VZ
The VZ function returns the z-component of the difference between the velocity vector of marker i and the velocity vector of marker j as computed in the coordinate system of marker k. All vector time derivatives are taken in the reference frame of marker l. Marker j defaults to the global coordinate system if it is not specified. Similarly, markers i and j default to the global coordinate system if they are not specified.
Format
VZ(i[,j][,k][,l])
Arguments
i | The marker whose velocity is being measured. |
j | The marker with respect to which the velocity is being measured. Set j = 0, while still specifying l, if you want j to default to the global coordinate system. |
k | The marker in whose coordinate system the velocity vector is expressed. Set k = 0, while still specifying l, 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 displacement vector is taken. Set l = 0 or omit the argument if you want the time derivatives to be taken in the ground coordinate system (GCS). |
Extended Definition
Mathematically, VZ is calculated as follows:
where:
■
is the displacement of marker i in ground.
is the displacement of marker i in ground.■
is the displacement of marker j in ground.
is the displacement 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.■
denotes time differentiation in the reference frame of the l marker.
denotes time differentiation in the reference frame of the l marker.Examples
MARKER/236, QP=4,6,7, EU=90D,90D,0, PART=23
MARKER/169, PART=16, FLOATING
MARKER/168, QP=1,2,3, EU=30D,45D,60D, PART=16
VFORCE/236, I=236, JFLOAT=169
,FX=-10*VX(236,168,168,168)/
,FY=-15*VY(236,168,168,168)/
,FZ=-20*VZ(236,168,168,168)
MARKER/169, PART=16, FLOATING
MARKER/168, QP=1,2,3, EU=30D,45D,60D, PART=16
VFORCE/236, I=236, JFLOAT=169
,FX=-10*VX(236,168,168,168)/
,FY=-15*VY(236,168,168,168)/
,FZ=-20*VZ(236,168,168,168)
This VFORCE statement defines a damper acting between Markers 236 and 168. Marker 169 is a floating marker that defines the reaction point on Part 16. The damping force components are proportional to the components of the velocity between Markers 236 and 168 as seen and measured by an observer at Marker 168.
See other Velocity measures available.