Function navtk::navutils::d_dcm_to_rpy(const Matrix3&, const Matrix3&, const Matrix3&, const Matrix3&, const Matrix3&, const Matrix3&, const Matrix3&, const Matrix3&)
Defined in File derivatives.hpp
Function Documentation
-
Matrix3 navtk::navutils::d_dcm_to_rpy(const Matrix3 &a, const Matrix3 &dadx, const Matrix3 &dady, const Matrix3 &dadz, const Matrix3 &b, const Matrix3 &dbdx, const Matrix3 &dbdy, const Matrix3 &dbdz)
Derivative of the dcm_to_rpy() function wrt 3 variables (usually RPY), where the DCM is composed of the product of 2 other DCMs.
The derivative does not exist at pitch = PI/2 (derived from the composite DCM) and this function is unreliable in that region; user beware.
Say there is a function such that:
\( f = \text{dcm_to_rpy}(C) \)
where
\( C = C_1C_2 \)
then
\( \dot{f(C)} = \dot{f}(C)\dot{C} = \dot{f}(C_1C_2)(\dot{C_1}C_2 + C_1\dot{C_2}) \)
With the above in mind, see below for how each parameter is defined.
- Parameters
a – DCM
C_1dadx – derivative of
C_1wrt variable 1 (x Euler angle).dady – derivative of
C_1wrt variable 2 (y Euler angle).dadz – derivative of
C_1wrt variable 3 (z Euler angle).b – DCM
C_2dbdx – derivative of
C_2wrt variable 1 (x Euler angle).dbdy – derivative of
C_2wrt variable 2 (y Euler angle).dbdz – derivative of
C_2wrt variable 3 (z Euler angle).
- Returns
Derivative of RPY representation of
Cwrt some 3-variable input.