[andrewingram]

I'm always reminded of snap, crackle and pop (https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_deriv...) for this topic. Essentially it's not enough to just have continuous acceleration, you have to ease into it (low snap), you can probably go into further derivatives for ultra smoothness but maybe not worth it?

[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”.

[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!