function

LieGroups.SO3.Quat.left_jacobian_inv_exact

Inverse left Jacobian J_l^-1(v) of SO(3), closed form down to 1e-4 rad

The same matrix as left_jacobian_inv, evaluated with the branch radius and the coefficient form of right_jacobian_inv_exact. C depends on the rotation vector only through t^2, so J_l^-1(v) = J_r^-1(-v) is exact.

Public declarations

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

Role	Name	Type	Dimensions / attributes / default	Description
input	`v`	`Real`	`[3]`	Rotation vector
output	`J_inv`	`Real`	`[3, 3]`	I - [v]x/2 + C [v]x^2

Modelica declarations and implementation

Show parameters, interfaces and source

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

function left_jacobian_inv_exact
  "Inverse left Jacobian J_l^-1(v) of SO(3), closed form down to 1e-4 rad"
  input Real v[3] "Rotation vector";
  output Real J_inv[3, 3] "I - [v]x/2 + C [v]x^2";
algorithm
  J_inv := LieGroups.SO3.Quat.right_jacobian_inv_exact(-v);
  annotation(Documentation(info="<html>
    <p>The same matrix as <code>left_jacobian_inv</code>, evaluated with the
    branch radius and the coefficient form of
    <code>right_jacobian_inv_exact</code>. C depends on the rotation vector only
    through t^2, so J_l^-1(v) = J_r^-1(-v) is exact.</p>
  </html>"));
end left_jacobian_inv_exact;