basic function of angular dynamics of particle More...

Classes
struct	EulerAngleToee

Enumerations
enum class	EulerAngleType { kXYZ = 0 , kXZY , kXYX , kXZX , kYXZ , kYZX , kYXY , kYZY , kZXY , kZYX , kZXZ , kZYZ }

Functions
template<typename T_real = double>
void	eeToRleft (const T_real e[], T_real R[])
	transfer Euler quaterions to left rotate matrix More...

template<typename T_real = double>
void	eeToRright (const T_real e[], T_real R[])
	transfer Euler quaterions to right rotate matrix More...

template<typename T_real = double>
void	eeToRboth (const T_real e[], T_real Rleft[], T_real Rright[])
	transfer Euler quaterions to both left and right rotate matrix More...

template<typename T_real = double>
void	eeNormalized (T_real e[])
	to keep norm of Euler quaterions equal to one More...

template<typename T_real = double>
void	eeFromRotateAxisAndAngle (const T_real dir[], const T_real theta, T_real e[])
	get Euler quaterins from a rotate axis and a rotate angle More...

template<typename T_real = double>
void	Rtranspose3DimSelf (T_real R[])
	transpose of Roation matrix (3x3) itself More...

template<typename T_real = double>
void	Rtranspose3Dim (const T_real Rin[], T_real Rout[])
	transpose of rotate matrix (3x3) More...

template<typename T_real = double>
void	RleftToee (const T_real Rleft[], T_real e[])
	transfer left rotate to Euler Quaterions More...

template<typename T_real = double>
void	RrightToee (const T_real Rleft[], T_real e[])
	transfer right rotate to Euler Quaterions More...

template<typename T_real = double>
void	Mat3xMat3 (const T_real matleft[], const T_real matright[], T_real matout[])
	dot between two 3x3 matrices More...

template<typename T_real = double>
void	Mat2xMat2 (const T_real matleft[], const T_real matright[], T_real matout[])
	dot between two 2x2 matrices More...

template<typename T_real = double>
void	Mat3xVec3 (const T_real mat[], const T_real vec[], T_real vecout[])
	dot between 3x3 matrix and 3x1 vector More...

template<typename T_real = double>
void	Mat2xVec2 (const T_real mat[], const T_real vec[], T_real vecout[])
	dot between 2x2 matrix and 2x1 vector More...

template<typename T_real = double>
void	DotVec3 (const T_real vec0[], const T_real vec1[], T_real &out)
	dot between two vectors More...

template<typename T_real = double>
void	DotVec2 (const T_real vec0[], const T_real vec1[], T_real &out)
	dot between two vectors More...

template<typename T_real = double>
void	CrossVec3 (const T_real vec0[], const T_real vec1[], T_real out[])
	cross between tow vector More...

template<typename T_real = double>
void	MatFromPFToIF3Dim (const T_real matin[], const T_real Rleft[], const T_real Rright[], T_real matout[])
	transfer 3x3 matrix from particle frame to inertial frame More...

template<typename T_real = double>
void	MatFromPFToIF3DimByee (const T_real matin[], const T_real ee[], T_real matout[])
	transfer 3x3 matrix from particle frame to inertial frame, by ee More...

template<typename T_real = double>
void	VecFromPFToIF3Dim (const T_real vecin[], const T_real Rleft[], const T_real Rright[], T_real vecout[])
	transfer 3x1 vec from particle frame to inertial frame More...

template<typename T_real = double>
void	VecFromPFToIF3DimByee (const T_real vecin[], const T_real ee[], T_real vecout[])
	transfer 3x1 vec from particle frame to inertial frame by ee More...

template<typename T_real = double>
void	MatFromIFToPF3Dim (const T_real matin[], const T_real Rleft[], const T_real Rright[], T_real matout[])
	transfer 3x3 matrix from inertial frame to particle frame More...

template<typename T_real = double>
void	MatFromIFToPF3DimByee (const T_real matin[], const T_real ee[], T_real matout[])
	transfer 3x3 matrix from inertial frame to particle frame by ee More...

template<typename T_real = double>
void	VecFromIFToPF3Dim (const T_real vecin[], const T_real Rleft[], const T_real Rright[], T_real vecout[])
	transfer 3x1 vec from particle frame to inertial frame More...

