What is the relation between the
velocity of the same object, as seen from two different frames
of reference? That is, how is **v**_{A} for the
object seen from viewpoint A related to **v**_{B},
the velocity of the object seen from viewpoint B?

We can instantly see that **r**_{B},
the position vector locating the object from coordinate system
B, and **r**_{A}, the position vector locating the
object from coordinate system A, are related by

If we take the time derivative, we instantly find the answer we are looking for:

If we take the time derivative again
and the velocity **u** of A seen from B is a *constant,*
then we get

which is sometimes called “the Newtonian Principle of Relativity.”

However if reference frame A is
accelerating as seen from reference frame B, then since the
derivative of **u** is not zero, but rather something like **a**_{AB},
we find