dynamics_rotation

Uses

- dynamics_helper
- iso_fortran_env

Functions

acceleration_transform rotate_x rotate_y rotate_z velocity_transform

Interfaces

public interface rotate

private pure function rotate_general_1(i, j, k, Ip, Jp, Kp) result(rst)

Constructs a rotation matrix when the orientation of the coordinate frame of interest is known relative to the parent coordinate frame.

The matrix is of the following form.

$\textbf{R} = \left[ \begin{matrix} \vec{I_p} \cdot \vec{i} & \vec{I_p} \cdot \vec{j} & \vec{I_p} \cdot \vec{k} \\ \vec{J_p} \cdot \vec{i} & \vec{J_p} \cdot \vec{j} & \vec{J_p} \cdot \vec{k} \\ \vec{K_p} \cdot \vec{i} & \vec{K_p} \cdot \vec{j} & \vec{K_p} \cdot \vec{k} \\ \end{matrix} \right]$

This routine does not check for orthogonallity or unit vector length; therefore, to ensure correct results it is the callers responsibility to ensure each vector is of unit length and that the unit vectors are properly orthogonal.

Arguments

Type	Intent		Name
real(kind=real64),	intent(in)	::	i(3)	The rotated coordinate frame x-axis unit vector.
real(kind=real64),	intent(in)	::	j(3)	The rotated coordinate frame y-axis unit vector.
real(kind=real64),	intent(in)	::	k(3)	The rotated coordinate frame z-axis unit vector.
real(kind=real64),	intent(in)	::	Ip(3)	The parent coordinate frame x-axis unit vector.
real(kind=real64),	intent(in)	::	Jp(3)	The parent coordinate frame y-axis unit vector.
real(kind=real64),	intent(in)	::	Kp(3)	The parent coordinate frame z-axis unit vector.

Return Value real(kind=real64), (3,3)

The resulting 3-by-3 matrix.

private pure function rotate_general_2(i, j, k) result(rst)

Constructs a rotation matrix when the orientation of the coordinate frame of interest is known relative to the parent coordinate frame.

The matrix is of the following form.

The parent coordinate frame is assumed to be as follows.

$\vec{I_p} = \left( \begin{matrix} 1 & 0 & 0 \end{matrix} \right)$

$\vec{J_p} = \left( \begin{matrix} 0 & 1 & 0 \end{matrix} \right)$

$\vec{K_p} = \left( \begin{matrix} 0 & 0 & 1 \end{matrix} \right)$

Arguments

Type	Intent		Name
real(kind=real64),	intent(in)	::	i(3)	The rotated coordinate frame x-axis unit vector.
real(kind=real64),	intent(in)	::	j(3)	The rotated coordinate frame y-axis unit vector.
real(kind=real64),	intent(in)	::	k(3)	The rotated coordinate frame z-axis unit vector.

Return Value real(kind=real64), (3,3)

The resulting 3-by-3 matrix.

Functions

public pure function acceleration_transform(alpha, omega, a, x) result(rst)

Computes the acceleration transformation matrix relating the position of a point expressed in a rotating and translating body relative to its parent frame.

Arguments

Type	Intent		Name
real(kind=real64),	intent(in)	::	alpha(3)	The angular acceleration vector.
real(kind=real64),	intent(in)	::	omega(3)	The angular velocity vector.
real(kind=real64),	intent(in)	::	a(3)	The translational acceleration vector describing the acceleration of the body in its parent coordinate frame.
real(kind=real64),	intent(in)	::	x(3)	The position vector of the body in its parent coordinate frame.

Return Value real(kind=real64), (4,4)

The 4-by-4 transformation matrix.

public pure function rotate_x(angle) result(rst)

Constructs the rotation matrix describing a rotation about an x-axis such that $\overrightarrow{r_2} = \textbf{R}_x \overrightarrow{r_1}$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	angle	The rotation angle, in radians.

Return Value real(kind=real64), (3,3)

The resulting 3-by-3 matrix.

public pure function rotate_y(angle) result(rst)

Constructs the rotation matrix describing a rotation about a y-axis such that $\overrightarrow{r_2} = \textbf{R}_y \overrightarrow{r_1}$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	angle	The rotation angle, in radians.

Return Value real(kind=real64), (3,3)

The resulting 3-by-3 matrix.

public pure function rotate_z(angle) result(rst)

Constructs the rotation matrix describing a rotation about a y-axis such that $\overrightarrow{r_2} = \textbf{R}_z \overrightarrow{r_1}$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=real64),	intent(in)			::	angle	The rotation angle, in radians.

Return Value real(kind=real64), (3,3)

The resulting 3-by-3 matrix.

public pure function velocity_transform(omega, v, x) result(rst)

Computes the velocity transformation matrix relating the position of a point expressed in a rotating and translating body relative to its parent frame.

Arguments

Type	Intent		Name
real(kind=real64),	intent(in)	::	omega(3)	The angular velocity vector.
real(kind=real64),	intent(in)	::	v(3)	The translation velocity vector describing the velocity of the body in its parent coordinate frame.
real(kind=real64),	intent(in)	::	x(3)	The position vector of the body in its parent coordinate frame.

Return Value real(kind=real64), (4,4)

The 4-by-4 transformation matrix.

dynamics_rotation Module

Contents

Interfaces

Functions

Uses

Contents

Interfaces

Functions

Interfaces

public interface rotate

private pure function rotate_general_1(i, j, k, Ip, Jp, Kp) result(rst)

Arguments

Return Value real(kind=real64), (3,3)

private pure function rotate_general_2(i, j, k) result(rst)

Arguments

Return Value real(kind=real64), (3,3)

Functions

public pure function acceleration_transform(alpha, omega, a, x) result(rst)

Arguments

Return Value real(kind=real64), (4,4)

public pure function rotate_x(angle) result(rst)

Arguments

Return Value real(kind=real64), (3,3)

public pure function rotate_y(angle) result(rst)

Arguments

Return Value real(kind=real64), (3,3)

public pure function rotate_z(angle) result(rst)

Arguments

Return Value real(kind=real64), (3,3)

public pure function velocity_transform(omega, v, x) result(rst)

Arguments

Return Value real(kind=real64), (4,4)