A spaceship moving in two dimensions is at position $(x, y)$ and has a velocity $(v_x, v_y)$. It also has a maximum acceleration $a_{max}$. Its goal is to be at position $(x', y')$ with a velocity of $(v'_x, y'_x)$. What path takes the smallest amount of time?
I see that the problem can be reduced to a spaceship at $(0, 0)$ with a velocity of $(0, 0)$, trying to intercept a object currently at $(x'-x, y'-y)$ with a velocity of $(v'_x - v_x, y'_x - y_x)$.
I have a hunch that the optimal path will always be constant acceleration in one direction, possibly with a reversal somewhere along the way.
I'm curious because I believe the total time will be a consistent and admissable heuristic for a Newtonian pathing algorithm that takes velocity into account.
Clarification
There are no additional constraints. The problem is to minimize time, not to conserve $\Delta v$.
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