[quietbritishjim]

As your link says, acceleration is 2nd derivative of position, so rate of change of acceleration is 3rd derivative, often called jolt. As you say, you want acceleration to vary slowly, so it's low jolt that you want.

Snap (or jounce), crackle and pop are 4th/5th/6th derivative. They're probably less of a problem.

[nkrisc]

I’ve also heard it called “jerk”.

[quietbritishjim]

Oops, that's what I meant to say! So much for my correction.

I actually heard, many years ago, the higher derivatives referred to as "jerk" (3rd, as you said), "jolt" (4th) and "jounce" (5th). But that contradicts the Wikipedia article that says "jounce" is 4th derivative.

[rcxdude]

It can help because the higher derivatives also tend to promote vibrations in the system, but I doubt it'd be perceptible by people. I have heard of 5th-order smooth curves being used for very sensitive structures, like the movement of big observatory telescopes.

[andrewingram]

Oops, yeah you’re right!