# X, v, a, j, ?

1. Aug 18, 2004

### Mark_W_Ingalls

Anyone-

From long ago IIRC a body that transitions from a rest state to a rectilinear moving state undergoes nearly infinite jerk (change in 'a'). On the one hand, my memory is reinforced by the idea that not all functions have infinitely many derivatives... But on the other hand, I may not have gone down the chain of differentiation far enough, so that jerk isn't "nearly infinite" ever, after all.

I am going to go soak my head while I await your wisdom...

Mark W. Ingalls

2. Aug 18, 2004

### Integral

Staff Emeritus

Can you give a better idea of what you mean by nearly infinite?

3. Aug 18, 2004

### pmb_phy

The kinematics of such a transition may be described mathematically as such and give a "nearly" infinite jerk (whatever that means) its different than what can actually happen in nature. Suppose a particle is described as having zero acceleration for t < 0 and constant acceleration for t > 0. The acceleration is then a step function. Then the jerk is infinite (delta function) at t = 0. This does not mean that this situation can happen like this in nature.

Pete

4. Aug 18, 2004

### Mark_W_Ingalls

Thanks for stopping by, integral and pmb_phy--

I am familiar with the delta function; I also know that we EE's blow off the natural response and (In my case) any forcing function that is not "harmonic," e.g. sinusoidal, but I was thinking about a car pulling away from a stop light, or a train pulling away from the station. Is there an instant when the vehicle under consideration goes from 'motionless' to 'moving'?

And in that *cusp* of an instant, the vehicle's position wrt time would (obviously) have to be continuous, but would its acceleration, necessarily? (This was many, many years ago; we had slide rules then.)

#:8-o

Anyway, thanks for helping scrape the rust off...

M

5. Aug 19, 2004

### Mark_W_Ingalls

I just wanted to shut all the gates on my way out...

I recalled the force - voltage analogy and I immedeiately visualized the response of an inductor-terminated X-line to a voltage step.

F = V
m = L
v = i

dV/dt = L di/dt, ...

#:8-D

M