How do I calculate a "medium" jerk value of my motion data?

[Maria_Porto]

I'm a psychologist and I'm currently studying physics but, because this is not my field of study, I'm having great difficulties.
I am currently studying biological motion and I have to calculate the jerk of my 2D motion data and I don't even know where to start. My data is basically a bunch of coordinates on the x and y-axis in time. I'll be using jerk as a measure of the "quantity of acceleration" of my stimuli. The aim is to compare the different jerk values of each of my stimulus (biological vs altered biological stimuli).
I have the velocity calculated per frame of my stimuli (i.e. I have a velocity value per time - because time is constant). I used this formula for calculating the velocity: =SQRT((X2-X1)^2+(Y2-Y1)^2)/1/60), where X1 is the initial position of the stimulus on the x-axis and X2 is the second position (and so on) and Y1 is the initial position of the Y axis and Y2 is the second position of the Y axis. This is data captured at 60Hz, thus, time variation is constant and is 1/60. Thus, I have the instantaneous velocity per frame calculated.

However, I want to calculate the "overall" jerk of my stimuli, kind of a "medium jerk"? How do I do that?
Any help would be truly important!

Thanks a lot!

 

[Dale]

Position, velocity, acceleration, and jerk are all vector quantities. That means that you keep the x and the y values separate. Usually written like this: $(x,y)$

So velocity would be $(x_1-x_0,y_1-y_0)/\Delta t$. So velocity is the change in position divided by the change in time. Similarly acceleration is the change in velocity divided by the change in time. And jerk is the change in acceleration...

Your main problem will be noise. This will make your noise levels skyrocket. You may not get useful values.

 

[Maria_Porto]

Thank you very much!
I am currently working on that and I calculated velocity, acceleration and finally jerk (per frame). You're right, jerk values are huge! I guess my data has a lot of noise..

 

[Dale]

What you may need to do is to fit your position data to some smooth function that you can then use to calculate the jerk analytically.

 

[nasu]

Do you have any reason to believe that the jerk is a significant quantity for what are you doing?
By the way, jerk is not "quantity of acceleration". Like acceleration is not quantity of velocity.
Jerk shows how fast the acceleration changes. If it does change.
What are your stimuli, do you have anything moving at all?

 

[Maria_Porto]

Thank you for all the helps and corrections.

My stimuli is biological motion stimuli - yeah it moves and has a very specific pattern of acceleration.

:)