acceleration_transform Function

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.

The transformation matrix takes the following form.

$$A = \left[ \begin{matrix} \tilde{\alpha} - \tilde{\omega} \tilde{\omega}^{T} & \vec{a} - \left( \tilde{\alpha} - \tilde{\omega} \tilde{\omega}^{T} \right) \vec{x} \\ 0 & 0 \end{matrix} \right]$$

where,

$$\tilde{\alpha} = \left[ \begin{matrix} 0 & -\alpha_z & \alpha_y \\ \alpha_z & 0 & -\alpha_x \\ -\alpha_y & \alpha_x & 0 \end{matrix} \right]$$

and,

$$\tilde{\omega} = \left[ \begin{matrix} 0 & -\omega_z & \omega_y \\ \omega_z & 0 & -\omega_x \\ -\omega_y & \omega_x & 0 \end{matrix} \right]$$

Given a vector describing the location on a moving body, $\vec{r_p}$, the matrix is used to report its acceleration $\vec{a_p} = A \vec{r_p}$.

Arguments

Type	Intent	Optional	Attributes		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.

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