template<typename T_real = double>
void	VecFromIFToPF3DimByee (const T_real vecin[], const T_real ee[], T_real vecout[])

template<typename T_real = double>
void	DirToee (const T_real dir[], const T_real base[], T_real e[])
	get euler quaterions from a director More...

template<typename T_real = double>
void	eeToDir (const T_real ee[], const T_real base[], T_real dir[])
	get director from euler quaterions More...

template<typename T_real = double>
void	RandomR (T_real R[])
	generate a random rotate matrix More...

template<typename T_real = double>
void	RandomDir (T_real vec[])
	generate a random direction More...

template<typename T_real = double>
void	MatFromIFToPF2Dim (const T_real matin[], const T_real Rleft[], const T_real Rright[], T_real matout[])
	transfer 2x2 matrix from inertial frame to particle frame More...

template<typename T_real = double>
void	MatFromIFToPF2DimByee (const T_real matin[], const T_real ee[], T_real matout[])
	transfer 2x2 matrix from inertial frame to particle frame by ee More...

template<typename T_real = double>
void	AngvelTodee (const T_real angvel[], const T_real ee[], T_real dee[])
	obtain the difference in ee from angular velocity More...

template<typename T_real >
T_real	DotVec3 (const Vec3< T_real > vec0, const Vec3< T_real > vec1)

template<typename T_real >
T_real	DotVec2 (const Vec2< T_real > &vec0, const Vec2< T_real > &vec1)

template<typename T_real >
void	MatFromIFToPF2DimByee (const T_real matin[], const T_real ee, T_real matout[])

template<typename T_real = double>
void	eeToRleft (Vec4< T_real > &e, Mat3< T_real > &R)

template<typename T_real = double>
Mat3< T_real >	eeToRleft (Vec4< T_real > &e)

template<typename T_real = double>
void	eeToRright (Vec4< T_real > &e, Mat3< T_real > &R)

template<typename T_real = double>
Mat3< T_real >	eeToRright (Vec4< T_real > &e)

template<typename T_real = double>
void	Mat3xMat3 (Mat3< T_real > &matleft, Mat3< T_real > &matright, Mat3< T_real > &matout)

template<typename T_real = double>
Mat3< T_real >	Mat3xMat3 (Mat3< T_real > &matleft, Mat3< T_real > &matright)

template<typename T_real = double>
void	Mat2xMat2 (Mat2< T_real > &matleft, Mat2< T_real > &matright, Mat2< T_real > &matout)

template<typename T_real = double>
Mat2< T_real >	Mat2xMat2 (Mat2< T_real > &matleft, Mat2< T_real > &matright)

template<typename T_real = double>
void	Mat3xVec3 (Mat3< T_real > &matleft, Vec3< T_real > &matright, Vec3< T_real > &matout)

template<typename T_real = double>
Vec3< T_real >	Mat3xVec3 (Mat3< T_real > &matleft, Vec3< T_real > &matright)

template<typename T_real = double>
void	Mat2xVec2 (Mat2< T_real > &matleft, Vec2< T_real > &matright, Vec2< T_real > &matout)

template<typename T_real = double>
Vec2< T_real >	Mat2xVec2 (Mat2< T_real > &matleft, Vec2< T_real > &matright)

template<typename T_real >
void	CrossVec3 (Vec3< T_real > &vec0, Vec3< T_real > &vec1, Vec3< T_real > &out)

template<typename T_real >
Vec3< T_real >	CrossVec3 (Vec3< T_real > &vec0, Vec3< T_real > &vec1)

template<typename T_real >
void	VecFromPFToIF3Dim (Vec3< T_real > &vecin, Mat3< T_real > &Rleft, Mat3< T_real > &Rright, Vec3< T_real > &vecout)

template<typename T_real >
Vec3< T_real >	VecFromPFToIF3Dim (Vec3< T_real > &vecin, Mat3< T_real > &Rleft, Mat3< T_real > &Rright)

template<typename T_real >
void	VecFromPFToIF3DimByee (Vec3< T_real > &vecin, Vec4< T_real > &ee, Vec3< T_real > &vecout)

template<typename T_real >
Vec3< T_real >	VecFromPFToIF3DimByee (Vec3< T_real > &vecin, Vec4< T_real > &ee)

template<typename T_real >
void	VecFromIFToPF3DimByee (Vec3< T_real > &vecin, Vec4< T_real > &ee, Vec3< T_real > &vecout)

template<typename T_real >
Vec3< T_real >	VecFromIFToPF3DimByee (Vec3< T_real > &vecin, Vec4< T_real > &ee)

