angles = TransformationMatrices.axesRotationsAngles(T, sequence, guessAngle1);
A call to this function of the form
TransformationMatrices.Orientation T;
parameter Integer sequence[3] = {1,2,3};
SI.Angle angles[3];
equation
angle = axesRotationAngles(T, sequence);
computes the rotation angles "angles[1:3]" to rotate frame 1 into frame 2 along axes sequence[1:3], given the transformation matrix T from frame 1 to frame 2. Therefore, the result of this function fulfills the following equation:
T = axesRotation(sequence, angles)
The rotation angles are returned in the range
-π <= angles[i] <= π
There are two solutions for "angles[1]" in this range. Via the third argument guessAngle1 (default = 0) the returned solution is selected such that |angles[1] - guessAngle1| is minimal. The orientation object T may be in a singular configuration, i.e., there is an infinite number of angle values leading to the same T. The returned solution is selected by setting angles[1] = guessAngle1. Then angles[2] and angles[3] can be uniquely determined in the above range.
Note, that input argument sequence has the restriction that only values 1,2,3 can be used and that sequence[1] ≠ sequence[2] and sequence[2] ≠ sequence[3]. Often used values are:
sequence = {1,2,3} // Cardan angle sequence
= {3,1,3} // Euler angle sequence
= {3,2,1} // Tait-Bryan angle sequence
function axesRotationsAngles
extends Modelica.Icons.Function;
input TransformationMatrices.Orientation T "Orientation object to rotate frame 1 into frame 2";
input Integer sequence[3](min = {1, 1, 1}, max = {3, 3, 3}) = {1, 2, 3} "Sequence of rotations from frame 1 to frame 2 along axis sequence[i]";
input SI.Angle guessAngle1 = 0 "Select angles[1] such that |angles[1] - guessAngle1| is a minimum";
output SI.Angle angles[3] "Rotation angles around the axes defined in 'sequence' such that T=TransformationMatrices.axesRotation(sequence,angles); -pi < angles[i] <= pi";
end axesRotationsAngles;