Are LVLH and RSW coordinate systems the same thing?

I've been reading into satellite relative motion, and I noticed that the literature split on using LVLH (local vertical local horizontal) and RIC/RSW (radial intrack crosstrack) coordinate frames. When I've looked into the definitions of each, it appears that LVLH has a z axis that points to the center of the earth, a y axis that is negative to the orbit normal. In contrast the x axis of RIC points in the direction of the spacecrafts position vector, and the z axis is pointing in the direction normal to the orbit plane.

However, I've found other sources, that have said RIC and LVLH are the same thing. Could anyone clear this up?

EDIT: Here is the source: https://public.ccsds.org/Pubs/500x0g4.pdf on page 23 (section 4.3.7.2) the LVLH frame is defined. In section 4.3.7.4 the RSW frame is defined, and the author says that RIC and RSW are the same thing. Should I just stick with Vallado's definition because his work seems to be the preeminent book in the field?

• Partial answer: the LVLH (Local Vertical Local Horizontal) name often is only enough information to know that two of your axes are aligned that way. The ordering and sign of the axes often varies depending on the convention of the algorithms you use. For example, the CW equations have Y radial, Z along angular momentum vector, and X as the cross product of those (velocity vector when circular). Commented Nov 16, 2020 at 2:11
• @uhoh There you go. Commented Nov 16, 2020 at 9:36
• You can use the Contact Us form to have your accounts merged, so that you can freely edit your question. Commented Nov 16, 2020 at 9:41
• @uhoh fixed it! thank you
– Syd
Commented Nov 16, 2020 at 13:10
• @Syd Thank you for sharing the CCSDS standard. I also want to give another source pointing to the same conclusion as your reference. The Space-Track.org Handbook for Spacecraft Operators has a footnote (page 41), equating the RIC and RTN frames. space-track.org/documents/…, I have been skeptical about this "simplification", and have been trying to be a bit more pedantic, because the book's explanation is more complete and has a rational for such a distinction. Commented Nov 18, 2020 at 1:41

Not all authors restrict themselves to right-handed, orthonormal frames. At the level of pure mathematics, all you need is a three-dimensional vector space at every point in three dimensions, but you can use a different vector space at every point, and the choice of connection between the vector spaces used at different points is arbitrary (and the term connection has a specific technical meaning which differs substantially from its use in other subjects). I would argue that the meaning most often encountered in spoken language is one of these: rather than argue about which one of "in-track" and "along-track" is parallel to velocity and which perpendicular to radius, most people talk as if they use unnormalized $$\vec{r}$$, $$\vec{v}$$, and $$\vec{h}=\vec{r}\times\vec{v}$$ (angular momentum per unit mass) as the local basis vectors, and just live with the fact that the angle between $$\vec{r}$$ and $$\vec{v}$$ is variable. I'll also note in passing that in my head, $$\vec{r}$$ is perifocal, but not everyone will think that, which has a significant impact on the definition of these frames for planets (orbiting the solar system barycenter, not the center of the sun).