
382 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
is the product matrix (or the full rotation matrix) and has the following matrix elements:
AB
ij ik kl lj
kl
=
,
AA
11 12
==coscos cossinψφ ψφ A
13
=
−
sincos
cossin sin
θφψ+
=−
coscos sin
sincos
θφψ
ψφA
21
22 23
=− =sinsin cossinψφ
−+cossin coscos coscθφ ψθφ oos
sinsin sinco
ψ
θφ θAA
31 32
==− s
os
A
33
=
. (12.17)
The inverse transformation from the body axes x, y, z to the x′-, y′-, z′-axes
−
x
1
(12.18)
is given by the transported matrix
t
, and for orthogonal matrices, the transposed matrix
is equal to the inverse matrix
−
.
12.3 RATE OF CHANGE OF VECTOR
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