c4dynamics.states.lib.rigidbody.rigidbody.RB

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c4dynamics.states.lib.rigidbody.rigidbody.RB#

property rigidbody.RB#

Returns a Reference-from-Body Direction Cosine Matrix (DCM).

Based on the current Euler angles, RB returns the transpose matrix of BR, where BR is the Body from Reference DCM in 3-2-1 order.

The transpose matrix of the DCM generated by three Euler angles \(\varphi\) (rotation about x), \(\theta\) (about y), and \(\psi\) (about z) in 3-2-1 order, is given by:

\[\begin{split}R = \begin{bmatrix} c\theta \cdot c\psi & s\varphi \cdot s\theta \cdot c\psi - c\varphi \cdot s\psi & c\varphi \cdot s\theta \cdot c\psi + s\varphi \cdot s\psi \\ c\theta \cdot s\psi & s\varphi \cdot s\theta \cdot s\psi + c\varphi \cdot c\psi & c\varphi \cdot s\theta \cdot s\psi - s\varphi \cdot c\psi \\ -s\theta & s\varphi \cdot c\theta & c\varphi \cdot c\theta \end{bmatrix}\end{split}\]

where

  • \(c\varphi \equiv cos(\varphi)\)

  • \(s\varphi \equiv sin(\varphi)\)

  • \(c\theta \equiv cos(\theta)\)

  • \(s\theta \equiv sin(\theta)\)

  • \(c\psi \equiv cos(\psi)\)

  • \(s\psi \equiv sin(\psi)\)

For the background material regarding the rotational matrix operations, see rotmat.

Returns:

out (numpy.ndarray) – A 3x3 DCM matrix uses to rotate a vector from a body frame to a reference frame of coordinates.

Example

>>> v_body = [np.sqrt(3), 0, 1]
>>> rb = c4d.rigidbody(theta = 30 * c4d.d2r)
>>> v_inertial = rb.RB @ v_body
>>> v_inertial   
[2.0  0.0  0.0]
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