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Coordinate systems

Ephemerides

TODO

Rotations and attitude frames

Trajectory centered frames

Nyx supports the RIC, VNC and RCN trajectory frames. These frames are right-handed and orthonormal. To retrieve the \(3\times 3\) rotation matrix of these frames, call the dcm_from_traj_frame function on an Orbit structure.

Here is how Nyx computes these frames, where \(\Omega\) refers to the RAAN, \(i\) to the inclination, and \(u\) to the argument of latitude. Moreover, \(R_1\), \(R_2\), \(R_3\) respectively correspond to a rotation about the first, second and third axes.

RIC

\[ [C] = R_3(-\Omega)\times R_1(-i)\times R_3(-u) \]

VNC

We start by computing the unit vectors of the velocity and orbit momentum.

\[\mathbf{\hat{v}} = \frac{\mathbf{v}}{v}\]
\[\mathbf{\hat{n}} = \frac{\mathbf{h}}{h}\]

Complete the orthonormal basis:

\[\mathbf{\hat{c}} = \mathbf{\hat{v}} \times \mathbf{\hat{n}}\]
\[ [C]= \left[\begin{matrix} \hat{v}_x & \hat{n}_x & \hat{c}_x \\ \hat{v}_y & \hat{n}_y & \hat{c}_y \\ \hat{v}_z & \hat{n}_z & \hat{c}_z \\ \end{matrix} \right] \]

Note

The VNC frame is called VNB in GMAT.

RCN

We start by computing the unit vectors of the radius and orbit momentum.

\[\mathbf{\hat{r}} = \frac{\mathbf{r}}{r}\]
\[\mathbf{\hat{n}} = \frac{\mathbf{h}}{h}\]

Complete the orthonormal basis:

\[\mathbf{\hat{c}} = \mathbf{\hat{r}} \times \mathbf{\hat{n}}\]
\[ [C]= \left[\begin{matrix} \hat{r}_x & \hat{c}_x & \hat{n}_x \\ \hat{r}_y & \hat{c}_y & \hat{n}_y \\ \hat{r}_z & \hat{c}_z & \hat{n}_z \\ \end{matrix} \right] \]

Example

let dcm_vnc2inertial = orbit.dcm_from_traj_frame(Frame::VNC)?;
let vector_inertial = dcm_vnc2inertial * vector_vnc;

Last update: 2021-06-30