Help with integral function implmentation for movement data analysis

Hi everyone,

I just read a paper ('Sensitivity of smoothness measures to movement duration, amplitude, and arrests.') which included a metric for 'dimensionless jerk', which may be applied to movement data to determine movement smoothness. I am attempting to apply this metric to some numerical biological data I have collected for the motion of a particle in three dimensions. It has been awhile since I have done this so would be greatful to know if I have implemented the function correctly.

The function looks like this: http://latex.codecogs.com/gif.latex?(\int_{t_1}^{t_2}\dddot{x}(t)^2dt){D^5}/{A^2}

Where the triple derivative of x is acceleration data, A is distance travlled (already calculated) and D is t2-t1. t1 and t2 are the start and end of my data so do not require explicit specification.

I am implementing the code as follows:

// Vel1..Vel3  - logs of particle velocity (x,y,z)

// Accel = Derivative of combined velocity terms (I am not sure if this is correct)
Accel = diff(Vel_1(:,1).^2 + Vel_2(:,2).^2 + Vel_3(:,3).^2);

for (y=1:length(Ax))
    Ax1(y) = Ax(y)*Ax(y);    % square each element of Accel
end

D = length(Ax1);    % Duration
A = Distance_Travelled1(Tn);     % Movement amplitude (already calculated)

Dimensionless_Jerk1 = (trapz(Ax1)) * ((D.^5)/A.^2)

Does this look okay to you?

Any comments or suggestions welcome, at the moment my results vary quite signigicantly, with a magnitude range of e3-e10 for quite similar motions. Any help gratefully recieved. Apologies if I have missed any important details.