Module with subroutines for manipulation of finite rotations. More...

Data Types
interface	eccexpand
	Takes into account possible eccentricity. More...

interface	ffa_eulerzyx
	Computes the EulerZYX angles for a relative rotation. More...

interface	ffa_glbeulerzyx
	Computes the EulerZYX angles for a global rotation. More...

Functions/Subroutines
real(dp) function, dimension(3)	mattoeulerxyz (R, eulerIn, err)
	Converts a rotation matrix (tensor) to EulerXYZ angles. More...

real(dp) function, dimension(3, 3)	eulertomat (euler)
	Converts a set of EulerXYZ angles into a rotation matrix. More...

subroutine	vec_to_mat (rvec, rten, lpu)
	Computes the rotation tensor from a rotation vector. More...

subroutine	mat_to_vec (rten, rvec)
	Computes the rotation vector from a rotation tensor. More...

subroutine	vec_to_quat (rvec, q, lpu)
	Computes the quaternion representation from a rotation vector. More...

subroutine	mat_to_quat (rten, q)
	Computes the quaternion representation from a rotation tensor. More...

subroutine	quat_to_mat (q, rten)
	Computes the rotation tensor from a quaternion representation. More...

subroutine	quat_to_vec (q, rvec)
	Computes the rotation vector from a quaternion representation. More...

real(dp) function, dimension(3)	deltarot (T1, T2)
	Computes the incremental rotation vector rotating tensor T1 to T2. More...

subroutine	orthonorm3 (rten)
	Makes a rotation tensor orthonormal through use of quaternions. More...

subroutine	spin (vec, mat)
	Computes the spin (skew-symmetric) tensor from the rotation vector. More...

subroutine	dtheta_domega (thetaVec, jacobiMat, lpu)
	Computes the variation of a rotation pseudo vector. More...

subroutine	domega_dtheta (thetaVec, jacobiMat, lpu)
	Computes the inverse of the variation of a rotation pseudo vector. More...

subroutine, private	eccexpandvec (e, v, vFull)
	Takes into account possible eccentricity. More...

subroutine, private	eccexpandmat (e, M, Mfull)
	Takes into account possible eccentricity. More...

subroutine, private	eccexpanddiagmat (e, D, Mfull)
	Takes into account possible eccentricity, for a diagonal matrix D. More...

Variables
real(dp), parameter, private	epsth2_p = 0.0005_dp
	Angles zero-tolerance. More...

Detailed Description

Module with subroutines for manipulation of finite rotations.

This module contains various utility subroutines (and functions) for manipulation of finite rotations in the nonlinear solver, like convertion of rotation tensors to angles, and vice versa.

Bjorn Haugen

Date: February 1999

Function/Subroutine Documentation

◆ deltarot()

real(dp) function, dimension(3) rotationmodule::deltarot	(	real(dp), dimension(3,3), intent(in)	T1,
		real(dp), dimension(3,3), intent(in)	T2
	)

Computes the incremental rotation vector rotating tensor T1 to T2.

◆ domega_dtheta()

subroutine rotationmodule::domega_dtheta	(	real(dp), dimension(3), intent(in)	thetaVec,
		real(dp), dimension(3,3), intent(out)	jacobiMat,
		integer, intent(in), optional	lpu
	)

Computes the inverse of the variation of a rotation pseudo vector.

Parameters

[in]	thetaVec	Initial rotation vector
[out]	jacobiMat	The inverse matrix of pseudo-vector variations
[in]	lpu	Optional file unit number for error messages

◆ dtheta_domega()

subroutine rotationmodule::dtheta_domega	(	real(dp), dimension(3), intent(in)	thetaVec,
		real(dp), dimension(3,3), intent(out)	jacobiMat,
		integer, intent(in), optional	lpu
	)

Computes the variation of a rotation pseudo vector.

Parameters

[in]	thetaVec	Initial rotation vector
[out]	jacobiMat	Matrix of pseudo-vector variations with respect to `w = (eps, 0, 0)`, `w = (0, eps, 0)` and `w = (0, 0, eps)`
[in]	lpu	Optional file unit number for error messages

The variation of the rotation vector r is computed with respect to the incremental rotation w, where the rotations obey the rule

R(r+w) = R(w)∗R(r)

The variation is given as

V = I - 0.5∗Spin(θ) + η∗Spin(θ)∗Spin(θ)

where η = (sin(0.5∗θ) - 0.5∗θ∗cos(0.5∗θ)) ⁄ (θ²∗sin(0.5∗θ))

◆ eccexpanddiagmat()

subroutine, private rotationmodule::eccexpanddiagmat	(	real(dp), dimension(3), intent(in)	e,
		real(dp), dimension(3), intent(in)	D,
		real(dp), dimension(6,6), intent(out)	Mfull
	)

private

Takes into account possible eccentricity, for a diagonal matrix D.

   | Mfull | = |    I    :  0 || D : 0 || I : Spin(e)' |
   |       |   | Spin(e) :  I || 0 : 0 || 0 :   I      |

Author: Knut Morten Okstad

Date: 21 Jan 2004

◆ eccexpandmat()

subroutine, private rotationmodule::eccexpandmat	(	real(dp), dimension(3), intent(in)	e,
		real(dp), dimension(3,3), intent(in)	M,
		real(dp), dimension(6,6), intent(out)	Mfull
	)

private

Takes into account possible eccentricity.

