I always got the sense from physics that outside of purely mathematical constructions such as Taylor series, higher order time derivatives aren't providing much interesting information. Though I'm not sure whether this is the inherent laziness of physicist math[1] or a property of the forces in nature.
[1] since e^x = 1 + x is generally true, why'd you even need a second order derivative
> Jerk and snap can be observed in various areas of physics and engineering. In physics and engineering jerk and snap should always be considered when vibration occurs and particularly when this excitation induces multi-resonant modes of vibration. They should also be considered at all times when a transition occurs such as: start up and shutdown; take-off and landing; and accelerating and decelerating.
> Acceleration without jerk is just a static load, and therefore constant acceleration alone could never cause vibration. In a machine shop, a toolmaker can damage the mill or the job if the setup starts vibrating. This vibration happens because of jerk and snap.
> In mechanical engineering it is important in automotive design to ensure that the cam-follower does not jump off the camshaft. It is also important in manufacturing processes as rapid changes in acceleration of a cutting tool can lead to premature tool wear and result in an uneven and rough surface finish.
> In civil engineering railway train tracks and roads should be designed for a smooth exit from a straight section into a curve, and it is common to use a transition called a clothoid, which is part of a Cornu spiral (also referred to as an Euler spiral). When a clothoid is implemented the change in acceleration is not abrupt and the levels of jerk and possibly snap are significantly reduced. If the transition between different radii of curvature is sudden, the transition is uncomfortable for passengers and potentially dangerous as it could cause the car or train to be thrown off the road or track. With good physics design engineers are attempting to produce a gradual jerk and constant snap, which gives a smooth increase in radial acceleration, or preferably a zero snap, constant jerk, and linear increase in radial acceleration. Just as road and railway engineers design out jerk and snap using the clothoid transition so, too, do roller coaster designers when they design loops and helices for the roller coasters [11, 12].
Genuinely curious.
More seriously though, I think this might be about driver training and maybe calibrating the foot pedal. It's great that EVs have a much better torque curve, but it means the old muscle memory of opening the throttle wide at low RPMs and letting the clutch slip is simply not the way to do it (nvm that there's no clutch to operate in an EV).
Every car can go from a standstill to accelerating in a split second.
>their maximum acceleration isn't very high
What is the maximum acceleration of an EV? Do you have some numbers?
>ICEs need more time to reach maximum acceleration
I don't think what you're describing is jerk, it's acceleration (and velocity).
It came as a surprise to me but it seems like jerk is something that can be felt in real life.
Going from a standstill to accelerating at say 3 m/s² is very different in a normal ICE car vs. an EV. It's anecdotal, but you must have noticed this if you've driven an EV before.
> What is the maximum acceleration of an EV?
I was talking specifically about the electric buses in my city. They don't have massive acceleration compared to, say, a Tesla.
> I don't think what you're describing is jerk
I am talking about how rapidly electric buses change acceleration. That's the definition of jerk.
But if the jerk (or higher derivatives) are non-zero, you have to change your "lean angle" quickly to avoid getting jerked around (which is obviously much more disruptive).
I cannot remember what it's called but essentially given a target position in space the missle uses parametric data about its current position/orientation/speed and their higher derivatives to dead reckon about where it is in regards to the target.
Anyone remember what that's called? I went on a rabbit hole with it a few years ago, it's really interesting math and programming. Everything works basically stateless except for current instrument data, last position and target position from what I remember.
Kalman filters come up a lot, maybe relevant to the terms you're looking for
I'm becoming seasick due to a jerkiness of a car. Not due to a speed or a acceleration, but it is jerk that does it for me. I watched it from my childhood, I hated trolleybuses for that: they are electric and they tend to change acceleration instantly. But I didn't understood how it works until much later.
Or in other words, you can approximate exp(x) as a set of first order taylor approximations that each covers a small window to arbitrary precision, but the combination of them is still has well defined higher derivatives that are not 0.