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.

Jerk is also very important for road or rail track design. If you imagine needing to make a 90 degree bend, the "obvious" way to do it is by rounding off the corner with a circular radius.

But if you do that, it means the vehicle goes from having 0 sideways acceleration to experiencing 100% of the centripetal acceleration to move an object on a circular path (a = v^2 / r) instantaneously.

As an occupant of the car, that means you go from sitting comfortably to suddenly being thrown sideways.

It's much more comfortable if you ease into the turn, with the track design considering the rate of change of acceleration. If the designer didn't consider jerk you would definitely notice.

That's why loops on roller coasters aren't perfect circles as well then, I guess?

In part, maybe. The bigger reason is the roller coaster slows down near the top of the loop, so even for an constant vertical acceleration you need a non-circular shape.