I'm studying the book "Classical Mechanics" by Goldstein together with a coursebook my professor provided.
I'm having trouble grasping how to intuitively determine what the rate of change of a vector is affected by.
Earlier on in the book, I saw a body with 3 frames of reference:
$Oxyz$ which is just an arbitrary coordinate system.
$O'x'y'z'$ which has a fixed origin in a point of the body and fixed axes that rotate corresponding to the body.(Body fixed?)
$O'xyz$ which has a fixed origin in a point of the body and fixed axes that are parallel with the original coordinate system.(Space fixed?)
Now, in my professors book it says the following:
It is clear that there are 2 sources of time-dependence in the Carthesian components of a general vector in the (body-fixed) coordinate system:
On one hand: The intrinsic time-dependence of the vector.
On the other hand: The time dependence of the basisvectors $\vec n'_i$ of the moving coordinate system, with respect to which the Carthesian components (orthogonal projection of the vector onto $\vec n'_i$) will be determined.
I'm confused as to what exactly is meant by this paragraph.
What exactly is the intrinsic time-dependence of the vector? To my knowledge, in the body-fixed coordinate system every vector stays constant, so there is no rate of change.
I understand that the $\vec n'_i$ vectors move through space, but during a translation they wouldn't change since they are their orientation stays the same. During a rotation however I understand they would change.
What am I getting wrong here? I have a feeling I'm mixing these frames of reference up since it's not so clear in my book. I think that I'm misunderstanding how these frames of reference behave as the body moves.