template<typename T_real = double>
void	EulerAngleToee_XYZ (const T_real theta[], T_real e[])

template<typename T_real = double>
void	EulerAngleToee_XZY (const T_real theta[], T_real e[])

template<typename T_real = double>
void	EulerAngleToee_XYX (const T_real theta[], T_real e[])

template<typename T_real = double>
void	EulerAngleToee_XZX (const T_real theta[], T_real e[])

template<typename T_real = double>
void	EulerAngleToee_YXZ (const T_real theta[], T_real e[])

template<typename T_real = double>
void	EulerAngleToee_YZX (const T_real theta[], T_real e[])

template<typename T_real = double>
void	EulerAngleToee_YXY (const T_real theta[], T_real e[])

template<typename T_real = double>
void	EulerAngleToee_YZY (const T_real theta[], T_real e[])

template<typename T_real = double>
void	EulerAngleToee_ZXY (const T_real theta[], T_real e[])

template<typename T_real = double>
void	EulerAngleToee_ZYX (const T_real theta[], T_real e[])

template<typename T_real = double>
void	EulerAngleToee_ZXZ (const T_real theta[], T_real e[])

template<typename T_real = double>
void	EulerAngleToee_ZYZ (const T_real theta[], T_real e[])

Detailed Description

basic function of angular dynamics of particle

transformation between different Euler angles and Euler quaterions

more information can be found in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf

Enumeration Type Documentation

◆ EulerAngleType

enum dmdyn::angular::EulerAngleType

strong

Enumerator
kXYZ
kXZY
kXYX
kXZX
kYXZ
kYZX
kYXY
kYZY
kZXY
kZYX
kZXZ
kZYZ

Function Documentation

◆ AngvelTodee()

template<typename T_real = double>

void dmdyn::angular::AngvelTodee	(	const T_real	angvel[],
		const T_real	ee[],
		T_real	dee[]
	)

obtain the difference in ee from angular velocity

Template Parameters

T_real

Parameters

angvel	3x1 vector, angular velocity
ee	4x1 vector, current ee
dee	4x1 vector, difference in ee

◆ CrossVec3() [1/3]

template<typename T_real = double>

void dmdyn::angular::CrossVec3	(	const T_real	vec0[],
		const T_real	vec1[],
		T_real	out[]
	)

cross between tow vector

Template Parameters

T_real

Parameters

[in]	vec0	3x1 vector
[in]	vec1	3x1 vector
[out]	out	3x1 vector

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◆ CrossVec3() [2/3]

template<typename T_real >

Vec3<T_real> dmdyn::angular::CrossVec3	(	Vec3< T_real > &	vec0,
		Vec3< T_real > &	vec1
	)

References CrossVec3().

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◆ CrossVec3() [3/3]

template<typename T_real >

void dmdyn::angular::CrossVec3	(	Vec3< T_real > &	vec0,
		Vec3< T_real > &	vec1,
		Vec3< T_real > &	out
	)

References CrossVec3().

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◆ DirToee()

template<typename T_real = double>

void dmdyn::angular::DirToee	(	const T_real	dir[],
		const T_real	base[],
		T_real	e[]
	)

get euler quaterions from a director

Template Parameters

T_real

Parameters

[in]	dir	director,3x1
[in]	base	base vector,3x1 [1,0,0]: base on x axis in particle frame [0,1,0]: base on y axis in particle frame [0,0,1]: base on z axis in particle frame
[out]	e	Euler quaterions, 4x1

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◆ DotVec2() [1/2]

template<typename T_real = double>

void dmdyn::angular::DotVec2	(	const T_real	vec0[],
		const T_real	vec1[],
		T_real &	out
	)

dot between two vectors

Template Parameters

T_real

Parameters

[in]	vec0	2x1 vector
[in]	vec1	2x1 vector
[out]	out	1 scalar

◆ DotVec2() [2/2]

template<typename T_real >

T_real dmdyn::angular::DotVec2	(	const Vec2< T_real > &	vec0,
		const Vec2< T_real > &	vec1
	)

◆ DotVec3() [1/2]

template<typename T_real = double>

void dmdyn::angular::DotVec3	(	const T_real	vec0[],
		const T_real	vec1[],
		T_real &	out
	)

dot between two vectors

Template Parameters

T_real

Parameters

[in]	vec0	3x1 vector
[in]	vec1	3x1 vector
[out]	out	1 scalar

◆ DotVec3() [2/2]

template<typename T_real >

T_real dmdyn::angular::DotVec3	(	const Vec3< T_real >	vec0,
		const Vec3< T_real >	vec1
	)

