My physics world was stunned today. I've been studying classical physics for several years now and just came across the concept of "Jerk"--the derivative of acceleration or the third derivative of position. I initially thought it was a joke or some some "fringe force" concept, perhaps something like centrifugal force. But then I did some research and found out the maths of these 3rd derivatives is routinely used by engineers in designing cars, rollercoasters, etc. I am blown away, I always thought that all we needed to understand classical mechanics was two time derivatives of position, that's it. Can someone explain to me why I've never seen this in full semester and year-long courses in classical mechanics?
There's technically infinite derivatives. You can't go from 0 acceleration to X m/s^2 without passing the values between, so a jerk is necessary for infinite precision. Likewise, a jerk can't go from 0 to x m/s^3. This is because spacetime is considered smooth classically.
Reason we rarely go to 3rd derivatives is that all equations of motion are written for 2nd derivative. You don't need higher order derivatives to figure out trajectories. There are, however, practical reasons to consider jerk. Say, you are sitting in a chair and experience 5G of acceleration. Unpleasant, but it won't cause you any damage. Now suppose your head starts out 10cm from head rest when that 5G acceleration kicks in. Your head will slam into a back rest at over 3m/s, equivalent to a fall from half a meter. That can cause a serious injury. So from perspective of mechanical damage, it's often not the acceleration that's important, but how suddenly the acceleration changes. Id est, jerk.
The third derivative also has a fundamental influence in 'classical electrodynamics'.See here http://en.wikipedia.org/wiki/Abraham%E2%80%93Lorentz_force
Thanks for the info, I'm just stunned that I never came across this even in passing, as it seems to, as K^2 points out, have practical significance.
Politicians recently found a use for higher derivatives. It used to be how much money we've got. Then is was rate of growth or recession. Then it was rate of change of growth or recession. Now it's rate of change of rate of change . . . . . . They stop differentiating once the 'sign' of the answer is in their favour.
Pretty soon they may just square the whole lot, call it black, and then take a long congressional break :/
When you have constant or uniform acceleration then you have exact results and simple equations, but when acceleration is non-uniform (jerk/jolt) then you have approximations and thus more complex (iterative) math with integrals and differential equations. I guess the reason you have not come across it is because in classical physics most of examples deal with motion of one or two entities with constant or uniform acceleration and thus it is not dealt with in physics books but rather in math books, concerning numerical modeling and algorithms, like computer simulations with interaction and complex trajectories of more than two entities, as is n-body problem and such.
If they're US politicians, they'd be better calling it "African American". I'm surprised American astrophysists are still allowed to mention "black holes" in their publications. The use of the third derivative in economics is not a recent invention: http://ideas.repec.org/p/geo/guwopa/gueconwpa~03-03-11.html And I vaguely remember Martin Gardner writing about it in one of his columns.