Page 79 - 4167

O

O

a b c
Figure 6.14

. In common case, when rotation takes place around the arbitrarily
axes of XYZ (fig. 4.17) relationship between the components of moment
of inertia becomes another aspect

L X  I  X  I   I  Z
XX
XY
Y
XZ

L  I  X  I   I  X , (6.39)
YX
YY
Y
YZ
 Y

L
Y
ZZ
ZX
 Z  I  X  I   I  Z
ZY
where I k i is the special moments of inertia of body. The first index i
determines rotation of axis of
body. The second index k
determines s rotation of the
principal axes of inertia
These special moments of
I
inertia k i determine the total

moment of inertia of a body
about arbitrary axis of rotation
and create tensor of inertia of

body (tensor – from Latin – to
Figure 6.15 extend):

78