WDTZ
The WDTZ function returns the z-component of the difference between the angular acceleration vector (in radians per unit of time squared) of marker i in the reference frame of marker l and the angular acceleration vector of marker j in the reference frame of marker l, as computed in the coordinate system of marker k. Marker j defaults to the global coordinate system if it is not specified. Similarly, marker k and l default to the global coordinate if they are not specified.
Note: | The values returned by the functions have the same units defined in the UNITS statement except for angular values. All angular values are returned in radians, all angular velocities are returned in radians per units of time (as defined in the UNITS statement), all angular accelerations are returned in radians per units of time squared. Functions RTOD and DTOR may be helpful to create angular expressions involving degrees and radians. For example, the below statements create a constraint to keep the angular velocity WX(8, 9) equal to 2.5 degrees per second. UNITS/SYSTEM = MKS ! Using seconds GCON/1, FUNCTION = WX(8, 9) – 2.5*DTOR ! Convert degrees to radians |
Format
WDTZ(i[,j][,k][,l])
Arguments
i | The marker whose acceleration is being measured. |
j | The marker with respect to which the acceleration is being measured. Set j = 0, while still specifying i, if you want j to default to the global coordinate system. |
k | The marker in whose coordinate system the acceleration vector is being expressed. Set k = 0, while still specifying i, if you want the results to be calculated along the z-axis of the global coordinate system. |
l | The reference frame in which the first time derivative of the angular acceleration vector is taken. Set l = 0 if you want the time derivatives to be taken in the ground coordinate system (GCS). |
Extended Definition
Mathematically, WDTZ is calculated as follows:
where:
■
is the angular velocity vector of marker i in ground.
is the angular velocity vector of marker i in ground.■
is the angular velocity vector of marker j in ground.
is the angular velocity vector of marker j in ground.■
is the unit vector along the z-axis of marker k.
is the unit vector along the z-axis of marker k.Examples
MARKER/1236, QP=4,6,7 EU=90D,90D,90D, PART=23
MARKER/2169, PART=16
REQUEST/16
,F1=WDTM(1236,2169)/
,F2=WDTX(1236,2169,2169,2169)/
,F3=WDTY(1236,2169,2169,2169)/
,F4=WDTZ(1236,2169,2169,2169)
MARKER/2169, PART=16
REQUEST/16
,F1=WDTM(1236,2169)/
,F2=WDTX(1236,2169,2169,2169)/
,F3=WDTY(1236,2169,2169,2169)/
,F4=WDTZ(1236,2169,2169,2169)
In its fourth column REQUEST/16 contains the z-component of the angular acceleration vector of Marker 1236 with respect to Marker 2169, as seen in the global coordinate system of Marker 2169 and measured in the reference frame containing Marker 2169.
See other Acceleration measures available.