I was wondering if there is an (analytical) solution to the problem where the position $\vec{r}_i = \vec{r}(t=t_i)$, $\vec{r}_f = \vec{r}(t=t_f)$ and the velocities $\vec{v}_i = \vec{v}(t=t_i)$, $\vec{v}_f = \vec{v}(t=t_f)$ as well as the magnitude of acceleration $|a|$ are given and the goal is to find the vector $\vec{a}(t)/|a| = \vec{e}_a(t)$ that minimizes the time need to transition from the initial state to the final state assuming there are no other forces present.
I tried to find an answer to this but all paper I could find on this topic dealt with spacecraft trajectory optimization and had the addition of a central force which made the problem much more complex.
I don't know much about optimal control and boundary value problems so and extended answer would be appreciated. Thanks in advance for your answers!
Without any other constraints, the time optimal solution to the BVP $r(0) = r_0$, $r(1) = r_f$ on $[0,1]$ for the ode $\ddot{r} = a(t)$ is along a straight line connecting the boundary points, so
$$\frac{a(t)}{|a|} = \frac{r_f-r_0}{|r_f-r_0|}.$$
To meet the velocity requirement, you need only suitably throttle $|a|$.
You probably have only found literature for optimal trajectories in a potential field because that problem is (a) classic and used frequently in spacecraft guidance, and (b) nontrivial.