[Spice_discussion] Two-vector frame accuracy

[Jacob Oost]

Can somebody clarify something in the documentation about two-vector frames?

On the page https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/C/req/frames.html we have:

"R(t) is defined via a two-vector frame using a velocity vector. The acceleration associated with the velocity vector is required to compute d(R(t))/dt, and this acceleration must be computed numerically. The results are likely to have at best single precision validity."

However, on the page https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/Tutorials/pdf/individual_docs/24_dynamic_frames.pdf  on slide 58 we have a similar sentence followed by this:

"However, if velocities are "well-behaved," numerically derived acceleration can be quite good. Example: GSE frame."

How should I determined if velocities are well-behaved?  Do any DE430/440/etc. velocities count as well-behaved?  Would this imply that a custom Earth-Moon rotating frame would be based on well-behaved velocities?  What about the velocities of, say, the Gateway reference ephemeris SPICE kernel?  Could I make a VUW frame centered on that ephemeris and expect it to be well-behaved?

In case it helps, this question arose from the context of either using SPICE frame kernels with SPICE frame transformation routines OR using custom frame transformation code in which the simplifying assumption dh/dt=0 (at the instant of the transformation) is made to avoid numerical issues.

Thanks!
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