Solve the differential eqation and then implement nonlinear least square?

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Kate on 6 Mar 2018
Commented: Kate on 7 Mar 2018
I have 3 dimentional positional data of a pitched baseball.
I would like to estimate the acceleration from the data but I want to avoid differentiating the positional data.
Therefore, I am wondering if I can get the instant acceleration without differentiation of the positions.
The, I firstly tried to fit the data with differential equations model and to determine the coefficients of each term.
The differential equations model were as follows:
diff(rx(t),t,2) == K*sqrt(diff(rx(t),t)^2+diff(ry(t),t)^2+diff(rz(t),t)^2)*(CL/(w)*(diff(rz(t),t)*wy-wz*diff(ry(t),t))-CD*diff(rx(t),t));% X-component
diff(ry(t),t,2) == K*sqrt(diff(rx(t),t)^2+diff(ry(t),t)^2+diff(rz(t),t)^2)*(CL/(w)*(diff(rx(t),t)*wz-wx*diff(rz(t),t))-CD*diff(ry(t),t));%Y-component
diff(rz(t),t,2) == K*sqrt(diff(rx(t),t)^2+diff(ry(t),t)^2+diff(rz(t),t)^2)*(CL/(w)*(diff(ry(t),t)*wx-wy*diff(rx(t),t))-CD*diff(rz(t),t));%z-component
%where rx,ry,rz are each component of the ball position.
%CL and CD are drag and lift coefficients.
%K is the constant value.
%w is the magnitude of the angular velocity and wx, wy, and wz are each of components of the angular velocity.
I tried to solve the differential equations yet there were no positive answers so I guess the equations should be solved numerically.
When I get the equations, which is like "rx(t)=", I guess I could fit the positional data what I have.
I am not good at math so the way I try might be entirely wrong so if there is any possible way to answer my question, it would be great, so please help me get a any hints.
Kind regards,
Kate on 7 Mar 2018
I will have a look at what you pasted and see how I can solve the problem. Thank you for the reply and the comment kindly.

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