◆ eeFromRotateAxisAndAngle()

template<typename T_real = double>

void dmdyn::angular::eeFromRotateAxisAndAngle	(	const T_real	dir[],
		const T_real	theta,
		T_real	e[]
	)

get Euler quaterins from a rotate axis and a rotate angle

Template Parameters

T_real

Parameters

[in]	dir	direction of rotate axis
[in]	theta	rotate angle about roatation axis
[out]	e	Euler quaterions, 4-length array

◆ eeNormalized()

template<typename T_real = double>

void dmdyn::angular::eeNormalized ( T_real e[] )

to keep norm of Euler quaterions equal to one

Template Parameters

T_real

Parameters

e	Euler quaterions, 4-length array

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◆ eeToDir()

template<typename T_real = double>

void dmdyn::angular::eeToDir	(	const T_real	ee[],
		const T_real	base[],
		T_real	dir[]
	)

get director from euler quaterions

Template Parameters

T_real

Parameters

[in]	ee	Euler quaterions, 4x1
[in]	base	base vector,3x1 [1,0,0]: base on x axis in particle frame [0,1,0]: base on y axis in particle frame [0,0,1]: base on z axis in particle frame
[out]	dir	director, 3x1

◆ eeToRboth()

template<typename T_real = double>

void dmdyn::angular::eeToRboth	(	const T_real	e[],
		T_real	Rleft[],
		T_real	Rright[]
	)

transfer Euler quaterions to both left and right rotate matrix

Template Parameters

T_real default: double

Parameters

[in]	e	Euler quaterions, 4-length array
[out]	Rleft	left rotate matrix, 3x3 matrix
[out]	Rright	right rotate matrix, 3x3 matrix

◆ eeToRleft() [1/3]

template<typename T_real = double>

void dmdyn::angular::eeToRleft	(	const T_real	e[],
		T_real	R[]
	)

transfer Euler quaterions to left rotate matrix

calculate left rotation matrix from euler quaternion

Template Parameters

T_real default: double

Parameters

[in]	e	Euler quaterions, 4-length array
[out]	R	left rotate matrix, 3x3 matrix

Template Parameters

T_real

Parameters

e	euler quaternion
R	left rotation matrix, R11 = R[0], R12 = R[1], ... R33 = R[8]

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◆ eeToRleft() [2/3]

template<typename T_real = double>

Mat3<T_real> dmdyn::angular::eeToRleft ( Vec4< T_real > & e )

inline

References eeToRleft().

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◆ eeToRleft() [3/3]

template<typename T_real = double>

void dmdyn::angular::eeToRleft	(	Vec4< T_real > &	e,
		Mat3< T_real > &	R
	)

inline

References eeToRleft().

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◆ eeToRright() [1/3]

template<typename T_real = double>

void dmdyn::angular::eeToRright	(	const T_real	e[],
		T_real	R[]
	)

transfer Euler quaterions to right rotate matrix

Template Parameters

T_real default: double

Parameters

[in]	e	Euler quaterions, 4-length array
[out]	R	right rotate matrix, 3x3 matrix

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◆ eeToRright() [2/3]

template<typename T_real = double>

Mat3<T_real> dmdyn::angular::eeToRright ( Vec4< T_real > & e )

inline

References eeToRright().

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◆ eeToRright() [3/3]

template<typename T_real = double>

void dmdyn::angular::eeToRright	(	Vec4< T_real > &	e,
		Mat3< T_real > &	R
	)

inline

References eeToRright().

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◆ EulerAngleToee_XYX()

template<typename T_real = double>

void dmdyn::angular::EulerAngleToee_XYX	(	const T_real	theta[],
		T_real	e[]
	)

◆ EulerAngleToee_XYZ()

template<typename T_real = double>

void dmdyn::angular::EulerAngleToee_XYZ	(	const T_real	theta[],
		T_real	e[]
	)

◆ EulerAngleToee_XZX()

template<typename T_real = double>

void dmdyn::angular::EulerAngleToee_XZX	(	const T_real	theta[],
		T_real	e[]
	)

◆ EulerAngleToee_XZY()

template<typename T_real = double>

void dmdyn::angular::EulerAngleToee_XZY	(	const T_real	theta[],
		T_real	e[]
	)

