Here is the problem I'm currently facing right now, I have set of ODEs which I can solve numerically given the initial condition. But I'm not sure how to go about giving algebraic solution with constraint.
Here is the image of the coupled ODES (image is taken from KEN BRAY & DAVID KERWIN's paper)
Context: $x, y, z$ are co-ordinates, equation of projectile for soccer ball
$K_d$, $k_l$ are constant.
So I would like to add the constraint such that given final condition and initial location condition (for instance $x(0),y(0),z(0) = 0$, and $x(t_final), y(t_{final}), z(t_{final}) = 100$, $k_d$, $k_l$ are known constants, gamma angle is known)
So How do I seek solution in which (when $x$ is between $10$ to $11$, $y$ is not between some range, and $z$ is not between $0$ to $10$).
Im trying to find x'(0), y'(0), z'(0).
It would be great if you can guide me on direction of goal-seeking algorithm exist for cases such as this. Thanks a lot !!