Usually, when performing trajectory optimizations for chemical rockets, the limiting factor is the $\Delta v$ budget. That means velocity change is the optimization factor, with things like transfer time being a secondary consideration. Some 'perfect' transfers, like an infinite apoapsis bi-elliptic transfer even have infinite transfer times.
By contrast, for example when discussing more advanced forms for propulsion, the $\Delta v$ budget is no longer setting a limit and instead minimizing the transfer time is the most important thing to consider. Typically, the spacecraft in question have a high continuous acceleration, and the (subjectively) more intuitive approach is to thrust towards the target and start to slow down half way. This is a brachistochrone transfer.
Here is what I am thinking: A spacecraft using an ion engine is not usually limited by $\Delta v$ either, and it also uses continuous thrust. However, it has a very low thrust, meaning that the trajectory looks nothing like the simple high-thrust transfers. Here is for instance the trajectory of the spacecraft Dawn:
So, given the similarities
- Continuous thrust
- Not limited by $\Delta v$
- Optimization is for transfer time
Are ion engine trajectories also classified as brachistochrones?