◆ EulerAngleToee_YXY()

template<typename T_real = double>

void dmdyn::angular::EulerAngleToee_YXY	(	const T_real	theta[],
		T_real	e[]
	)

◆ EulerAngleToee_YXZ()

template<typename T_real = double>

void dmdyn::angular::EulerAngleToee_YXZ	(	const T_real	theta[],
		T_real	e[]
	)

◆ EulerAngleToee_YZX()

template<typename T_real = double>

void dmdyn::angular::EulerAngleToee_YZX	(	const T_real	theta[],
		T_real	e[]
	)

◆ EulerAngleToee_YZY()

template<typename T_real = double>

void dmdyn::angular::EulerAngleToee_YZY	(	const T_real	theta[],
		T_real	e[]
	)

◆ EulerAngleToee_ZXY()

template<typename T_real = double>

void dmdyn::angular::EulerAngleToee_ZXY	(	const T_real	theta[],
		T_real	e[]
	)

◆ EulerAngleToee_ZXZ()

template<typename T_real = double>

void dmdyn::angular::EulerAngleToee_ZXZ	(	const T_real	theta[],
		T_real	e[]
	)

◆ EulerAngleToee_ZYX()

template<typename T_real = double>

void dmdyn::angular::EulerAngleToee_ZYX	(	const T_real	theta[],
		T_real	e[]
	)

◆ EulerAngleToee_ZYZ()

template<typename T_real = double>

void dmdyn::angular::EulerAngleToee_ZYZ	(	const T_real	theta[],
		T_real	e[]
	)

◆ Mat2xMat2() [1/3]

template<typename T_real = double>

void dmdyn::angular::Mat2xMat2	(	const T_real	matleft[],
		const T_real	matright[],
		T_real	matout[]
	)

dot between two 2x2 matrices

Template Parameters

T_real

Parameters

[in]	matleft
[in]	matright
[out]	matout

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◆ Mat2xMat2() [2/3]

template<typename T_real = double>

Mat2<T_real> dmdyn::angular::Mat2xMat2	(	Mat2< T_real > &	matleft,
		Mat2< T_real > &	matright
	)

inline

References Mat2xMat2().

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◆ Mat2xMat2() [3/3]

template<typename T_real = double>

void dmdyn::angular::Mat2xMat2	(	Mat2< T_real > &	matleft,
		Mat2< T_real > &	matright,
		Mat2< T_real > &	matout
	)

inline

References Mat2xMat2().

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◆ Mat2xVec2() [1/3]

template<typename T_real = double>

void dmdyn::angular::Mat2xVec2	(	const T_real	mat[],
		const T_real	vec[],
		T_real	vecout[]
	)

dot between 2x2 matrix and 2x1 vector

Template Parameters

T_real

Parameters

[in]	mat	2x2 matrix
[in]	vec	2x1 vector
[out]	vecout	2x1 vector

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◆ Mat2xVec2() [2/3]

template<typename T_real = double>

Vec2<T_real> dmdyn::angular::Mat2xVec2	(	Mat2< T_real > &	matleft,
		Vec2< T_real > &	matright
	)

inline

References Mat2xVec2().

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◆ Mat2xVec2() [3/3]

template<typename T_real = double>

void dmdyn::angular::Mat2xVec2	(	Mat2< T_real > &	matleft,
		Vec2< T_real > &	matright,
		Vec2< T_real > &	matout
	)

inline

References Mat2xVec2().

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◆ Mat3xMat3() [1/3]

template<typename T_real = double>

void dmdyn::angular::Mat3xMat3	(	const T_real	matleft[],
		const T_real	matright[],
		T_real	matout[]
	)

dot between two 3x3 matrices

Template Parameters

T_real

Parameters

[in]	matleft
[in]	matright
[out]	matout

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◆ Mat3xMat3() [2/3]

template<typename T_real = double>

Mat3<T_real> dmdyn::angular::Mat3xMat3	(	Mat3< T_real > &	matleft,
		Mat3< T_real > &	matright
	)

inline

References Mat3xMat3().

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◆ Mat3xMat3() [3/3]

template<typename T_real = double>

void dmdyn::angular::Mat3xMat3	(	Mat3< T_real > &	matleft,
		Mat3< T_real > &	matright,
		Mat3< T_real > &	matout
	)

inline

References Mat3xMat3().

