Earth-centered frame with Earth-Sun line fixed

[PeterDonis]

TL;DR

Looking for references to an Earth-centered frame rotating with the angular velocity of the Earth around the Sun.

I have seen plenty of references to Earth centered inertial frames (axes fixed with respect to the stars) and Earth-centered Earth fixed frames (axes fixed with respect to the Earth, rotating at the Earth's angular velocity of rotation with respect to the stars).

Does anyone know of a reference that uses a frame in which the origin is the Earth (or the barycenter of the Earth-Moon system), and in which the line from the origin to the Sun is fixed (so that the frame rotates at the angular velocity of the Earth around the Sun)?

 

[Bandersnatch]

I think you're looking for the synodic coordinate system. It's used in analysing the circular restricted three-body problem (aka 'CR3BP').
I'm not sure what references you're after, exactly, but maybe looking those keywords up will nett you something. Anything on Lyapunov and horseshoe orbits, or Lagrange points, might be a good place to check.

 

[PeterDonis]

I'm not sure what references you're after, exactly

Basically looking for something that will discuss the equations of motion in the type of frame I described.

 

[A.T.]

Does anyone know of a reference that uses a frame in which the origin is the Earth (or the barycenter of the Earth-Moon system), and in which the line from the origin to the Sun is fixed (so that the frame rotates at the angular velocity of the Earth around the Sun)?

If the origin is at the barycenter of the Earth-Sun system, it's the synodic coordinate system. Used for example to compute the effective potential for Lagrangian points:
https://en.wikipedia.org/wiki/Lagrangian_point#Mathematical_details

If the origin is the Earth's center (or the barycenter of the Earth-Moon system), the rotation axis of the frame is non-inertial, so you have an additional linear inertial force. Like in this link below, Case 5 (just replace Earth & Moon with Sun & Earth):
https://www.vialattea.net/content/tides-and-centrifugal-force/