
342 Classical Mechanics
the change in
in a short time dt resulting from
is
. Thus, the total change in
in time
dt is
12 3
or
d
ˆ
ˆˆ ˆ
′
=
′
−
′
′′
e
ee e
xx
1
23
32
ωωω
. (11.16)
Similarly,
d
ˆ
ˆˆ ˆ
′
=
′
−
′
′
′′
e
ee e
xx
2
31 2
13
ωωω
(11.17)
d
ˆ
ˆˆ ˆ
′
=
′
−
′
′′
e
ee e
xx
3
12
21
ωωω
. (11.18)
Substituting Equations 11.16 through 11.18 into the third term on the right-hand side of Equa-
tion11.13,we obtain
′′
=×
′′
==
∑∑
xe
t
ex r
jj
jj
jj
d
d
ˆ
ˆ
0
1
3
1
3
. (11.19)
Alternatively, we can obtain Equation 11.19 in the following way: because we are investigating,
from the inertial frame Ox
1
x
2
x
3
, the change in
resulting on ...