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◆ Mat3xVec3() [1/3]

template<typename T_real = double>

void dmdyn::angular::Mat3xVec3	(	const T_real	mat[],
		const T_real	vec[],
		T_real	vecout[]
	)

dot between 3x3 matrix and 3x1 vector

Template Parameters

T_real

Parameters

[in]	mat	3x3 matrix
[in]	vec	3x1 vector
[out]	vecout	3x1 vector

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◆ Mat3xVec3() [2/3]

template<typename T_real = double>

Vec3<T_real> dmdyn::angular::Mat3xVec3	(	Mat3< T_real > &	matleft,
		Vec3< T_real > &	matright
	)

inline

References Mat3xVec3().

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◆ Mat3xVec3() [3/3]

template<typename T_real = double>

void dmdyn::angular::Mat3xVec3	(	Mat3< T_real > &	matleft,
		Vec3< T_real > &	matright,
		Vec3< T_real > &	matout
	)

inline

References Mat3xVec3().

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◆ MatFromIFToPF2Dim()

template<typename T_real = double>

void dmdyn::angular::MatFromIFToPF2Dim	(	const T_real	matin[],
		const T_real	Rleft[],
		const T_real	Rright[],
		T_real	matout[]
	)

transfer 2x2 matrix from inertial frame to particle frame

Template Parameters

T_real

Parameters

[in]	matin	2x2, matrix in inertial frame
[in]	Rleft	2x2, left rotate matrix
[in]	Rright	2x2, right rotate matrix
[out]	matout	2x2, matrix in particle frame

◆ MatFromIFToPF2DimByee() [1/2]

template<typename T_real >

void dmdyn::angular::MatFromIFToPF2DimByee	(	const T_real	matin[],
		const T_real	ee,
		T_real	matout[]
	)

◆ MatFromIFToPF2DimByee() [2/2]

template<typename T_real = double>

void dmdyn::angular::MatFromIFToPF2DimByee	(	const T_real	matin[],
		const T_real	ee[],
		T_real	matout[]
	)

transfer 2x2 matrix from inertial frame to particle frame by ee

Template Parameters

T_real

Parameters

[in]	matin	2x2, matrix in inertial frame
[in]	ee	4, Euler quaterions
[out]	matout	2x2, matrix in particle frame

◆ MatFromIFToPF3Dim()

template<typename T_real = double>

void dmdyn::angular::MatFromIFToPF3Dim	(	const T_real	matin[],
		const T_real	Rleft[],
		const T_real	Rright[],
		T_real	matout[]
	)

transfer 3x3 matrix from inertial frame to particle frame

Template Parameters

T_real

Parameters

[in]	matin	3x3, matrix in inertial frame
[in]	Rleft	3x3, left rotate matrix
[in]	Rright	3x3, right rotate matrix
[out]	matout	3x3, matrix in particle frame

◆ MatFromIFToPF3DimByee()

template<typename T_real = double>

void dmdyn::angular::MatFromIFToPF3DimByee	(	const T_real	matin[],
		const T_real	ee[],
		T_real	matout[]
	)

transfer 3x3 matrix from inertial frame to particle frame by ee

Template Parameters

T_real

Parameters

[in]	matin	3x3, matrix in inertial frame
[in]	ee	4, Euler quaterions
[out]	matout	3x3, matrix in particle frame

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◆ MatFromPFToIF3Dim()

template<typename T_real = double>

void dmdyn::angular::MatFromPFToIF3Dim	(	const T_real	matin[],
		const T_real	Rleft[],
		const T_real	Rright[],
		T_real	matout[]
	)

transfer 3x3 matrix from particle frame to inertial frame

Template Parameters

T_real

Parameters

[in]	matin	3x3, matrix in particle frame
[in]	Rleft	3x3, left rotate matrix
[in]	Rright	3x3, right rotate matrix
[out]	matout	3x3, matrix in inertial frame

◆ MatFromPFToIF3DimByee()

template<typename T_real = double>

void dmdyn::angular::MatFromPFToIF3DimByee	(	const T_real	matin[],
		const T_real	ee[],
		T_real	matout[]
	)

transfer 3x3 matrix from particle frame to inertial frame, by ee

Template Parameters

T_real

Parameters

[in]	matin	3x3, matrix in particle frame
[in]	ee	4, Euler quaterions
[out]	matout	3x3, matrix in inertial frame

◆ RandomDir()

template<typename T_real = double>

void dmdyn::angular::RandomDir ( T_real vec[] )

generate a random direction

Template Parameters

T_real

Parameters

vec	3x1 vector

References mathconst::PI, and RandomNumber< T_real >::randr().

