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AY

The AY function returns the rotational displacement (in radians) of marker i about the y-axis of marker j, and accounts for angle wrapping.
Marker j defaults to the global coordinate system if it is not specified. The values are computed as follows: assume rotations about the other two axes (x-, z-axes) of marker j are zero. Then AY is the angle between the two x-axes (or the two z-axes). AY is measured counter-clockwise from the z-axis of the J marker to the z-axis of the I marker (see the figure below).
Measurement of AY

Format

AY(i[,j])

Arguments

 
i
The marker whose rotations are being sought.
j
The marker with respect to which the rotations are being measured.

Extended Defintion

Mathematically, AY is calculated as:
where:
■ is the z-axis of marker i
■ is the x-azis of marker j
■ is the z-axis of marker j
 
Tip:  
If you want to change the AY function so it does not account for angle wrapping, use the MOD function. For example, use the function:

(MOD(AY(2,1)+PI,2*PI)-PI)

The MOD function achieves the cyclic effect and the +PI and -PI shift the curve accordingly.
Caution:  
For large rotations (greater than 10 degrees) about the x-axis or z-axis of marker j, the AY function becomes increasingly non-physical. Moreover, AY is undefined when both arguments to ATAN2 are zero. This occurs when the z-axis of marker i is orthogonal to the plane defined by the x and z-axis of the j marker.

Examples

SFORCE/10, ROTATION, I=23, J=34
, FUNCTION=-4*(AY(46,57)**2)
This SFORCE statement applies a moment about the common z-axes of Markers 23 and 34. The torque acts on Marker 23; the reaction torque acts on Marker 34.
The value of the torque being applied is -4 times the square of the angle between the z axes of Markers 46 and 57. The angle is measured in a counterclockwise sense from the z-axis of Marker 57 to the z-axis of Marker 46.
See other Displacement available.