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fmatvec::Der< Matrix< Rotation, DepMatShape, DepMatShape, double >, Vector< IndepVecShape, double > > Struct Template Reference

#include <function.h>

Public Types

typedef Matrix< General,
DepMatShape, IndepVecShape,
double > 
type
 

Detailed Description

template<typename DepMatShape, typename IndepVecShape>
struct fmatvec::Der< Matrix< Rotation, DepMatShape, DepMatShape, 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:

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

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:

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