Beyond velocity and acceleration: jerk, snap and higher derivatives (2016)

I know, this is an old paper, but I don't follow the this assumption:

> The terms jerk and snap mean very little to most people, including physicists and engineers.

Almost 20 years ago we defined jerk into our standards for lift applications. I know jerk is an important parameter for any modern rotating machine that includes gears.

While in lift applications it is known as the roller coaster effect, people in different parts of the world have a different taste on when they want to use a lift. I know I over simplify when I say, that American people want to have the gut feeling when riding a lift, especially an express lift in those high buildings. In difference in Asian countries the lift ride must be smooth as possible. They don't like to have the feeling of riding a lift at all. In Europe it is something in between. Lift manufacturers have to respect those (end) costumers otherwise the are not chosen.

The same in any rotating machine with some sort of gears. Because jerk and those higher orders contribute to the wear and tear of gears. As you want to have longer lasting gears many modern machine manufacturers limit those parameters to reduce wear and tear. So, with a little software change I can demand a higher price because service and maintenance can be reduced.

One thing that is strange is that we can easily imagine the first two derivatives: position we can just imagine a static point, velocity we can imagine a constant speed i.e. a straight line on a position-time graph, acceleration we just imagine a parabola, but jerk is somehow conceptually indistinguishable. The difference between a point, a line, and a parabola are stark, the third order jerk is not so easy to distinguish, instead still just looking like the parabola.

I've always wondered why this is, why curves in general are perceptually similar if scaled correctly, while a straight line is so clearly different. Perhaps it is because our perceptions developed to distinguish between inertial and non inertial reference frames?

Tje difference is because we cannot easily tell between “curve of second order” and “curve of other order”.

You can get an idea when you try to understand why the function

y=0 for x<0 y=x^2 for x>=0

has two derivativea but not three.

But the issue is infinitesimal, so very hard to tell.

Jerk you can “linearise” if you think of a car (with no air friction) and its accelerator. Somehow…