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system of co-ordinates (“to freeze”). Freezing of the moving system of
co-ordinates mathematically is noted ,, =i j k const . Therefore, the
relative position vector, relative velocity and relative acceleration
according are
dr
r / B A = r / B A i ,, =jk const , v r = v / BA = dt / BA ,

2
d r i ,, =jk const
a r = a / BA = 2 / BA .
dt
i ,, =jk const
Translation motion. The movement of the moving frame to the
common origin O of the fixed x, y, z reference frame is named the
translation motion. The translation motion is not motion of the origin
A. It includes both translate and rotate motion moving reference
frame.

51 Relative-Motion Analysis of Particle: Velocity

Position. Consider the particle B, what moves along the arbitrary
path. Using vector addition, the absolute position r of the particle B,
B
what shown in Fig. 2-21, can be related by the equation
r B = r A + r / BA . 2-64
We may rewrite this equation
r B = r A + r / BA = r A + (x +i y +j zk ), 2-65

where i, j and k are unit vectors attached to the x-y-z frame and
r / BA = (x +i y +j zk ) is the position vector of A with respect to B
We now take the time derivative of the position-vector equation
for A and B to obtain the relative-velocity relation. Differentiation of
Eq. 2-65 gives

k
dr B = dr A +  dx i + dy j + dz  x di + y dj + z d  , 2-66
k
+
 
dt dt   dt dt dt  dt dt dt  
 di dj d  k
The expression x + y + z  is a derivative at times from

 dt dt dt 
a position-vector r / BA on condition that ,,x y z const= , obtain
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