Best way to measure velocity, acceleration and jerk

[Marc]

Hello,

I have a one-dimensional path associated with timings, similar to:

t0=0, x0=0
t1=0.1, x1=2
t2=0.2, x2=3
etc.

Now I want to measure the velocity, acceleration and jerk at each time position. The first (and easy) way of doing this would be to loop through all points and compute:

v1=(x1-x0)/(t1-t0)
v2=(x2-x1)/(t2-t1)
etc.

then

a1=(v1-v0)/(t1-t0)
a2=(v2-v1)/(t2-t1)
etc.

and finally

j1=(a1-a0)/(t1-t0)
j2=(a2-a1)/(t2-t1)
etc.

But something tells me this is not the most precise way of computing this. Any suggestions?

 

[DrClaude]

You should use the finite difference approximation to the derivatives.