function

LieGroups.SO3.Quat.product_left_factor_jacobian

Right-trivialized derivative of product with respect to its left factor

Rule for product, left slot. Both the perturbed slot and the group-valued result use the right trivialization, so

log_map(product(q,p)^-1 * product(q*exp_map(dq), p)) = J*dq

with J = Ad(p^-1) = R(p)^T. The identity is exact, not first order: conjugation by p carries the perturbation unchanged apart from the frame change, so no series and no evaluation of q enter the result.

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]`	Left quaternion {w,x,y,z}
input	`p`	`Real`	`[4]`	Right quaternion {w,x,y,z}
output	`J`	`Real`	`[3, 3]`	d/d(dq) of log_map(product(q,p)^-1 * product(q*exp_map(dq), p))

Modelica declarations and implementation

Show parameters, interfaces and source

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

function product_left_factor_jacobian
  "Right-trivialized derivative of product with respect to its left factor"
  input Real q[4] "Left quaternion {w,x,y,z}";
  input Real p[4] "Right quaternion {w,x,y,z}";
  output Real J[3, 3] "d/d(dq) of log_map(product(q,p)^-1 * product(q*exp_map(dq), p))";
algorithm
  J := transpose(LieGroups.SO3.Quat.to_DCM(p));
  annotation(Documentation(info="<html>
    <p>Rule for <code>product</code>, left slot. Both the perturbed slot and the
    group-valued result use the right trivialization, so</p>
    <pre>log_map(product(q,p)^-1 * product(q*exp_map(dq), p)) = J*dq</pre>
    <p>with J = Ad(p^-1) = R(p)^T. The identity is exact, not first order:
    conjugation by p carries the perturbation unchanged apart from the frame
    change, so no series and no evaluation of q enter the result.</p>
  </html>"));
end product_left_factor_jacobian;