I decided to see if there are any explanations for what the higher-order derivatives (3rd, 4th, 5th) of position actually feels like, and I didn't get much of an answer. However, they all have names. The best source of info on this subject that I was able to find is this article:
'Crackle' (the change in the 'Jounce'), which to me don't relay any kind of physical sensation.
In the case of the motions of Jupiter's Galilean moons, I can now look at the past seven days of motion: