Indefinite Integral

Introduction

Compute an indefinite integral from the start event to the stop event.

This is a cumulative integral, starting from an initial value (and a start event). Each frame is computed from the previous frame as follows:

integral (t) = integral (t-1) + x(t) * dt

The command integrates a signal using the trapezoidal rule.

The integral between two frames += ( (ValueAtFrame1+ValueAtFrame2)*DeltaT / 2 )

where T = time between frames (this is the data rate)

The Metric_Integrate command will return the integral as a metric.

Command

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

Indefinite_Integral /Signal_Types=The type of signal to be evaluated /Signal_Folder=The name of the signal folder /Signal_Names=The name of the signal to be evaluated /Result_Types=The type of signal to be evaluated /Result_Folder= The name of the resulting folder /Result_Names= The names of the resulting signal. If left blank the same number is used /Apply_As_Suffix_To_Signal_Name= The result is given the same name as the original signal with the suffix added /Event_Sequence= The event sequence /Exclude_Events= The exclude events /Event_Instance= The instance of the event sequence /Initial_Value= The value of the integral at the start event ;

Result_Types are restricted by the Signal_Types

If the Signal_Types= TARGET, the result type can only be TARGET, DERIVED, or METRIC

The Initial_Value is a signal expression that can return multiple components.

The same Initial_Value expression is used for all signals.

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Examples

This example calculates the velocity of the center of mass from force platform data during a vertical jump using the Indefinite_Integral command. Constants of integration (initial value) must be determined. In this case, the initial value is the initial velocity at the start of the preparation for the jump which is zero.

Note: This is only an example and you should check the constants of integration for your analysis.

!************************************************************************
! Take the vertical GRF, subtract the body weight, and divide the
! result by body mass to get the vertical CoM acceleration
!************************************************************************ 

! Add the two signals from F1 and F2 - end result is GRF for both plates
Add_Signals
/SIGNAL_TYPES=FORCE+FORCE
/SIGNAL_NAMES=FP1+FP2
/SIGNAL_FOLDER=PROCESSED+PROCESSED
/RESULT_NAME=GRF
/RESULT_FOLDER=PROCESSED
;

! Subtract the body weight in N - Metric is MASS_N
Subtract_Signals
/SIGNAL_TYPES=DERIVED+METRIC
/SIGNAL_FOLDER=PROCESSED
/SIGNAL_NAMES=GRF+MASS_N
/COMPONENT_SEQUENCE=Z, ALL
/RESULT_NAME=GRF_R
! /RESULT_FOLDER=PROCESSED
;

! Divide the result by body mass to get the vertical CoM acceleration
Divide_Signals
/SIGNAL_TYPES=DERIVED+METRIC
/SIGNAL_FOLDER=PROCESSED
/SIGNAL_NAMES=GRF_R+MASS
/COMPONENT_SEQUENCE=ALL
/RESULT_NAME=COM_GRF_Z_ACCEL
! /RESULT_FOLDER=PROCESSED
;

!************************************************************
! Integrate the vertical CoM acceleration over time to get the
! change in vertical CoM velocity. Initial value is zero
!*********************************************************** 

Indefinite_Integral
/SIGNAL_TYPES=DERIVED
/SIGNAL_NAMES=COM_GRF_Z_ACCEL
/SIGNAL_FOLDER=PROCESSED
/RESULT_SUFFIX=_VEL
! /RESULT_FOLDER=PROCESSED
! /START_AT_EVENT=
! /END_AT_EVENT=
! /INITIAL_VALUE=0
;

Legacy Parameters

Indefinite_Integral /Signal_Types=The type of signal to be evaluated /Signal_Names=The name of the signal to be evaluated /Signal_Folder=The name of the signal folder /Result_Folder= The name of the resulting folder /Result_Suffix= The result is given the same name as the original signal with the suffix added /Start_At_Event= The event at the beginning of the range /End_At_Event= The event at the end of the range /Initial_Value= The value of the integral at the start event