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◆ RandomR()

template<typename T_real = double>

void dmdyn::angular::RandomR ( T_real R[] )

generate a random rotate matrix

Template Parameters

T_real

Parameters

R	rotate matrix,3x3

References mathconst::PI, and RandomNumber< T_real >::randr().

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◆ RleftToee()

template<typename T_real = double>

void dmdyn::angular::RleftToee	(	const T_real	Rleft[],
		T_real	e[]
	)

transfer left rotate to Euler Quaterions

Template Parameters

T_real

Parameters

[in]	Rleft	left rotate matrix, 3x3 array
[out]	e	Euler quaterions, 4-length array

References quadpack::max().

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◆ RrightToee()

template<typename T_real = double>

void dmdyn::angular::RrightToee	(	const T_real	Rleft[],
		T_real	e[]
	)

transfer right rotate to Euler Quaterions

Template Parameters

T_real

Parameters

[in]	Rright	right rotate matrix, 3x3 array
[out]	e	Euler quaterions, 4-length array

References quadpack::max().

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◆ Rtranspose3Dim()

template<typename T_real = double>

void dmdyn::angular::Rtranspose3Dim	(	const T_real	Rin[],
		T_real	Rout[]
	)

transpose of rotate matrix (3x3)

Template Parameters

T_real

Parameters

[in]	Rin	in, rotate materix,3x3 array
[out]	Rout	out, rotate materix,3x3 array

◆ Rtranspose3DimSelf()

template<typename T_real = double>

void dmdyn::angular::Rtranspose3DimSelf ( T_real R[] )

transpose of Roation matrix (3x3) itself

Template Parameters

T_real

Parameters

R	rotate materix,3x3 array

◆ VecFromIFToPF3Dim()

template<typename T_real = double>

void dmdyn::angular::VecFromIFToPF3Dim	(	const T_real	vecin[],
		const T_real	Rleft[],
		const T_real	Rright[],
		T_real	vecout[]
	)

transfer 3x1 vec from particle frame to inertial frame

Template Parameters

T_real

Parameters

[in]	vecin	3x1, matrix in inertial frame
[in]	Rleft	3x3, left rotate matrix
[in]	Rright	3x3, right rotate matrix
[out]	vecout	3x1, matrix in particle frame

◆ VecFromIFToPF3DimByee() [1/3]

template<typename T_real = double>

void dmdyn::angular::VecFromIFToPF3DimByee	(	const T_real	vecin[],
		const T_real	ee[],
		T_real	vecout[]
	)

Template Parameters

T_real

Parameters

[in]	vecin	3x3, matrix in inertial frame
[in]	ee	4, Euler quaterions
[out]	vecout	3x3, matrix in particle frame

References eeToRright().

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◆ VecFromIFToPF3DimByee() [2/3]

template<typename T_real >

Vec3<T_real> dmdyn::angular::VecFromIFToPF3DimByee	(	Vec3< T_real > &	vecin,
		Vec4< T_real > &	ee
	)

References eeToRright().

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◆ VecFromIFToPF3DimByee() [3/3]

template<typename T_real >

void dmdyn::angular::VecFromIFToPF3DimByee	(	Vec3< T_real > &	vecin,
		Vec4< T_real > &	ee,
		Vec3< T_real > &	vecout
	)

References eeToRright().

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◆ VecFromPFToIF3Dim() [1/3]

template<typename T_real = double>

void dmdyn::angular::VecFromPFToIF3Dim	(	const T_real	vecin[],
		const T_real	Rleft[],
		const T_real	Rright[],
		T_real	vecout[]
	)

transfer 3x1 vec from particle frame to inertial frame

Template Parameters

T_real

Parameters

[in]	vecin	3x1, matrix in particle frame
[in]	Rleft	3x3, left rotate matrix
[in]	Rright	3x3, right rotate matrix
[out]	vecout	3x1, matrix in inertial frame

◆ VecFromPFToIF3Dim() [2/3]

template<typename T_real >

Vec3<T_real> dmdyn::angular::VecFromPFToIF3Dim	(	Vec3< T_real > &	vecin,
		Mat3< T_real > &	Rleft,
		Mat3< T_real > &	Rright
	)

