fmatvec 0.0.0

Public Types | List of all members
fmatvec::Der< Matrix< Rotation, Fixed< 3 >, Fixed< 3 >, double >, Vector< IndepVecShape, double > > Struct Template Reference

`#include <function.h>`

## Public Types

using | type = Matrix< General, Fixed< 3 >, IndepVecShape, double >

## Detailed Description

### template<typename IndepVecShape>
struct fmatvec::Der< Matrix< Rotation, Fixed< 3 >, Fixed< 3 >, double >, Vector< IndepVecShape, double > >

Defines the type of the derivative of a rotation matrix with respect to a vector as matrix. The partial derivative operator \( \texttt{parDer}_{\boldsymbol{x}}(\boldsymbol{R}_{12}) \) of a rotation matrix \( \boldsymbol{R}_{12} \) with respect to a vector \( \boldsymbol{x} \) in defined by the Function class (member functions parDerX) as follows:

\[ \texttt{parDer}_{\boldsymbol{x}}(\boldsymbol{R}_{12}) = \left[ \widetilde{\left(\frac{\partial\boldsymbol{R}_{12}}{\partial x_1}\boldsymbol{R}^T_{12}\right)}, \widetilde{\left(\frac{\partial\boldsymbol{R}_{12}}{\partial x_2}\boldsymbol{R}^T_{12}\right)}, \dots \right] \in \mathbb{R}^{3\times N} \quad \text{when}\quad \boldsymbol{x} \in \mathbb{R}^{N\times 1} \]

where the "inverse tilde" operator ( \( \widetilde{o} \)) transform a skew symmetric matrix to a vector. This class spezialization define the type of \( \texttt{parDer}_{\boldsymbol{x}} \).

The documentation for this struct was generated from the following file:

- /mbsim-env/fmatvec/fmatvec/function.h