Adding Position Vectors

In many situations, there is a need to examine the motion of two or more points relative to each other.

Consider two points, A and B, both in motion relative to the origin O. This section will examine the motion of B relative to A.



If rB/A is the position vector of B relative to A, then it can be stated that
rB = rA + rB/A

This is simply adding two position vectors to get a new total vector. This is illustrated in the diagram at the left.



To find the relative velocities of two points, take the time derivative of the position, giving

     d(rB)/dt = d(rA + rB/A)/dt

vB = vA + vB/A


Relative acceleration is found by taking the time derivative of the velocity,

     d(vB)/dt = d(vA + vB/A)/dt

aB = aA + aB/A
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