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