   | Mfull | = |    I    :  0 || M : 0 || I : Spin(e)' |
   |       |   | Spin(e) :  I || 0 : 0 || 0 :   I      |

Author: Bjorn Haugen

Date: Feb 2002

◆ eccexpandvec()

subroutine, private rotationmodule::eccexpandvec	(	real(dp), dimension(3), intent(in)	e,
		real(dp), dimension(3), intent(in)	v,
		real(dp), dimension(6), intent(out)	vFull
	)

private

Takes into account possible eccentricity.

    | vFull | = |    I    :  0 || v |
    |       |   | Spin(e) :  I || 0 |

Author: Bjorn Haugen

Date: Feb 2002

◆ eulertomat()

real(dp) function, dimension(3,3) rotationmodule::eulertomat ( real(dp), dimension(3), intent(in) euler )

Converts a set of EulerXYZ angles into a rotation matrix.

◆ mat_to_quat()

subroutine rotationmodule::mat_to_quat	(	real(dp), dimension(3,3), intent(in)	rten,
		real(dp), dimension(4), intent(out)	q
	)

Computes the quaternion representation from a rotation tensor.

Parameters

[in]	rten	The rotation tensor
[out]	q	The rotation quaternions (Euler parameters)

The computation is performed by means of equations from Richard A. Spurrier comments on "Singularity free Extraction of a Quaternion from a Direction-Cosine Matrix" in Journal of Rockets and Spacecraft, 1978.

◆ mat_to_vec()

subroutine rotationmodule::mat_to_vec	(	real(dp), dimension(3,3), intent(in)	rten,
		real(dp), dimension(3), intent(out)	rvec
	)

Computes the rotation vector from a rotation tensor.

Parameters

[in]	rten	The rotation tensor
[out]	rvec	The rotation vector

◆ mattoeulerxyz()

real(dp) function, dimension(3) rotationmodule::mattoeulerxyz	(	real(dp), dimension(3,3), intent(in)	R,
		real(dp), dimension(3), intent(in)	eulerIn,
		integer, intent(out)	err
	)

Converts a rotation matrix (tensor) to EulerXYZ angles.

Parameters

[in]	R	The rotation matrix to convert
[in]	eulerIn	Euler angle set to use as a hint
[out]	err	Error flag (=1: singularity encountered, infinite solutions for Z and X rotation. = -1: Failed to find a valid solution, try orthonormalizing the coordinate system)

Returns: The EulerXYZ rotation angles

This function tries to find the Euler angle set that is closest to the set given as input.

Note: This function is no longer in use, consider remove?

◆ orthonorm3()

subroutine rotationmodule::orthonorm3 ( real(dp), dimension(3,3), intent(inout) rten )

Makes a rotation tensor orthonormal through use of quaternions.

◆ quat_to_mat()

subroutine rotationmodule::quat_to_mat	(	real(dp), dimension(4), intent(inout)	q,
		real(dp), dimension(3,3), intent(out)	rten
	)

Computes the rotation tensor from a quaternion representation.

Parameters

[in]	q	The quaternion representation of the rotation
[out]	rten	The rotation tensor

◆ quat_to_vec()

subroutine rotationmodule::quat_to_vec	(	real(dp), dimension(4), intent(inout)	q,
		real(dp), dimension(3), intent(out)	rvec
	)

Computes the rotation vector from a quaternion representation.

Parameters

[in]	q	The quaternion representation of the rotation
[out]	rvec	The rotation vector

◆ spin()

subroutine rotationmodule::spin	(	real(dp), dimension(:), intent(in)	vec,
		real(dp), dimension(3,3), intent(out)	mat
	)

Computes the spin (skew-symmetric) tensor from the rotation vector.

◆ vec_to_mat()

subroutine rotationmodule::vec_to_mat	(	real(dp), dimension(3), intent(in)	rvec,
		real(dp), dimension(3,3), intent(out)	rten,
		integer, intent(in), optional	lpu
	)

Computes the rotation tensor from a rotation vector.

Parameters

[in]	rvec	The rotation vector
[out]	rten	The rotation tensor
[in]	lpu	Optional file unit number for error messages

◆ vec_to_quat()

subroutine rotationmodule::vec_to_quat	(	real(dp), dimension(3), intent(in)	rvec,
		real(dp), dimension(4), intent(out)	q,
		integer, intent(in), optional	lpu
	)

Computes the quaternion representation from a rotation vector.

Parameters

[in]	rvec	The rotation vector
[out]	q	The quaternion representation of the rotation
[in]	lpu	Optional file unit number for error messages

Variable Documentation

◆ epsth2_p

real(dp), parameter, private rotationmodule::epsth2_p = 0.0005_dp

private

Angles zero-tolerance.

Data Types

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ deltarot()

◆ domega_dtheta()

◆ dtheta_domega()

◆ eccexpanddiagmat()

◆ eccexpandmat()

◆ eccexpandvec()

◆ eulertomat()

◆ mat_to_quat()

◆ mat_to_vec()

◆ mattoeulerxyz()

◆ orthonorm3()

◆ quat_to_mat()

◆ quat_to_vec()

◆ spin()

◆ vec_to_mat()

◆ vec_to_quat()

Variable Documentation

◆ epsth2_p