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52 Relative-Motion Analysis of Particle: Acceleration

The acceleration of B, observed from the X, Y, Z coordinate
system, may be expressed in terms of its motion measured with
respect to the system of x, y, z coordinates by taking the time
derivative of Eq. 2-66,
2
2
2
d r B = d r A + i dx + j d y + k d z  2 +

2
dt 2 dt 2   dt 2 dt 2 dt 2   2-72
2
2
2
j
 d dx d dy d dz  i k  d i d j d k 
+ 2  + +  +  x + y + z  .
 dt dt dt dt dt dt   dt 2 dt 2 dt 2 
Consider the every element of equalization:
2
d r B = a = a - the absolute acceleration of B, Fig. 2-21;
dt 2 B
d r A = a - the acceleration of A observed from the origin O;
2
dt 2 A
2
2
 d i d j d 2  k d r / B A 
2

 2 x + 2 y + 2 z =  2  - the rate of rotation motion
 dt dt dt   dt x  ,, y z const
=
of the moving x, y, z reference frame;
2
2
2
 d x d y d z  2  d r / BA 
 i 2 + j 2 + k 2  =  2  = a r - the relative
 dt dt dt   dt  i ,, =jk const
acceleration of the particle B;
j
 d dx d dy d dz  i k
2  + +  = a - the Coriolis (additional or
C
 dt dt dt dt dt dt 
rotation) acceleration. Named after the French military engineer G.
Coriolis (1792–1843), who was the first to call attention to this term.
Take into account, that translation acceleration equals
2
 d r 
a t = a A  + 2  / B A . 2-73
 dt x  ,, y z const
=
Finally we obtain theorem about absolute acceleration of
particle
a = a t + a r + a . 2-74
C
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