dynamics_rotation Module

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.

$$\textbf{R} = \left[ \begin{matrix} \vec{I_p} \cdot \vec{i} & \vec{I_p} \cdot \vec{j} & \vec{I_p} \cdot \vec{k} \\ \vec{J_p} \cdot \vec{i} & \vec{J_p} \cdot \vec{j} & \vec{J_p} \cdot \vec{k} \\ \vec{K_p} \cdot \vec{i} & \vec{K_p} \cdot \vec{j} & \vec{K_p} \cdot \vec{k} \\ \end{matrix} \right]$$ For orthonormal frames this is a proper rotation, so $R^T R=I$ and $\det(R)=1$.

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

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.

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

The parent coordinate frame is assumed to be as follows.

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

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

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

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

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

The resulting 3-by-3 matrix.

private pure function translate_1(x, y, z) result(rst)

Computes the 4-by-4 homogeneous transformation matrix describing a rigid-body translation.

Arguments

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

The resulting 4-by-4 matrix.

private pure function translate_2(d) result(rst)

Computes the 4-by-4 homogeneous transformation matrix describing a rigid-body translation.

Arguments

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

The resulting 4-by-4 matrix.