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Classical Mechanics, Second Edition, 2nd Edition
book

Classical Mechanics, Second Edition, 2nd Edition

by Tai L. Chow
May 2013
Intermediate to advanced content levelIntermediate to advanced
639 pages
23h 12m
English
CRC Press
Content preview from Classical Mechanics, Second Edition, 2nd Edition
567Appendix 1
a1.2.4 divergence oF a vecTor
If
V(, ,)
ˆˆˆ
xxxVeVeVe
123112233
=++
is a differentiable vector eld [i.e., it is dened and differentiable
at each point (x
1
, x
2
, x
3
) in a certain region of space], the divergence of V, written V or div V, is
dened by the scalar product
∇⋅ =++
⋅++
V
x
e
x
e
x
eVeVe
1
1
2
2
3
31122
ˆˆˆˆˆ
VVe
V
x
V
x
V
x
33
1
1
2
2
3
3
ˆ
()
=++
.
(A1.34)
It is obvious that the result is a scalar eld. Note the analogy with A B = A
1
B
1
+ A
2
B
2
+ A
3
B
3
, but
also note that V V (bear in mind that is an operator). V is a scalar differential operator:
VV
x
V
x
V
x
⋅∇=++
1
1
2
2
3
3
.
The physical meaning of the divergence is best ...
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Publisher Resources

ISBN: 9781466569980