Blockquote A rocket moves with uniform rectilinear motion with speed $v(0) = V_0$, without friction. The pilot can brake by decelerating. We call $A$ the maximum deceleration that the motor can achieve. The tank contains a limited amount of gasoline equal to $K$. We assume that there is a quadratic (or more generally a superlinear) relationship between the fuel consumed and the acceleration e.g.
$$ k (t) dt = a (t) ^ 2 dt $$ where $k(t)$ is the amount of gasoline consumed at time t. Find $a(t)$ for $0 \leq t \leq T$ (in the space of bounded functions) which minimizes the time $T$ to stop the rocket, such that the speed at time $T$ is $v(T) = 0$. Blockquote
Do you know some references/notes/books that contain the solution to this problem? Or do you know the solution?