function

LieGroups.SO3.Quat.adjoint

Adjoint Ad_X: for SO(3), Ad_q = R (the rotation matrix)

For SO(3), the adjoint representation is simply the rotation matrix: Ad_R(v) = R*v. This rotates Lie algebra elements (angular velocities) from one frame to another.

Used to transport local Lie-group error coordinates: A_k = Ad_{Exp(-xi*dt)}

Public declarations

Explicit source declarations; dimensions, modifications and defaults are shown as written, without evaluation.

Role	Name	Type	Dimensions / attributes / default	Description
input	`q`	`Real`	`[4]`	Unit quaternion {w,x,y,z}
output	`Ad`	`Real`	`[3,3]`	3x3 adjoint matrix (equals the DCM)

Modelica declarations and implementation

Show parameters, interfaces and source

Parameters, inputs, outputs, defaults and equations from the source file.

function adjoint "Adjoint Ad_X: for SO(3), Ad_q = R (the rotation matrix)"
  input Real q[4] "Unit quaternion {w,x,y,z}";
  output Real Ad[3,3] "3x3 adjoint matrix (equals the DCM)";
algorithm
  Ad := LieGroups.SO3.Quat.to_DCM(q);
  annotation(Documentation(info="<html>
    <p>For SO(3), the adjoint representation is simply the rotation matrix:
    Ad_R(v) = R*v. This rotates Lie algebra elements (angular velocities)
    from one frame to another.</p>
    <p>Used to transport local Lie-group error coordinates:
    A_k = Ad_{Exp(-xi*dt)}</p>
  </html>"));
end adjoint;