Change of acceleration

[PWrong]

I have a short question about motion in 3D before we start motion in 4D. Would you ever use a 3rd order derivative in motion i.e. can you change your acceleration instantly? Obviously you can't change your velocity in an instant, but I've never learnt anything in physics or calculus about a changing acceleration.

(Split from: 4D vegetarians by BobXP)

[jinydu]

Ok, anyway. I have a short question about motion in 3D before we start motion in 4D. Would you ever use a 3rd order derivative in motion i.e. can you change your acceleration instantly? Obviously you can't change your velocity in an instant, but I've never learnt anything in physics or calculus about a changing acceleration.

I read in a textbook that the rate of change of acceleration is called "jerk". Thus, jerk is the third derivate of distance with respect to time. I also read that engineers often try to minimize jerk to make things more comfortable for people. But that's really all I know.

Here are the first few search results on Google. As can be seen, most of them only mention jerk briefly:

http://math.ucr.edu/home/baez/physics/General/jerk.html
http://www.machinedesign.com/ASP/strArt ... rticle.asp
http://www.rose-hulman.edu/Class/Calcul ... 3_1_0.html
http://www.sparknotes.com/physics/kinem ... ion2.rhtml

[pat]

Would you ever use a 3rd order derivative in motion i.e. can you change your acceleration instantly? Obviously you can't change your velocity in an instant, but I've never learnt anything in physics or calculus about a changing acceleration.

As another poster mentioned, engineers are often concerned with jerk. However, you've probably not come across it in physics or calculus before because of Newton's second law of motion: F = ma.

Acceleration is proportional to the force applied. In most physics and calculus problems, the force is fairly constant... gravity of a planet on an object only falling a short distance, the amount of force with which one pushes a block of wood on an inclined plane, etc.

It may well be that we cannot go from applying zero-force to applying full-force instantaneously when we flex our muscles. Thus, jerk is probably useful if you really need precise descriptions of human motion. But, for the most part, assuming we can instantaneously apply full-force with a muscle (once the nerve impulses get to the muscle), is a great simplification that doesn't lose too much resolution.

All of that said, in the "orbits" thread, the n-th derivatives are never constant (except for the circular orbit).... they're harmonic.

[PWrong]

Ok, so how would motion work in 4D? In physics, we generally study circular and parabolic motion. Is there any other kind of motion in 3D or 4D?

It seems like a 4D being would tend to run in straight line or turn by moving in a circle, with centripetal acceleration always towards the same point. When changing direction, you simply pick another point to accelerate towards, and thus run in a different circle. I'm just not sure whether friction from the ground will have the right effect. It might turn out just like gravity.

[pat]

For the most part, I would think that frictionless motion in 4-D would be pretty similar except that gravity would be an inverse-cube of the distance rather than an inverse-square. As we've shown in another thread, this means that orbits wouldn't be able to be elliptical (except for the special/unstable circular orbit).

As for motion with friction, the friction would now be a function of the realmar volume (amount of realm?) touching as opposed to the amount of area touching. So, there may be significantly more drag on sliding things.

And, of course, there are more ways to spin something in 4-D. So, a 4-D billiard ball would have lots of ways to move on a realmar table top depending on what sort of English one puts on it. Of course, if you assume that the cue stick only makes contact with a single point on the ball for an instant, then you cannot get some of the funner varieties of English where you might bend the ball very slowly toward the left while bending it very sharply in the ana direction.