question, but perhaps this will help: debugging in MATLAB

Answer 1

[John D'Errico]

This is almost a classical problem, and the reason stiff ODE solvers were provided. Essentially, when you get that error using ODE45, the problem is probably stiff. You can do some reading here:

https://en.wikipedia.org/wiki/Stiff_equation

The stiff ODE solvers in MATLAB are ode15s and ode23s. Hint: The last character in the name is s. :)

Call it the same way as you did ode45, just change the name.