During high-school and college I modeled all dynamic mechanical systems with displacement, velocity and acceleration. This was more than enough to address the systems and determine their behavior in the time domain for a certain external stimulation.
However, some part of my intuition keeps on telling me that further derivation past the second order of the displacement should also play a role, that is, the derivative of the acceleration should also be important when talking about dynamic systems.
For example, I feel completely different when accelerating smoothly but steadily harder (I get gradually pressed into my seat, as the derivative of the acceleration is small), compared to when I brake very hard (I go from no acceleration to full acceleration). (See this question for other examples).
I know this is a weird question, but somehow I fail to reason about it and none of my text-books even mentions deriving the acceleration.
jerkin English, and so failed during my google search. ¿Shall I delete my question then?¿Or could you close it please? Sorry again – andresgongora Oct 07 '16 at 10:53