In Shivam Sarodia's answer to Escape Velocity question he states:
"For a rocket launched exactly at escape velocity"
This seems to be a repeated, and unclear way of discussing the matter of escape velocity since it doesn't say when or how long escape velocity is occurring for the rocket.
Does the escape velocity only need to occur momentarily and then thrust can be removed ( so therefore an initial velocity to a ballistic trajectory)
Or does the velocity need to be maintained for some period of time before thrust is cut?
Or are there other details/conditions that need to be considered?
I suspect 1. above is the correct interpretation, and that if I write the equations of motion I can demonstrate that's so in simulation. But it seems so many text books and discussions on the subject do not really make it clear the circumstances surrounding the definition of escape velocity. Even Feynman's lectures are not clear on this point - but they do have other interesting aspects.