.Modelica.Mechanics.MultiBody.Frames.Quaternions.from_T

Information

Syntax

Q = Quaternions.from_T(T, Q_guess);

Description

This function returns a quaternions orientation Q. computed from a transformation matrix T and depending on the initial guess Q_guess. Generally, the transformation matrix T can be gained using a function from the TransformationMatrices package.

See also

to_T. from_T_inv, Frames.from_T, TransformationMatrices.from_T.

Interface

function from_T
  extends Modelica.Icons.Function;
  input Real T[3, 3] "Transformation matrix to transform vector from frame 1 to frame 2 (v2=T*v1)";
  input Quaternions.Orientation Q_guess = nullRotation() "Guess value for Q (there are 2 solutions; the one close to Q_guess is used";
  output Quaternions.Orientation Q "Quaternions orientation object to rotate frame 1 into frame 2 (Q and -Q have same transformation matrix)";
end from_T;

Revisions

• January 2021 by Jakub Tobolar
  reimplemented for more efficient and numerically stable algorithm according to https://d3cw3dd2w32x2b.cloudfront.net/wp-content/uploads/2015/01/matrix-to-quat.pdf. It compares only one particular diagonal element with another to select one of the four code parts. Then, the selected code delivers four components which are close to the desired quaternion, so that it has only be scaled by an appropriate factor.
  We appreciate the effort of Mike Day, the author of the abovementioned document. Credit also goes to Matthias Hellerer (DLR) for making inquiries and the first Modelica implementation.