function

LieGroups.SO3.Quat.inverse_jacobian

Right-trivialized derivative of inverse with respect to its quaternion

Rule for inverse. Perturbing on the right and reading the inverted result back on the right gives

log_map(inverse(q)^-1 * inverse(q*exp_map(dq))) = -Ad(q) dq = -R(q) dq

The identity is exact: inversion turns the right perturbation into a left one and negates it, and the adjoint carries it back to the right.

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	`J`	`Real`	`[3, 3]`	d/d(dq) of log_map(inverse(q)^-1 * inverse(q*exp_map(dq)))

Modelica declarations and implementation

Show parameters, interfaces and source

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

function inverse_jacobian
  "Right-trivialized derivative of inverse with respect to its quaternion"
  input Real q[4] "Unit quaternion {w,x,y,z}";
  output Real J[3, 3] "d/d(dq) of log_map(inverse(q)^-1 * inverse(q*exp_map(dq)))";
algorithm
  J := -LieGroups.SO3.Quat.to_DCM(q);
  annotation(Documentation(info="<html>
    <p>Rule for <code>inverse</code>. Perturbing on the right and reading the
    inverted result back on the right gives</p>
    <pre>log_map(inverse(q)^-1 * inverse(q*exp_map(dq))) = -Ad(q) dq = -R(q) dq</pre>
    <p>The identity is exact: inversion turns the right perturbation into a left
    one and negates it, and the adjoint carries it back to the right.</p>
  </html>"));
end inverse_jacobian;