The brachistochrone problem says: If we were to have two objects separated by a horizontal distance $X$ and vertical distance $Y$ under free fall acceleration $g$, and then put a bead through a wire, we would find that the path that warrants the shortest time between both points is not a line, but rather the tautochrone curve.
I want to generalise this problem to add more practicality:
If we were to have two points $A (0, 0)$ and $B (x, y)$ in a Cartesian plane and an object starts at point $A$ with a velocity vector $\vec v$, what path would give the shortest time of travel between both points if the plane is in a force field $\vec F (x,y)$ that induces acceleration (assuming bounds of acceleration are finite and continuous, i.e. $-a \leq 0 \leq a$).