# What is meant by “instantaneously aligned” with regards to rotating reference frames/coordinate axes?

I'm trying to understand a set of lecture notes I found online from MIT which describe the derivation of the equations of motion for an object in a rotating reference frame, this is for an essay on Lagrange points. It describes the fixed and rotating reference frames as being "instantaneously aligned" however I can't find any definition or intuitive description of what is meant by this. Could anyone please explain this term? I've copied in the relevant sentence and linked the pdf file:

"Let us consider a very simple situation, in which a point a at rest with respect to the fixed observer A located at the origin of the coordinates $$x, y, z$$, point $$O$$, is also observed by a rotating observer, B, who is also located at point $$O$$. The coordinate system used by B, $$\bar{x},\bar{y},\bar{z}$$ is instantaneously aligned with $$x, y, z$$ but rotating with angular velocity $$\Omega$$."

https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec08.pdf

Since we have defined our coordinate system as having a common origin $$O$$ and being instantaneously aligned, the position vector $$\mathbf r$$ seen by both the fixed observer A and the rotating observer B at this instant are the same. $$\mathbf r_{a/A}=\mathbf r_{a/B}$$ Note that this is an instantaneous concept, and therefore it is immaterial whether the observer B is rotating or not. In other words, the above expression is valid at any given instant.
From reading where they use this term in the article, instantaneously aligned seems to mean that at any instant we can assume that $$\mathbf r_{a/A}=\mathbf r_{a/B}$$ for the stationary frame A and the rotating frame B. How we choose to express these vectors within a certain coordinate system, however, can change over time.