WXYZ
The WXYZ measure returns the difference between the angular velocity vector (in radians per units of time) of marker i and the angular velocity vector of marker j resolved in the coordinate system of marker k.
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
WXYZ(i[,j][,k])
Arguments
i | The marker whose velocity is being measured. |
j | The marker with respect to which the angular velocity is being measured. If j is not specified, it defaults to the global origin. Specify j = 0 if you want to use this default, and then specify k. |
k | The marker in whose coordinate system the angular velocity vector is being expressed. If not specified, k defaults to the global coordinate system. |
Extended Definition
Mathematically, WXYZ is calculated as:
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.■WX is the WX measure.
■WY is the WY measure.
■WZ is the WZ measure.
■
is the unit vector along the x-axis of marker k.
is the unit vector along the x-axis of marker k.■
is the unit vector along the y-axis of marker k.
is the unit vector along the y-axis of marker k.■
is the unit vector along the z-axis of marker k.
is the unit vector along the z-axis of marker k.Examples
A vector expression for angular velocity might be used directly in the definition of a vector torque element:
VTORQUE/3, I=310, JFLOAT=9911, RM=310,
, TXYZ = -6.*WXYZ(310,9900,310)
, TXYZ = -6.*WXYZ(310,9900,310)
See other Vector measures available.