◆ VecFromPFToIF3Dim() [3/3]

template<typename T_real >

void dmdyn::angular::VecFromPFToIF3Dim	(	Vec3< T_real > &	vecin,
		Mat3< T_real > &	Rleft,
		Mat3< T_real > &	Rright,
		Vec3< T_real > &	vecout
	)

◆ VecFromPFToIF3DimByee() [1/3]

template<typename T_real = double>

void dmdyn::angular::VecFromPFToIF3DimByee	(	const T_real	vecin[],
		const T_real	ee[],
		T_real	vecout[]
	)

transfer 3x1 vec from particle frame to inertial frame by ee

Template Parameters

T_real

Parameters

[in]	vecin	3x1, matrix in particle frame
[in]	ee	4, Euler quaterions
[out]	vecout	3x1, matrix in inertial frame

References eeToRleft().

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◆ VecFromPFToIF3DimByee() [2/3]

template<typename T_real >

Vec3<T_real> dmdyn::angular::VecFromPFToIF3DimByee	(	Vec3< T_real > &	vecin,
		Vec4< T_real > &	ee
	)

References eeToRleft().

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◆ VecFromPFToIF3DimByee() [3/3]

template<typename T_real >

void dmdyn::angular::VecFromPFToIF3DimByee	(	Vec3< T_real > &	vecin,
		Vec4< T_real > &	ee,
		Vec3< T_real > &	vecout
	)

References eeToRleft().

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Classes

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

◆ EulerAngleType

Function Documentation

◆ AngvelTodee()

◆ CrossVec3() [1/3]

◆ CrossVec3() [2/3]

◆ CrossVec3() [3/3]

◆ DirToee()

◆ DotVec2() [1/2]

◆ DotVec2() [2/2]

◆ DotVec3() [1/2]

◆ DotVec3() [2/2]

◆ eeFromRotateAxisAndAngle()

◆ eeNormalized()

◆ eeToDir()

◆ eeToRboth()

◆ eeToRleft() [1/3]

◆ eeToRleft() [2/3]

◆ eeToRleft() [3/3]

◆ eeToRright() [1/3]

◆ eeToRright() [2/3]

◆ eeToRright() [3/3]

◆ EulerAngleToee_XYX()

◆ EulerAngleToee_XYZ()

◆ EulerAngleToee_XZX()

◆ EulerAngleToee_XZY()

◆ EulerAngleToee_YXY()

◆ EulerAngleToee_YXZ()

◆ EulerAngleToee_YZX()

◆ EulerAngleToee_YZY()

◆ EulerAngleToee_ZXY()

◆ EulerAngleToee_ZXZ()

◆ EulerAngleToee_ZYX()

◆ EulerAngleToee_ZYZ()

◆ Mat2xMat2() [1/3]

◆ Mat2xMat2() [2/3]

◆ Mat2xMat2() [3/3]

◆ Mat2xVec2() [1/3]

◆ Mat2xVec2() [2/3]

◆ Mat2xVec2() [3/3]

◆ Mat3xMat3() [1/3]

◆ Mat3xMat3() [2/3]

◆ Mat3xMat3() [3/3]

◆ Mat3xVec3() [1/3]

◆ Mat3xVec3() [2/3]

◆ Mat3xVec3() [3/3]

◆ MatFromIFToPF2Dim()

◆ MatFromIFToPF2DimByee() [1/2]

◆ MatFromIFToPF2DimByee() [2/2]

◆ MatFromIFToPF3Dim()

◆ MatFromIFToPF3DimByee()

◆ MatFromPFToIF3Dim()

◆ MatFromPFToIF3DimByee()

◆ RandomDir()

◆ RandomR()

◆ RleftToee()

◆ RrightToee()

◆ Rtranspose3Dim()

◆ Rtranspose3DimSelf()

◆ VecFromIFToPF3Dim()

◆ VecFromIFToPF3DimByee() [1/3]

◆ VecFromIFToPF3DimByee() [2/3]

◆ VecFromIFToPF3DimByee() [3/3]

◆ VecFromPFToIF3Dim() [1/3]

◆ VecFromPFToIF3Dim() [2/3]

◆ VecFromPFToIF3Dim() [3/3]

◆ VecFromPFToIF3DimByee() [1/3]

◆ VecFromPFToIF3DimByee() [2/3]

◆ VecFromPFToIF3DimByee() [3/3]