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What does it mean that two frames are " in a state of constant, rectilinear motion with respect to one another"?
This expression ( applied to reference frames) " being in a state of constant, rectilinear motion with respect to one another "is frequently used as self explanatory . Though I might appear as stupid, ...
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Defining what it means for a reference frame to move with a velocity $\mathbf{u}$ with respect to another
In describing a Galilean transformation, for example, one might say that if a reference frame $S'$ is moving at a velocity $\mathbf{u}$ with respect to $S$, then an object traveling at a velocity $\...