In class EquinoctialOrbit, I see you have renamed the two equinoctial elements, commonly referred to as p and q [e.g. 1, p.305], as hy and hx respectively. You then describe hx and hy as being the first and second components of the inclination vector. This I do not follow, as I understand the inclination vector to be
(see Soop’s “Introduction to geostationary orbits”).
If we were really dealing with the components of the inclination vector, then the notation hx and hy would make perfect sense, since the inclination vector (as I understand it) is just another name for the unit vector in the direction of the orbital angular momentum. (Danby uses the notation hx and hy for the first two components of this vector in [2, p.203].) But I do not believe that any of the equinoctial elements correspond to components of the inclination vector. Please correct me if I am wrong!
[1] R. A. Broucke and P. J. Cefola. On the Equinoctial Orbit Elements. Celestial Mechanics, 5:303–310, May 1972.
[2] J. M. A. Danby. Fundamentals of Celestial Mechanics. Willmann-Bell, Inc., second edition, 1992.
The 3D inclination vector as used by Soop is the normal to the orbit. It is different from the 2D inclination vector used by Cefola. You could even see other 2D conventions for geo (using i instead of tan(i/2)), but they are mainly used in institutions that relied on an old software suite that was created in one agency and then spread over a few satellites operators.
We did follow Cefola definition, but are aware we did not use the proper naming convention, I am to blame for that. I am not sure if we can fix that now, as it is a very low level class, deep down in the architecture.
Thank you for your reply. Yes, I am aware that there are several sets of elements in use and that the inclination vectors used by Soop—b.t.w. he also defines a 2D inclination vector (the projection of the 3D inclination vector onto the xy-plane)—are quite different. What I was querying was simply your notation. The elements you call hx and hy are also referred to as \psi and \chi (Arsenault et al.), q and p (Broucke and Cefola), h and k (Walker et al.) and q1 and q2 (Peterson et al.).* It is just that nowhere in the literature am I able to find anyone referring to these two elements as being the components of an inclination vector. Perhaps, if this is the case and you are introducing new notation here, then you could simply add a comment saying so. What drew my attention to this was when I found code written by my colleagues—code that does not even use Orekit—describing these two elements as being the components of the ‘regular inclination vector’. Do you know of any published papers which define an inclination vector using these two equinoctial elements or is it purely Orekit notation? Sorry if this seems pedantic, but I have often seen such confusion of notation lead to errors.
Peterson uses the notation q1 and q2 as he identifies these elements as being the first two classic Rodrigues parameters, i.e. elements of the Rodrigues (or Gibbs) vector.
I am not aware of published papers using the same notation.
Our notation only come from past experience and colloquial discussions with colleagues at former jobs. We used to call this inclination vector (and we used similar naming for eccentricity), but it was most probably a misnomer.
Thank you very much for your reply, Luc. Sorry I did not acknowledge it sooner, but I have only just become aware of it. (I must have missed the email notification.) – Craig.
P.S. My colleagues and I are using Orekit—and I think we are all, in general, very happy with the product! This is why I suspect that, although (as I said earlier) Orekit is not used in the particular piece of code I was looking at, it was probably the origin of the notation.
