The Second Derivative pipeline command can be used to compute the second derivative of a signal at each point through the signal. This command may be used to determine the linear or angular acceleration of a signal when given its linear or angular position.

The Second Derivative command can be found in the Pipeline Workshop within the Signal Math folder as so:

Second_Derivative
! /SIGNAL_TYPES=
! /SIGNAL_FOLDER=ORIGINAL
! /SIGNAL_NAMES=
! /RESULT_TYPES=
! /RESULT_FOLDERS=PROCESSED
! /RESULT_NAME=
! /APPLY_AS_SUFFIX_TO_SIGNAL_NAME=
;

The parameters that can be used to control the command are as follows:

The command can be edited via text editor or via a dialog. The details on the command and the dialog are found below:

The first and last data points become DATA_NOT_FOUND (identified in the C3D file as a POINT Reliability value of –1).

Calculation Method: Derivatives are calculated using Finite Difference Algorithms.

Given the signal:

x(ti) for i=1, 2, …, n The second derivative is calculated using:

xDDot(ti)= (x(ti+1)-2x(ti)+x(ti-1))/( (ti+1)-(ti) )^2

The Second_Derivative command is useful for calculating the acceleration of targets, landmarks, etc., since acceleration is the second derivative of position. The following example calculates the acceleration of the center of mass by using the Second_Derivative command.

! Given a signal representing the center of mass's position as follows:
Compute_Model_Based_Data
/RESULT_NAME=COM
/FUNCTION=MODEL_COG
/SEGMENT=
/REFERENCE_SEGMENT=
! /RESOLUTION_COORDINATE_SYSTEM=LAB
! /USE_CARDAN_SEQUENCE=FALSE
! /NORMALIZATION=FALSE
! /NORMALIZATION_METHOD=
! /NORMALIZATION_METRIC=
! /NEGATEX=FALSE
! /NEGATEY=FALSE
! /NEGATEZ=FALSE
! /AXIS1=X
! /AXIS2=Y
! /AXIS3=Z
;

! The acceleration of the center of mass can be computed as follows:
Second_Derivative
/SIGNAL_TYPES=LINK_MODEL_BASED
/SIGNAL_NAMES=COM
! /SIGNAL_FOLDER=ORIGINAL
/RESULT_NAMES=COM_ACCELERATION
/RESULT_TYPES=LINK_MODEL_BASED
/RESULT_FOLDER=ACCELERATION
! /RESULT_SUFFIX=
;