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 di dj d   k dr / BA 
 x + y + z  =   . 2-67
 dt dt dt   dt x  ,, y z const
=
 dx dy dz 
By analogy the expression  i + j + k is a derivative at

 dt dt dt 
times from a position-vector r / BA on condition that ,, =i j k const ,
obtain
 dx dy dz   dr / BA 
 i + j + k  =   . 2-68
 dt dt dt   dt  i ,, =jk const
Substitute our results in Eq. 2-66 we get
dr B = dr A +  dr / BA  +  dr / B A  , 2-69
dt dt   dt   i ,, =jk const   dt  x  , , y z const
=
dr
where B = v = v - the absolute velocity of the particle B;
dt B
 dr / B A 
  - the rate of rotation motion of the moving x, y, z
 dt x  , , y z const
=
 dr 
reference frame;  / BA  = v - the relative velocity of the
r
 dt  i ,, =jk const
dr
particle B; A = v - the velocity of the origin A of moving x, y, z
dt A
reference frame.
If we take into account both the velocity of the origin A and the
rotation motion of x, y, z frame, we obtain the translation velocity
dr  dr 
v = A +  / BA  . 2-70
t
dt  dt x  ,, y z const
=
Finally we obtain theorem about absolute velocity of particle
v = v t + v , 2-71
r
the absolute velocity of particle equals a geometrical sum
translation and relative velocities.

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