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Well the question in the title basically sums everything up but to put it in more context...

I am trying to wrap my head around the relativistic Geocentric Celestial Reference System (GCRS). Reading the introductory documents such as IAU Resolution 2000 I notice they state that the GCRS is kinematically non-rotating with respect to the Barycentric Reference Frame. I've seen elsewhere as reference frames being described as dynamically non-rotating. I don't understand the difference.

It is not clear at all what they mean. Is the GCRS rotating or not? Any suggestions?

In the document, it is stated about being kinematically non-rotating in the introduction and mentioned about being dynamically non-rotating just before Eq. $24$. To be clear the document is just an example of where I have seen the terminology used. I am sure it will be used elsewhere.

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  • $\begingroup$ Ah that's a shame about the link. It works fine on this end. However, I don't think the link is important it was given as an example. I am really just confused about what it means for a reference frame to be kinematically rotating versus dynamically rotating. $\endgroup$ Jul 24, 2017 at 11:43
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    $\begingroup$ @Farcher -- The original link worked fine for me, but the link was to a PDF. Rumplestillskin: It's always preferable to link to the arxiv.org abstract rather than the PDF. $\endgroup$ Jul 24, 2017 at 14:05
  • $\begingroup$ @DavidHammen Thank you for the information. I have now been able to download the PDF. $\endgroup$
    – Farcher
    Jul 24, 2017 at 15:44

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The distinction between the two is more readily understood from a Newtonian perspective, where reference frames are global (i.e., universe-spanning). A kinematically non-rotating reference frame is one in which the remote stars, or more recently, the remote quasars, do not appear to be rotating with respect to the origin of the frame of reference. A dynamically non-rotating reference frame is one in which none of the fictitious accelerations due to rotation (centrifugal, Coriolis, and Euler accelerations) are needed to explain the dynamical behavior of a moving object.

That reference frames are local as opposed to global in general relativity makes this distinction a bit tougher in general relativity. The distinction still applies if the space in the vicinity of two reference systems is close to Newtonian. The remote stars (remote quasars) are still assumed to form the foundation of a kinematically non-rotating reference system, while descriptions of the equations of motion of a local object are still assumed to distinguish between dynamically non-rotating and rotating reference systems.

For more, see Klioner and Soffel.


References:

Klioner, Sergei A., and Michael Soffel. "Nonrotating astronomical relativistic reference frames." Astronomy and Astrophysics 334 (1998): 1123-1135.

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  • $\begingroup$ It's interesting that you mention this Euler acceleration. I had never heard of it until recently. Is there a GR equivalent of it? $\endgroup$ Jul 24, 2017 at 23:04

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